Abstract
Human exploration of Mars will require habitat morphologies that reduce long-term resupply and maintenance burdens under extreme environmental forcing, yet transferable geometric design laws remain poorly constrained. An explainable reverse-engineering framework is developed using refurbishment-phase embodied-carbon intensity as an Earth-analog proxy for maintenance-driven material replacement and logistics load. Across 59192 extreme-environment built habitats sampled from 384 cities, prefabrication-enabled benefits are quantified by absolute savings Δ and relative improvement η. Δ spans 0.211–3.942 kgCO2e m⁻³ (mean 1.874) and η spans 0.026–0.427 (mean 0.114), with weak coupling between national means (r = −0.154), indicating distinct drivers for absolute versus proportional gains. SHAP interaction topology reveals non-additive plateau/ridge/saddle optima, defining a narrow, mutually reinforcing proportion band (Shape Factor ≈ 1.01–1.06; Footprint Ratio ≈ 0.92–0.94; Aspect Ratio ≈ 0.93–0.96). Dual-objective screening yields a sparse non-dominated frontier (n = 7) and a best-balanced solution (Δ = 4.02 kgCO2e m⁻³; η = 0.186), supporting a constrained, testable morphology-threshold law. A synthesis of 530 algorithm-driven extra-terrestrial habitat morphology studies (1981–2025) shows rapid post-2015 expansion and a shift toward deep/generative approaches, while a scan of 74 Mars-habitat R&D platforms across 19 countries indicates that most real-world efforts cluster at TRL 4–6, with high-maturity field sites dominating TRL 7–9. Together, these results connect a transferable geometric threshold corridor to the evolving algorithmic toolkit and current technology-maturity pathways for Mars habitat development.
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Introduction
Human expansion into off-Earth environments is transitioning from short-duration missions toward sustained presence, where habitats must remain safe and operable under persistent environmental forcing1,2,3. On Mars, extreme cold, low atmospheric pressure, dust abrasion, radiation exposure, and large diurnal thermal swings impose chronic degradation pathways on envelopes, interfaces, and mechanical systems4,5,6. In such settings, the limiting constraint is often not initial construction feasibility but the long-term burden of maintenance, refurbishment, and replacement under restricted logistics7,8. A central scientific and engineering question therefore emerges: which habitat morphologies minimize maintenance-driven material demand and resupply burden while remaining compatible with heterogeneous construction routes and mission architectures?
Habitat morphology is not a purely aestheticim variable in planetary contexts9,10. Geometry governs envelope exposure relative to usable volume, thermal exchange area, wind-driven and particle-driven loading surfaces, and the scaling of joints and seams that frequently dominate failure and repair events11,12,13. Even under simplified assumptions, surface-area-to-volume efficiency, plan compactness, and height–perimeter scaling affect both operational energy demand and the rate at which envelope and structural components require repair or replacement14,15,16. These geometric influences become more pronounced under extreme forcing because marginal increases in exposure can trigger non-linear increases in degradation, such as accelerated corrosion or abrasion in high-salt or high-dust regimes, amplified heat-loss penalties in cold climates, or elevated maintenance frequency due to wind-driven rain and particulate infiltration17,18,19. Despite this intuitive linkage, the field still lacks a transferable, quantitative “morphology-threshold law” that maps a small set of interpretable geometric descriptors to predictable improvements in long-term maintenance and refurbishment burden20,21,22.
A major obstacle is the scarcity of long-horizon empirical data for extraterrestrial habitats23,24. Most Mars habitat studies are necessarily conceptual, simulation-based, or prototype-based, and their performance metrics vary widely across assumptions about materials, shielding, energy systems, and in-situ resource utilization25,26. This heterogeneity complicates synthesis and prevents consensus on robust geometric thresholds that remain valid across construction systems25,27. Earth analogs provide an underused empirical bridge28. The intent is not to transfer hospitality program requirements (e.g., daylighting/views) to Mars, but to extract low-dimensional geometric regularities governing envelope exposure and interface scaling under persistent forcing. Hospitality buildings are used only as a large-sample Earth envelope dataset, while Mars-specific objectives (shielding, airtightness, life-support integration) are treated as additional constraints in translation. Extreme terrestrial environments can expose built envelopes to strong, persistent stressors, offering large-sample observations of how form interacts with environmental forcing to shape refurbishment demand29,30. If suitable proxy measures for maintenance-driven material turnover can be defined, Earth analog datasets can be leveraged to infer transferable geometric regularities relevant to Mars habitat design7,25,31.
Refurbishment-phase embodied carbon intensity offers one such proxy32,33,34. Although embodied carbon is not a direct mission metric, -phase embodied carbon captures the material and process burdens associated with repair, replacement, and renewal during service life35,36,37. In constrained logistics settings, the same drivers that increase refurbishment-phase embodied carbon on Earth—higher replacement mass, more frequent interventions, and larger envelope exposure—also plausibly increase the equivalent resupply and maintenance burden for off-world habitats38,39. Importantly, refurbishment-phase proxies can be compared across construction systems to isolate the contribution of fabrication and assembly approaches, including prefabricated or modularized methods that are often proposed for planetary deployment40,41. This study therefore uses refurbishment-phase embodied carbon intensity as an Earth-analog, quantitative surrogate for maintenance-driven material demand and logistics load, enabling large-sample inference of geometry–maintenance coupling42,43,44. Here, refurbishment-phase embodied carbon intensity is treated as an Earth-analog surrogate for maintenance-driven material turnover, rather than a validated causal equivalent of mission logistics. The rationale is that refurbishment emissions predominantly arise from replacement mass and intervention extent, which are expected to co-vary with logistics-relevant quantities (e.g., spares mass/volume and maintenance cadence) under constrained supply. However, important mission determinants—such as astronaut labor hours, accessibility, fault diagnosis, and risk—are not directly represented by rpECI. Accordingly, the main claim of this study concerns transferable geometric regularities and threshold corridors under persistent forcing, while the rpECI-to-mission mapping is posed as a testable proxy assumption. In this study, rpECI is used primarily to approximate maintenance-driven material turnover and intervention extent under terrestrial refurbishment systems, rather than to represent mission logistics cost directly. Because refurbishment emissions embed both replacement quantities and Earth-specific emission factors, Mars translation is framed at the level of geometry–exposure–replacement coupling (i.e., how form modulates the scale and frequency of renewal), while downstream mission metrics (spares mass/volume, crew time, downtime) require scenario-specific mapping. This framing is particularly important under ISRU, where material availability and cost weights may differ from terrestrial supply chains.
In parallel, the methodological landscape for extraterrestrial habitat morphology design has rapidly evolved45,46. Algorithm-driven design studies have expanded sharply in the last decade, shifting from classical topology and shape optimization toward deep learning, generative models, and hybrid pipelines that combine parametric modeling, simulation, and multi-objective search47. This expansion reflects both improved computational capabilities and growing interest in automated exploration of design spaces under competing constraints (radiation shielding, pressurization, manufacturability, thermal performance, and structural safety)48. However, the same diversification has produced a fragmented evidence base: methods proliferate faster than transferable, empirically anchored design law49,50s. As a result, many studies optimize within narrow model assumptions, and the broader field lacks a shared, interpretable corridor of geometric thresholds that can serve as a common prior for different algorithms and mission scenarios51,52.
A second translation barrier arises from technology maturity53,54. Mars habitat development is carried by a distributed ecosystem of organizations, analog sites, field stations, and engineering teams spanning multiple countries and sectors55. These efforts occupy a broad range of technology readiness levels, from early conceptual studies to high-maturity field infrastructure and long-duration analog operations. Without an explicit link between quantitative morphology laws and the maturity structure of real-world development routes, it remains unclear how geometric insights can be operationalized across pathways such as regolith-based construction, additive manufacturing, inflatable habitats, subsurface or bermed architectures, and hybrid modular systems. Connecting transferable geometric thresholds to the ecosystem’s maturity distribution is therefore essential for turning scientific inference into actionable design guidance.
Against this background, this study proposes an integrated framework that connects (i) Earth-analog empirical inference, (ii) interpretable reverse engineering of morphology–maintenance coupling, and (iii) a structured view of the extraterrestrial habitat design and development landscape. First, a global Earth-analog dataset of extreme-environment built habitats is assembled to quantify the potential reductions in refurbishment-phase embodied carbon intensity enabled by prefabrication relative to conventional construction. Two complementary indicators are evaluated: absolute refurbishment-phase savings and relative improvement ratio, capturing both the magnitude of potential burden reduction and its proportional significance. Second, explainable machine-learning attribution and interaction analysis are used to identify whether optimal performance arises from single-variable compactness or from higher-order geometric coupling, and to localize interpretable threshold bands in morphology space. Third, a two-objective screening is conducted to isolate non-dominated cases that jointly maximize absolute and proportional savings, providing a reproducible feasibility corridor and an operational best-balanced solution in morphology space. These steps jointly yield a testable morphology-threshold law expressed as an interpretable proportion band rather than a single optimum, addressing robustness and transferability concerns.
Results
Earth analog priors: Reverse engineering (rpECI3DCC)
Using ISO-3 country-level aggregation across 70 countries/territories, two carbon-reduction indicators were mapped (Fig. 1abbcd): absolute refurbishment-phase reduction intensity rpECI3DCC − rpECI3DPC (kgCO2e/m³) and relative reduction ratio (ECI3DCC − ECI3DPC)/ECI3DCC. Both metrics exhibit pronounced spatial heterogeneity, indicating substantial geographic variability in carbon-reduction potential. Mean rpECI3DCC − rpECI3DPC spans 0.211–3.942 kgCO2e/m³ (unweighted mean 1.874; sample-size-weighted mean 1.669). Higher values occur in Oman (3.942; n = 6), Finland (3.513; n = 12) and Australia (3.100; n = 20), whereas lower values occur in Bahrain (0.211; n = 3), Niger (0.407; n = 3) and China (0.733; n = 86). For more robust estimates (n ≥ 10), the upper tail remains dominated by Finland, Australia and Sweden (2.866; n = 13), suggesting elevated means are not solely driven by single-observation outliers. The mean reduction ratio ranges from 0.026 to 0.427 (unweighted mean 0.114; weighted mean 0.112), with higher values in Tonga (0.427; n = 2) and Tunisia (0.162; n = 9) and lower values in Japan (0.026; n = 3), Namibia (0.042; n = 2) and India (0.080; n = 44). Among countries with n ≥ 10, relatively higher ratios cluster in Egypt (0.137; n = 34), Algeria (0.135; n = 17) and Morocco (0.131; n = 21), indicating a more stable “moderate-high” regime for the relative metric than for the absolute metric. The two national mean metrics are only weakly coupled (Pearson r = −0.154), implying that larger absolute refurbishment-phase reductions do not necessarily yield larger proportional reductions in conventional construction intensity, consistent with partially distinct underlying drivers rather than a single unified gradient. Country-level means in Fig. 1 are presented as descriptive summaries and are inherently sensitive to sample-size imbalance across ISO-3 units. To mitigate this, uncertainty is reported via bootstrap 95% confidence intervals for national means, and key conclusions are cross-checked in EI3-stratified subsets; inferential claims are primarily supported by building-level geometry models and the independent literature and platform evidence streams.
a–d, ISO-3 country means (70 countries/territories) of absolute savings ΔrpECI = rpECI3DCC − rpECI3DPC and relative savings η = (ECI3DCC − ECI3DPC)/ECI3DCC show strong spatial heterogeneity and weak coupling (r = −0.154). e SHAP interactions (Shape Factor, Footprint Ratio, Aspect Ratio) reveal plateau/ridge/saddle optima defining a proportion band. f–h Pareto screening (n = 629; trimmed n = 587) yields a sparse frontier (n = 7), a Tchebycheff compromise (Δ=4.02; η = 0.1855), and an interpretable threshold corridor. i plan geometry samples.
To quantify how morphology jointly governs prefabrication-enabled embodied-carbon reduction, SHAP interaction values were evaluated among Shape Factor, Footprint Ratio and Aspect Ratio (Fig. 1e) for y = (rpECI3DCC − rpECI3DPC)/rpECI3DCC. The 3D interaction surfaces show higher-order, non-additive effects, with Shape Factor acting as the dominant coupling variable. Shape Factor × Footprint Ratio exhibits a plateau-like optimum, with the top-3% region at Shape Factor ≈ 1.01–1.03, Footprint Ratio ≈ 0.93–0.94 and carbon-reduction ratio ≈ 0.87–0.89. Shape Factor × Aspect Ratio forms a ridge-like optimum, with the top-3% region at Shape Factor ≈ 1.01–1.06, Aspect Ratio ≈ 0.93–0.94 and carbon-reduction ratio ≈ 0.88–0.90. Footprint Ratio × Aspect Ratio shows a saddle topology, with the optimal region localized at Footprint Ratio ≈ 0.92–0.94, Aspect Ratio ≈ 0.93–0.96 and carbon-reduction ratio ≈ 0.88–0.91. Together, these plateau/ridge/saddle patterns indicate that neither planar nor vertical compactness alone is sufficient; maximal performance arises only within a mutually reinforcing proportion band, providing quantitative evidence of multi-dimensional shape thresholds underpinning the proposed Explainable Reverse Engineering Model.
To identify morphologies that simultaneously maximize absolute and proportional savings, a two-objective Pareto screening was conducted using (1) Delta_rpECI = rpECI3DCC − rpECI3DPC (kgCO2e/m³) and (2) Delta_ECI_over_ECI = (ECI3DCC − ECI3DPC)/ECI3DCC on a cleaned dataset (n = 629) and a robustly trimmed dataset (1st–99th percentiles; n = 587). The Pareto set (n = 7) defines a sparse non-dominated frontier (Fig. 1f), indicating that only a small subset of cases achieves concurrent improvements in both objectives. A best-balanced solution was selected via a Tchebycheff (min–max) criterion, achieving Delta_rpECI = 4.02 kgCO2e/m³ and Delta_ECI_over_ECI = 0.1855. Reverse projection of Pareto solutions into morphology space yields interpretable threshold combinations: the Pareto (10–90) box (Fig. 1g) defines a feasibility corridor of Footprint Ratio = 0.357–1.000, Aspect Ratio = 0.00378–0.0209 and Shape Factor = 0.05699–0.45690, while the Tchebycheff-selected optimum lies at Footprint Ratio = 1.000, Aspect Ratio = 0.00299 and Shape Factor = 0.3245. In 3D morphology space (Footprint Ratio–Aspect Ratio–Shape Factor), Pareto solutions cluster tightly and the best-balanced point sits near the dense core (Fig. 1h), supporting a constrained, designable optimal region and providing a reproducible route from dual-objective targets to actionable morphology thresholds for low-carbon prefabricated refurbishment. Figure 1i shows the plan geometry samples.
Earth analog priors: Pareto-optimal forms ((rpECI3DCC vs (rpECI3DPC))
Across 59192 extreme-environment built habitats using hotel buildings, the absolute reduction in refurbishment-phase embodied carbon intensity (y1 = rpECI3DCC − rpECI3DPC) exhibited a strong monotonic dependence on plan compactness (Fig. 2a). Footprint ratio (building footprint area/total building area) was near-perfectly correlated with y1 (Pearson r = 0.991, p < 1×10⁻¹⁶;), whereas Aspect ratio showed a moderate negative association (r = −0.511, p = 5.41×10⁻⁴³) and Shape factor (surface area/volume) was strongly positively associated (r = 0.843, p = 1.46×10⁻¹⁷⁰). In contrast, the relative reduction ratio (y2 = (ECI3DCC − ECI3DPC)/ECI3DCC) showed only weak-to-moderate negative correlations with geometry): shape factor (r = −0.371, p = 6.78×10⁻²²), aspect ratio (r = −0.236, p = 2.09×10⁻⁹), and footprint ratio (r = −0.163, p = 4.12×10⁻⁵). The two objectives were largely decoupled at the population level (y1 vs y2: r = −0.075, p = 0.061), indicating that maximizing absolute refurbishment-phase reductions does not necessarily translate into higher proportional reductions in conventional construction intensity. The Pearson correlation matrix in Figs. 2a-3 was seriated using hierarchical clustering (average linkage) with a signed distance d = 1 – r, which groups positively correlated indices and separates negative contrasts. The reordered map reveals three coherent bundles: (i) vertical scale (total height and floors), (ii) overall size (total area and volume), and (iii) compactness (shape factor and footprint ratio). Notably, y1 clusters with the compactness bundle, whereas y2 shows weaker associations and remains structurally separated from y1, supporting their population-level decoupling. A key structural feature is strong collinearity between footprint ratio and shape factor (r = 0.868, p = 7.48×10⁻¹⁹³), implying that plan compactness and envelope-to-volume efficiency co-vary and should be interpreted jointly. Such covariation may also reflect regulatory and planning constraints (e.g., height limits and setback rules) in addition to engineering-driven trade-offs.
a Pearson correlations among morphology descriptors and objectives: y1 = rpECI3DCC − rpECI3DPC is dominated by Footprint Ratio (r = 0.991), whereas y2 = (ECI3DCC − ECI3DPC)/ECI3DCC shows weaker negative associations and y1–y2 decoupling (r = −0.075); The correlation matrix is reordered by seriation using hierarchical clustering (average linkage) with a signed distance. d = 1 − r to group positively correlated indices and emphasize negative contrasts b multivariate regression predicts y1 (test R² = 0.979) but not y2 (0.335). c bivariate monotonic patterns. d–e k-means (k = 3) regimes separate high-y1 versus high-y2 clusters. f Pareto set (n = 5) highlights non-dominated exemplars of the Delta–Eta trade-off in this dataset. g Sensitivity of Pareto-set size to tail trimming (reported across multiple percentile ranges). h Full Delta–Eta cloud (trim 1–99%) with Pareto points highlighted and a 95th-quantile envelope indicating the upper boundary structure. i Near-Pareto set under epsilon-dominance (eps = 2% of objective ranges; trim 1–99%), providing a relaxed frontier to visualize robust boundary patterns beyond strict Pareto sparsity.
A multivariate linear model using footprint ratio, aspect ratio, and shape factor predicted y1 with high fidelity (test R² = 0.979; Fig. 2b), consistent with the near-deterministic bivariate patterns (Fig. 2c), whereas the same model explained substantially less variance in y2 (test R² = 0.335; Fig. 2b), suggesting additional drivers beyond gross geometry (e.g., envelope composition and detailing, joint/penetration strategies, shielding/berming configuration, and operations). Feature attribution further separated the objectives: random-forest importance identified footprint ratio as the dominant driver of y1 (0.942 of total importance), while y2 was driven primarily by shape factor (0.486) and aspect ratio (0.302), with footprint ratio contributing less (0.213). Thus, absolute reductions respond primarily to footprint compactness, whereas proportional reductions are more sensitive to envelope-to-volume efficiency and height–perimeter scaling.
Unsupervised clustering (k = 3) in the three-parameter morphology space identified three regimes with distinct carbon outcomes (Fig. 2d,e). Cluster 0 (n = 447) comprised mid-range footprint ratio and low-to-moderate shape factor, achieving the highest mean y2 (0.1166 ± 0.0465) despite moderate y1 (1.131 ± 0.583). Cluster 1 (n = 141) contained footprint-ratio-saturated cases (mean = 1.00) with higher shape factor (0.557 ± 0.223), yielding the highest mean y1 (3.797 ± 0.260) but lower mean y2 (0.101 ± 0.045). Cluster 2 (n = 40) captured slender/high aspect-ratio forms (0.513 ± 0.182) with extremely low shape factor (0.0078 ± 0.0056) and the weakest performance (y1 = 0.155 ± 0.064; y2 = 0.094 ± 0.043). Radar profiles indicate separation primarily along footprint ratio and aspect ratio, while shape factor differentiates the high-y1 regime. Joint maximization of y1 and y2 produced a small strict Pareto set (Fig. 2f). Because the size of the strict non-dominated set can be sensitive to tail handling, we report Pareto-set size across multiple trimming thresholds (Fig. 2g) and treat frontier sparsity as a descriptive property of this sample rather than a universal constant. To avoid over-interpreting a small number of Pareto points, we visualize the full Delta–Eta cloud (trim 1–99%) and its upper boundary via a 95th-quantile envelope (Fig. 2h), and we additionally report a relaxed epsilon-dominance near-Pareto set (eps = 2% of objective ranges; Fig. 2i). Together, these views indicate a consistent boundary pattern in this dataset: higher Delta values are most often achieved by footprint-saturated compact plans, whereas higher Eta values occur in forms with reduced exposure relative to volume, suggesting an empirical trade-off structure under the chosen objectives.
Earth analog priors: Algorithm-Driven Design Studies
The study analysed 530 publications (1981–2025) on algorithm-driven extra-terrestrial habitat/morphology design. The corpus is strongly recent-skewed: 463/530 papers (87.4%) were published in 2016–2025, peaking at 98 papers in 2025. Consistent with this concentration, the paradigm time series (Fig. 3a) shows most methodological categories expanding rapidly after 2015 and diversifying through the 2020 s. Rule-based keyword tagging of titles/abstracts/takeaways identifies topology/shape optimisation as the dominant primary paradigm (138/530; 26.0%), followed by evolutionary methods (84; 15.8%), deep/generative AI (75; 14.2%), and parametric/rule-based generation (56; 10.6%). Decade-level composition shifts markedly (Fig. 3a): topology/shape optimisation declines from ~42.6% in the 2010s to ~19.0% in the 2020 s, coincident with deep/generative AI rising from ~1.0% (2010s) to ~18.8% (2020 s) and an expansion of heterogeneous “Other” approaches to ~25.1%. Keyword frequency (Fig. 3b word cloud) is dominated by the expected design/optimisation lexicon (for example, design, optimization, shape, structural, shell, parametric, generative, lunar, space, habitat). Primary objective tagging indicates that mission-specific extra-terrestrial constraints (radiation/pressurisation/ISRU and related terms) are a major focus (129; 24.3%), alongside structural performance (91; 17.2%) and manufacture/assembly (62; 11.7%). Paradigm–objective coupling (Fig. 3f,g) is anchored by two high-volume links: topology/shape optimisation → structural objectives (49 papers; 35.5% of topology/shape-optimisation papers) and “Other” paradigms → extra-terrestrial constraints (69 papers; 55.2% of “Other” papers). To improve interpretability, the paradigm–goal heatmap (Fig. 3f) was seriated by reordering both paradigms and objectives based on similarity in their co-occurrence profiles (cosine distance; hierarchical clustering). The reordered matrix reveals clearer coupling structure: topology/shape optimisation concentrates on structural objectives, whereas simulation-driven and evolutionary approaches distribute more broadly across extraterrestrial constraints, structural performance, and manufacture/assembly. Parametric/rule-based and deep/generative methods show mixed goal profiles spanning structural and mission-oriented constraints, while robust/uncertainty and habitability/layout remain comparatively low-frequency across paradigms. Overall, seriation makes the dominant links and contrasts across methodological families visually explicit. Beyond these anchors, evolutionary and deep/generative methods distribute more broadly across objectives (e.g., evolutionary methods span extra-terrestrial constraints, thermal/energy, and manufacture/assembly at comparable shares), consistent with their role as flexible search frameworks under mixed constraints.
a publication time series and decade composition show rapid post-2015 expansion (463/530 in 2016–2025; peak 98 in 2025) and a shift from topology/shape optimisation ( ~ 42.6% → ~ 19.0%) toward deep/generative AI ( ~ 1.0% → ~ 18.8%) and “Other” ( ~ 25.1%). b keyword cloud summarizes dominant design lexicon. c–d LDA (8 topics) tracks rising generative/AI pipelines and declining construction- and shell-heavy threads. e right-skewed citations (median 4; max 1,370) by paradigm. f–g paradigm–objective coupling highlights topology→structural and “Other”→mission constraints.
Citation counts are highly right-skewed (log distribution shown previously), with a median of 4 (IQR 0–15), 90th percentile 46, maximum 1,370, and 25.7% uncited records. By paradigm (Fig. 3e), topology/shape optimisation shows higher central tendency (median 6; IQR 1–28) and a high mean (37.3) driven by a small number of highly cited works (Max 1,370). Morphogenesis/growth has the highest median (8; IQR 4–21) but a small sample (n = 11) and an extreme maximum (670), indicating concentrated influence rather than broad volume. For records with SJR quartiles available (318/530; 60.0%), Q1 journals dominate (220/318; 69.2%); Q1 papers have markedly higher citation central tendency (median 12; IQR 3–28) than Q2 (median 4; IQR 1–12), whereas Q4 remains sparsely cited (median 0). Semantic analyses show keyword frequency dominated by the expected design/optimisation lexicon (e.g., design, optimization, shape, structural, shell, parametric, generative, lunar, space, habitat;). Topic modelling (LDA; Fig. 3c,d) resolves 8 recurrent topics spanning (i) lunar/martian habitat and regolith construction language, (ii) generative/parametric/evolutionary design pipelines, and (iii) structural shell/topology-optimisation threads. From 2000–2009 to 2016–2025, the strongest increases occur in Topic3 (generative + genetic + parametric pipelines; Δ +0.082), Topic6 (parametric/architectural + AI modelling; Δ +0.069), and Topic7 (morphology/thermal/comfort + deep terms; Δ +0.057), while Topic2 (lunar/mars construction-heavy; Δ −0.105) and Topic4 (shell/topology-optimisation-heavy; Δ −0.103) decline, aligning with the diversification observed.
Earth analog priors: Platforms
TRL spans 1–9 (median 5.5; IQR 4–7), with entries concentrated in TRL 4–6 (34/74, 46%), followed by TRL 7–9 (22/74, 30%) and TRL 1–3 (18/74, 24%) (Fig. 4b). Mode classification resolves six groups: Surface stations/field sites (25/74, 34%); buildable HAB technology companies (14/74, 19%); leading architecture/commercial teams (10/74, 14%); aerospace agency–led platforms (10/74, 14%); universities/research centers (10/74, 14%); and Mars analog/physical simulation bases (5/74, 7%). TRL differs sharply by Mode: Surface stations/field sites show the highest maturity (mean TRL 7.24; 19/25 in TRL 7–9), universities/research centers cluster at low-to-mid maturity (mean TRL 3.30; 6/10 in TRL 1–3), buildable HAB technology companies and agency-led platforms are predominantly mid-TRL (mean TRL 4.29 and 4.10), and analog/physical simulation bases concentrate near TRL 6.00 (Fig. 4b). Founded years span 1842–2022 (median 1988), with 45/74 (61%) founded <2000 and 29/74 (39%) founded ≥2000; all universities/research centers (10/10) and most Surface stations/field sites (20/25) are founded <2000, whereas post-2000 entries are enriched for companies (10/14), commercial teams (7/10), and analog bases (4/5). The United States spans all Mode groups and all TRL bands (TRL 1–3: 7; TRL 4–6: 20; TRL 7–9: 7), whereas several countries exhibit narrower pathways (e.g., China dominated by Surface stations/field sites, 3/4; France weighted toward agency-led platforms, 3/7, and mid-TRL, 3/7 in TRL 4–6).
a Country counts show a right-skewed ecosystem (US 34/74; 46%). b TRL spans 1–9 (median 5.5) with strong mode stratification (field sites highest; universities lowest). c Founded year versus high-frequency keywords indicates a post-2000 shift from polar/analog language to regolith/modular systems. d TF–IDF–NMF topic–term heatmap (7 topics); rows (topics) and columns (terms) are seriated via hierarchical clustering (average linkage) on cosine distance of weight profiles; color indicates normalized weight. e Cosine-similarity network (74 nodes, 191 edges) identifies hubs and 6 communities. f Technology-route taxonomy by country is dominated by analog/field simulation and regolith/3D printing; the route–country count matrix is seriated (average linkage, cosine distance); color indicates count. France 7/74 (9%), China 4/74 (5%). Routes are non-exclusive; cells report route-assignment counts and should not be summed across routes to infer unique platform totals.
Using concatenated concept texts (Mars HAB Concept, descriptions; n = 74; founded 1842–2022), unigram keywords (stopwords removed; excluding “Mars/habitat”) show structured temporal signatures (Fig. 4c). Most frequent terms are extreme (37), analog (36), polar (27), systems (24), human (21), structural (20), regolith (17), modular (17), and space (18). Peaks separate 1950s polar/analog/extreme (13/10/9) from post-2000 regolith (2010s: 6) and systems/space (2020 s: 5 each). Topic modeling (TF–IDF unigrams+bigrams; NMF, 7 topics) resolves recurring themes: polar/analog environments, structural/material systems, regolith/additive construction, long-duration operations, inflatable/modular habitation, station/extreme inland analogs, and subsurface/covered architecture (Fig. 4d). The reordered map reveals several coherent bundles: an analog/extreme-environment cluster (e.g., polar, antarctic/arctic, inland station, long-duration), an engineering-materials cluster centered on regolith and construction-related terms, and an operations/protection cluster linking mission logistics with shielding-related language. Topics align with these bundles rather than appearing as isolated stripes, clarifying that the concept space is anchored by analog testing narratives while multiple comparably sized engineering subthemes (materials, protection, modularity/inflatables, subsurface strategies) form distinct but adjacent clusters. Dominant-topic counts are: Topic1 15/74; Topics2 and 5 11/74 each; Topic4 10/74; Topics3, 6, and 7 9/74 each, indicating strong analog/extreme anchoring with comparably sized engineering subthemes.
A cosine-similarity network in TF–IDF space links each organization to its top-4 nearest neighbors, yielding 74 nodes and 191 edges and a fully connected graph (largest component 74/74; mean degree 5.16) (Fig. 4e). High-degree hubs include Pyramiden (10) and degree-8 nodes (Branch Technology, Colorado School of Mines, Mawson Station, Spartan Space). Greedy modularity community detection identifies 6 communities (22, 17, 13, 9, 9, 4), consistent with topic partitions. A rule-based, multi-label technology-route taxonomy maps concept text to non-exclusive routes. Overall assignments are dominated by Analog/Field Simulation (34) and Regolith/3D Printing (18), followed by Subsurface/Underground (8), Inflatable/Soft Habitat (7), ISRU (7), Thermal/Power/Energy (7), Radiation/Shielding (6), Greenhouse/Agriculture (5), and Closed-loop Life Support (1) (Fig. 4f). Two routes emerge as dominant anchors across the matrix—Analog/Field Simulation and Regolith/3D Printing—while ISRU, Thermal/Power/Energy, Radiation/Shielding, and Subsurface/Underground appear as smaller, more specialized patterns concentrated in fewer countries. The reordered layout highlights a broad, multi-route profile for high-activity countries (notably the United States), contrasted with narrower national profiles that emphasize specific routes. Overall, seriation sharpens the visual contrast between generalist and specialist country strategies. Using a de-duplicated breadth metric (Supplementary file Table – number of distinct routes covered), the United States shows the broadest portfolio, while route-assignment counts (e.g., Regolith/3D Printing and Analog/Field Simulation) indicate coverage intensity under the non-exclusive labeling scheme.
Discussion
This study proposes a transferable, testable morphology–maintenance law for Mars-habitat-relevant design by integrating three evidence streams: Earth-analog refurbishment proxies across extreme environments, explainable reverse engineering of non-additive geometric coupling, and a structured map of algorithmic and technology-maturity pathways for extra-terrestrial habitat development. Performance is not governed by a single compactness gradient. Instead, maximal prefabrication-enabled refurbishment savings occur only within a narrow, mutually reinforcing proportion band, and joint maximization of absolute and proportional gains concentrates into a sparse Pareto set. These results support a corridor-based concept of “optimal form,” where robust solutions occupy a constrained region in morphology space rather than a single optimum.
Plan compactness, envelope exposure, and height–perimeter scaling form an empirically coupled interaction structure associated with refurbishment outcomes under persistent forcing, as revealed by model-based interaction patterns. Shape Factor × Footprint Ratio shows a plateau, indicating diminishing returns as planar compactness saturates in exposure-limited regimes. Shape Factor × Aspect Ratio forms a ridge, implying a narrow corridor where height–perimeter scaling minimizes refurbishment burden; deviations impose disproportionate penalties, consistent with rising interface count, façade articulation, and joint density with increasing slenderness. Footprint Ratio × Aspect Ratio exhibits a saddle, indicating that marginal benefits switch sign depending on the companion variable. These interaction topologies are descriptive of the fitted model (SHAP interaction patterns) and should not be interpreted as causal “control laws.” For Mars-relevant habitats, where maintenance events incur fixed overheads in crew time, risk, spares staging, and downtime, such non-additive coupling is expected and supports a morphology-threshold corridor as a candidate structural invariant for exposed habitats. For Mars deployment, the corridor should be interpreted as a geometry feasibility prior, not a complete objective function. The feasible set is the intersection Feasible_Mars = Corridor_geometry ∩ Constraints_mission (e.g., shielding areal density, leakage tolerance, penetrations/airlocks, life-support integration), which narrows the search manifold before multi-physics optimization. In this framing, curvature, shielding/berming depth, interface density, and connectivity can be introduced as secondary descriptors or explicit constraints layered on top of the corridor.
Environmental constraints should be treated as explicit feasibility filters on “optimal” morphology. A form that is Pareto-efficient in aggregate may be unsuitable under specific forcing regimes (e.g., dust ingress/abrasion, thermal cycling, wind-driven particle impact, salt/freeze–thaw in Earth analogs), because exposure mediates interface failure rates and maintenance cadence. This provides a plausible mechanism for part of the observed geographic heterogeneity in national means, without requiring a single global compactness gradient: differences in dominant stressors could shift or contract the admissible corridor in joint morphology space. For Mars exploration, environment-conditioned constraints (shielding strategy, pressurization leakage tolerance, dust control, thermal-control loads) can be incorporated as priors to narrow the feasible design manifold before expensive multi-physics evaluation.
Weak coupling between absolute savings (Δ) and proportional improvement (η) provides a second mechanistic insight. Hospitality geometries are influenced by objectives not mission-relevant for Mars, whereas Mars habitats prioritize shielding continuity, airtightness, and reliability of sealed interfaces. Nevertheless, the descriptors used here (footprint ratio, aspect ratio, shape factor) parameterize exposure and interface scaling, which directly affect sealing burden, leakage risk, and shielding mass; thus mission objectives may reweight and contract (not negate) the admissible corridor. Δ is near-deterministically driven by plan compactness, indicating that geometry controls the scale of material turnover and intervention extent. In contrast, η is only weak-to-moderately explained by gross geometry, implying sensitivity to system-level factors beyond the three primary descriptors, including envelope composition and detailing, modular joint strategies, baseline construction quality, supply-chain structure, and climate–operations coupling. This supports a two-mechanism view: Δ behaves as a mass-dominant lever tied to replaceable extent, whereas η is an efficiency-dominant lever reflecting suppression of baseline vulnerability modes. Mission translation maps Δ to resupply mass/storage volume and η to maintainability, reliability improvement, and logistics-chain resilience.
Pareto sparsity adds a third interpretive layer. Across the evaluated trimming ranges, the strict non-dominated set is typically small, suggesting that concurrent improvement in both Δ and η is uncommon in this dataset under the chosen objectives. This is consistent with intrinsic geometric trade-offs: footprint-saturated compactness can increase Δ yet reduce proportional advantage if prefabrication benefits saturate or conventional baselines are already efficient. Conversely, morphologies yielding high η may mitigate specific vulnerability modes but not maximize Δ when total intervention mass is moderate. In this dataset, the concentration of near-frontier cases suggests practical designability, as high-performing solutions occupy a constrained region in morphology space. For algorithmic design pipelines, this converts a broad continuous search into a constrained target manifold, supporting prescreening before expensive multi-physics evaluation and improving convergence toward robust candidates.
The literature synthesis explains why an empirically anchored corridor is timely. Algorithm-driven habitat morphology research expanded rapidly after 2015 and diversified through the 2020 s, with deep/generative approaches rising alongside topology optimization and evolutionary search rather than replacing them. This pluralism increases exploration capacity but fragments comparability across studies because objectives, assumptions, and representation spaces vary widely. A morphology-threshold corridor provides a unifying scaffold and a common prior across paradigms: it can serve as a prescreening filter to discard off-corridor candidates, a soft constraint/regularizer that penalizes distance from the corridor, or a curriculum for generative models that learn a high-performing morphology manifold before adding mission constraints (radiation shielding, pressurization, thermal control). The corridor complements, rather than replaces, physics-based simulation by stabilizing design-space exploration and improving interpretability. Boundary conditions for transfer can be stated as follows: the proposed morphology-threshold corridor is intended as a conditionally transferable geometry prior for habitats whose dominant degradation and maintenance burdens scale with envelope exposure and interface density under persistent forcing, and its applicability is therefore route-dependent. It is expected to be most directly applicable to exposed surface habitats (pressurized shells with sustained external exposure) as a prescreening prior for geometry–exposure–renewal coupling; for subsurface/bermed/shielded concepts, embedment and shielding reduce effective exposure so the corridor may shift or relax and should be re-parameterized with exposure-modified descriptors; for inflatable/soft habitats, exposure scaling remains relevant but seam/penetration strategies and material aging can dominate, so the corridor should be used alongside explicit interface and sealing constraints; and for reduced-gravity cantilevered or highly articulated configurations, structural feasibility constraints change under reduced gravity, so the corridor should be treated as a maintenance/exposure prior and coupled with route-specific structural and multi-physics constraints rather than interpreted as a stand-alone geometric optimum.
The ecosystem scan strengthens translational relevance by identifying where corridor-based guidance is most actionable across technology-maturity pathways. Many Mars habitat efforts concentrate in mid-TRL development, while high-maturity field sites dominate the upper TRL band. This distribution is consistent with the corridor’s intended domain: TRL 7–9 platforms are dominated by surface stations/field sites, which operate under long-duration exposure and thus provide natural arenas for validating whether off-corridor morphologies exhibit higher intervention cadence, replaced mass, or downtime. In contrast, shielded routes (e.g., subsurface/bermed concepts) are expected to modify the effective forcing and therefore to shift or relax the corridor, reinforcing the need for route-conditioned boundary conditions rather than a single universal rule. Two opportunities follow. Mid-TRL concept-to-prototype workflows can adopt corridor constraints to reduce iteration cycles and avoid exposure-prone morphologies with high maintenance burden. High-maturity surface stations and field sites offer validation arenas due to long-duration operation under persistent stressors, enabling tests of whether off-corridor morphologies exhibit steeper intervention rates, greater replaced mass, or higher downtime. Route dependence is expected: bermed, subsurface, or shielded strategies may relax corridor constraints by reducing exposure, whereas highly modular, multi-interface systems may tighten them unless joint strategies and sealing solutions improve.
Several limitations delineate claims and point to strengthening steps. The Earth-analog dataset is based on hospitality buildings, differing from Mars habitats in pressurization, shielding, system integration, and operations; the aim is inference of geometric regularities under persistent forcing, not typological transfer. Operational regimes can shift the baseline refurbishment cadence (intercept)—for example, hotels may exhibit higher interior turnover than long-duration habitats—while geometry primarily affects the scaling (slope) of exposure- and interface-driven interventions. Accordingly, the corridor is interpreted as a structural constraint on how form modulates renewal burden, whereas absolute Mars maintenance rates depend on operations, access strategy, redundancy, and subsystem reliability. Refurbishment-phase embodied carbon intensity is an indirect proxy for maintenance logistics; it likely correlates with replacement mass and intervention frequency but embeds Earth-specific supply chains, labor practices, and regulatory contexts. A direct empirical mapping from rpECI to Mars mission maintenance outcomes (e.g., crew labor hours, spares mass, and system downtime) is not established in this study, and the proxy should therefore be interpreted cautiously. Strengthening validation can proceed along three tractable routes: (i) benchmarking rpECI against observed maintenance records (intervention frequency, replaced mass, and downtime) in closer Earth analogs (polar stations, desert analog bases, long-duration isolated facilities); (ii) decomposing refurbishment contributions into envelope/structure/MEP replacement intensities and comparing them with component-level reliability and repair metrics (MTBF/MTTR) where available; and (iii) embedding replacement-intensity outputs as inputs to mission logistics models to translate corridor distance into spares mass/volume and maintenance-window occupancy. These steps would convert the proxy assumption into a quantitatively calibrated link for Mars-habitat design studies. A related caveat is that rpECI can be dominated by terrestrial emission factors (e.g., grid carbon intensity) and by energy-intensive material production, whereas Mars maintenance burden is governed by mass, reliability, and operational risk. Under ISRU, materials that are carbon-intensive on Earth (e.g., cementitious/regolith-based composites) may become comparatively more accessible, so the carbon-based ranking of material choices could change and, in extreme cases, appear to reverse. For this reason, the present contribution is the morphology-threshold corridor (geometry–exposure–renewal coupling), while Mars deployment studies should apply scenario-specific reweighting that maps renewal intensity to mission objectives (spares mass/volume, crew time, downtime) under assumed ISRU and power architectures. Geometry-only descriptors omit material composition, detailing complexity, and operational regimes, likely explaining residual variance in η. Additionally, several Mars-relevant configuration attributes are not represented by the three-parameter morphology vector, including curvature, embedment depth/berming, interface/penetration density, and internal compartmentalization/connectivity. These omitted factors are consistent with the weaker predictability of η (test R² = 0.335) under geometry-only modeling. National aggregation introduces sample-size imbalance, and some country-level estimates remain sensitive despite robustness checks. More generally, unobserved institutional constraints (building codes, height restrictions, zoning) may induce geometry covariation that is not causal, motivating stratified and residualized robustness checks. Strengthening steps include integrating direct maintenance observables (intervention frequency, replaced mass, downtime), adding exposure mediators (wind, salt/dust indices, thermal cycling), using hierarchical models to separate within-region geometry effects from between-region system effects, and validating transferability using closer analogs (polar stations, desert analog bases, long-duration closed environments). Transferability can be tested by repeating the geometry–outcome analyses on closer analogs with sealed, reliability-critical operation (e.g., polar stations, desert analog bases, long-duration closed facilities/offshore platforms) where maintenance logs exist. Such datasets allow explicit evaluation of corridor stability when daylighting/view-driven pressures are absent and airtightness/reliability constraints dominate.
Mars’s near-vacuum atmosphere shifts dominant degradation pathways relative to many terrestrial climates: wind-driven rain penetration and salt-spray corrosion are absent or strongly reduced, whereas dust abrasion/ingress, CO₂-rich particulate infiltration, and large-amplitude thermal cycling fatigue can dominate maintenance. Accordingly, the corridor is not meant to optimize against any single terrestrial weathering mechanism, but to constrain how morphology scales effective exposure and interface burden under persistent stress. Mars-specific physics may reweight geometric preferences (e.g., curvature/dome benefits) beyond the current three-parameter descriptors, so the corridor should be used as a prescreening prior conditioned by Mars forcing and route-specific constraints (dust sealing, thermal margins, shielding/berming). A further limitation is mechanism mismatch: some terrestrial exposure mediators do not translate to Mars, so future work should explicitly incorporate Mars-relevant forcing terms (dust abrasion/ingress, CO₂ infiltration, thermal cycling fatigue) and curvature-related metrics when conditioning the corridor for mission design.
The results yield falsifiable predictions for Mars habitats. Under increasing forcing, the admissible high-performance corridor in joint morphology space should contract, and off-corridor designs should show steeper degradation slopes and higher intervention cadence. Joint optimization of mass-like savings (Δ) and reliability-like proportional improvements (η) should remain Pareto-sparse, requiring explicit trade-off management rather than assuming a single best form. Exposure-mitigating routes should widen the corridor and shift interaction topology, whereas interface-intensifying routes should narrow it unless joint and sealing strategies improve. Algorithmic pipelines incorporating corridor priors should show measurable efficiency gains, including faster convergence and higher candidate survival through multi-physics evaluation relative to unconstrained search, enabling testing via controlled simulations and long-duration analog operations.
Methods
Main framework
This study combines three linked analyses to derive transferable morphology–maintenance insights for Mars-habitat-relevant design: (1) an Earth-analog reverse-engineering analysis of refurbishment-phase embodied carbon intensity under conventional versus prefabricated construction, using a global sample of extreme-environment built habitats; (2) a structured synthesis of algorithm-driven extra-terrestrial habitat morphology design studies; and (3) a global scan of Mars habitat research-and-development ecosystem platforms with technology readiness level (trl) and route taxonomies. The workflow is organized around shared, interpretable morphology descriptors and explicitly separates absolute savings from proportional improvement to avoid single-metric inference.
Reverse engineering extreme-environment built habitats
The Earth-analog dataset comprises 2,0192 building forms and 39,000 standardized metrics from 631 extreme-environment built habitats distributed across 384 cities and 70 countries/territories. The unit of analysis is the individual building. Buildings are associated with a city and country (iso-3), enabling both city-level environmental annotation and country-level aggregation. Each building is mapped to a host city. City-level extreme-environment descriptors are used to represent persistent environmental forcing relevant to long-horizon maintenance, including variables such as thermal stress, moisture stress, wind exposure, salinity or aerosol stress, and related composite extremeness indices when available. City-level persistent forcing was operationalized using the composite Extremeness Index (EI3) provided in the dataset (Extremeness_Index_EI3), which aggregates multiple stress dimensions (e.g., thermal and moisture stress, wind exposure, and aerosol/salinity-related stress) into a single comparable score across locations. The main analysis uses the cleaned building-level set (n = 630) spanning 312 cities and 70 ISO-3 countries/territories. To avoid arbitrary single-variable thresholds (e.g., temperature-only cutoffs) and to enable a reproducible definition of “extreme” forcing, sensitivity analyses stratify the sample by EI3 percentiles: high-forcing cases are defined as EI3 > = 0.769 (75th percentile), and low-forcing cases as EI3 < = 0.026 (25th percentile). Environmental descriptors are treated as contextual covariates rather than direct causal drivers, and are primarily used for stratification and interpretation of interaction amplification. Refurbishment-phase embodied carbon intensity is used as an Earth-analog proxy for maintenance-driven material replacement and associated logistics load. Proxy validity and scope were treated explicitly. In this study, rpECI is interpreted as a quantitative surrogate for maintenance-driven material replacement intensity (i.e., the amount of component renewal implied by refurbishment processes), not as a direct measure of astronaut labor time, spare-part handling complexity, or downtime. The proxy is used because refurbishment-phase embodied carbon is structurally linked to material throughput and intervention scale, which are mission-relevant through their implications for resupply mass/volume and intervention frequency. Nonetheless, rpECI embeds Earth-specific supply chains and practices; therefore, all Mars-relevant interpretations are framed at the level of geometry–exposure–replacement coupling. This framing yields falsifiable predictions: if rpECI is a useful analog, then environment-stratified datasets with direct maintenance observables should show aligned directionality between rpECI-derived replacement intensity and measured maintenance burden. Because embodied-carbon intensity is conditioned on terrestrial energy structures and emission factors, rpECI was not interpreted as a direct proxy for Mars logistics cost. Instead, it was used to infer the geometry-dependent component of refurbishment burden—namely, maintenance-driven replacement intensity and intervention scale—while recognizing that absolute carbon magnitudes can vary with country- and time-specific supply chains. Accordingly, Mars-relevant implications are discussed in terms of how morphology modulates exposure, interfaces, and renewal extent, whereas any translation to mission cost must be reweighted under different production pathways (including ISRU and low-carbon power scenarios). Two construction-system counterfactuals are defined for each building: a conventional construction system (cc) and a prefabricated construction system (pc). The following quantities are computed at the building level:
- a.
Absolute refurbishment-phase reduction intensity
$$Delta {rpECI}={rpECI}3{DCC}-{rpECI}3{DPC}left({kgCO}2e/{m}^{3}right)$$(1) - b.
Relative reduction ratio
Here, rpECI3DCC and rpECI3DPC represent refurbishment-phase embodied carbon intensity per unit building volume for the conventional and prefabricated scenarios, respectively. ECI3DCC and ECI3DPC represent the corresponding baseline embodied-carbon intensities used to compute proportional improvement. Absolute and relative indicators are intentionally treated as distinct objectives because they reflect different mechanisms: scale of replacement (mass-dominant) versus efficiency gain relative to baseline (efficiency-dominant). Three primary morphology descriptors are computed for each building, forming the morphology vector g = (footprint ratio, aspect ratio, shape factor). These descriptors are selected to capture plan compactness, vertical scaling, and envelope exposure efficiency in an interpretable, low-dimensional form suitable for explainable interaction analysis.
- a.
Footprint ratio (fr). Defined as building footprint area divided by total building area, capturing plan compactness and the degree of footprint “saturation.”
- b.
Aspect ratio (ar). Defined to capture vertical slenderness or height–plan scaling, representing the relative emphasis of vertical development versus plan spread.
- c.
Shape factor (sf). Defined as surface-area-to-volume proxy (s/v or an equivalent normalized measure), representing envelope exposure per unit enclosed volume.
All morphology variables are standardized (z-scored) for model fitting when required, while original units are retained for reporting thresholds and corridor bounds. Collinearity diagnostics are computed using Pearson correlation and variance inflation checks to interpret coupled effects and avoid misleading single-variable attribution. A cleaned analysis set is defined by excluding records with missing core variables, implausible geometry values, or incomplete construction-system counterfactuals. Two complementary datasets are used for robustness:
- a.
Cleaned dataset (n = 629). Used for main Pareto screening and interpretability analyses.
- b.
Robustly trimmed dataset (n = 587; 1st–99th percentile trimming). Used to reduce sensitivity to extreme tails in ΔrpECI and η and to test stability of Pareto sparsity and corridor bounds.
Unless otherwise stated, reported interaction patterns and corridor locations are considered robust only if consistent across the cleaned and trimmed sets. For spatial heterogeneity analyses, buildings are aggregated to iso-3 country/territory means for both ΔrpECI and η. Two summary statistics are reported:
- a.
Unweighted mean across countries (country means treated equally).
- b.
Sample-size-weighted mean across countries (countries weighted by number of buildings).
To mitigate instability from small-n countries, sensitivity checks are conducted using thresholds such as n ≥ 10 for “more robust” country-level interpretation. Coupling between national mean metrics is assessed using Pearson correlation. Bivariate associations between morphology descriptors and each objective (ΔrpECI and η) are quantified using Pearson correlation with two-sided significance testing. The relationship between the two objectives is also assessed to evaluate population-level coupling or decoupling. A multivariate linear model is fitted using (fr, ar, sf) to predict each objective. Train/test splits are used to report out-of-sample performance (test R²) and to illustrate the contrast between near-deterministic predictability of ΔrpECI and weaker predictability of η under geometry-only modeling. Where appropriate, residual analyses are used to motivate additional drivers beyond gross geometry.
To separate feature attribution for ΔrpECI versus η and to characterize non-additive coupling, tree-based models are used alongside explainability tools. Random forest regression is used for non-linear prediction and feature-importance extraction. Linear regression is used as a baseline for interpretability and to quantify how much variance can be explained by geometry alone. Global feature importance is computed from the random forest model (e.g., impurity-based or permutation-based, depending on implementation). Importances are normalized to sum to one and interpreted comparatively across objectives. SHAP interaction analysis Shapley additive explanations (shap) interaction values are computed for the model predicting the proportional objective y = (rpECI3DCC − rpECI3DPC) / rpECI3DCC. Pairwise interaction surfaces are constructed for:
- a.
Shape factor × footprint ratio
- b.
Shape factor × aspect ratio
- c.
Footprint ratio × aspect ratio
Interaction surfaces are evaluated over the observed feature domain using gridded evaluation and partial dependence-style visualization. Top-performing regions are defined by percentile thresholds on predicted y. The “top-3%” region is used to identify compact optimal plateaus, ridges, and saddles and to extract an interpretable proportion band (threshold corridor) in morphology space. Reported corridor bounds are expressed in original feature units to support direct design translation. To identify morphology regimes with distinct carbon outcomes, k-means clustering is performed in the standardized three-parameter morphology space (fr, ar, sf). The number of clusters is selected to balance interpretability and separation, with k = 3 used to produce three regimes consistent with observed outcome stratification. For each cluster, descriptive statistics are computed for morphology descriptors and both objectives, including mean and standard deviation. Cluster profiles are visualized using radar-style summaries to highlight which morphology dimensions primarily differentiate regimes. Cluster interpretation focuses on whether high-Δ and high-η regimes align with different geometric signatures, supporting the two-mechanism interpretation.
Joint optimization is framed as a two-objective problem:
Objective 1:
Objective 2:
A non-dominated sorting procedure is applied to identify the Pareto set P, defined as the set of cases for which no other case improves both objectives simultaneously. Pareto sparsity is evaluated by reporting |P| for both cleaned and trimmed datasets.
To select a single compromise solution from the Pareto set, a min–max (Tchebycheff) criterion is applied after normalizing both objectives to comparable scales. The selected case minimizes the maximum normalized distance to the ideal point (component-wise best on the Pareto set). The resulting solution is reported as the best-balanced point. Pareto solutions are projected back into the morphology feature space. To provide a robust, designable corridor rather than a single point, percentile-based bounds are extracted from Pareto solutions. Specifically, a Pareto (10–90) “threshold box” is computed for each morphology descriptor, yielding a feasibility corridor that captures the central spread of Pareto-consistent geometries while avoiding overfitting to a very small Pareto set. The position of the Tchebycheff-selected solution relative to the corridor core is reported to support interpretability.
Extraterrestrial habitat morphology design studies
The 530 publications (1981–2025) on algorithm-driven extra-terrestrial habitat and morphology design is assembled through structured search, deduplication, and relevance screening. Each record contains bibliographic metadata and text fields (title, abstract, and extracted takeaways when available). Primary methodological paradigms are assigned via rule-based keyword tagging over these fields, including topology/shape optimization, evolutionary methods, deep/generative ai, parametric/rule-based generation, and an “other” class for heterogeneous approaches not captured by main tags. Primary objectives are tagged similarly, covering extra-terrestrial constraints (radiation, pressurization, isru), structural performance, manufacture/assembly, thermal/energy, and other mission-relevant goals. Publications are summarized by year and decade, with decade-level paradigm composition used to quantify long-run shifts. Paradigm–objective coupling is measured using contingency counts and normalized shares. Text is tokenized, stopwords removed, and lemmatized where applicable. A tf-idf matrix is reduced by svd, then pca for embedding visualization. Topic modeling uses lda to extract recurrent topics and temporal prevalence changes.
Mars habitat research-and-development ecosystem platforms
A dataset of 74 Mars habitat research-and-development ecosystem platforms is compiled, comprising 49 organizations and 25 extreme-environment field stations across 19 countries. Each entry includes organization type (mode classification), founding year, headquarters city and country, and a short textual description of activities. Trl (1–9) is assigned using a standardized rubric anchored to evidence of conceptual maturity, laboratory validation, ground prototypes, analog operations, and deployment-like demonstrations. Trl is treated as an ordinal measure and summarized by median, interquartile range, and mode-stratified distributions. Each entry is classified into one of six modes: surface stations/field sites, buildable habitat technology companies, leading architecture/commercial teams, aerospace agency–led platforms, universities/research centers, and Mars analog/physical simulation bases. A non-exclusive technology-route taxonomy is derived via rule-based tags (e.g., analog/field simulation, regolith/3 d printing, subsurface/underground, inflatable/soft habitat, isru, thermal/power/energy, radiation/shielding, greenhouse/agriculture, closed-loop life support), and country-level route profiles are computed as assignment counts. Routes are non-exclusive: a single platform can be assigned to multiple technology routes. Therefore, country-level values in Fig. 4f represent route-assignment counts (not unique platforms) and must not be summed across routes to infer country totals. Platform descriptions are analysed using tf-idf+nmf topic modeling and a cosine-similarity nearest-neighbour network; graph statistics and modularity-based community detection identify thematic hubs. Analyses are reproducible in scientific Python with fixed random seeds and consistent figure scaling.
Data availability
The datasets generated and analyzed during the current study are not publicly available due to ongoing related research and intellectual property protection considerations but are available from the corresponding author on reasonable request.
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Acknowledgements
Funding of ZJU100 Young Professor, Tongji Architectural Design (Group) Co., Ltd. Open Competition and Leading Research Independent Project (2025J-JB05), Zhejiang Sci-Tech University Start-up Fund (22052138-Y).
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G.C. conceived the research idea, wrote the main manuscript text, prepared the figures and tables, and conducted data analysis. Z.Z., D.M., L.S., and F.L. contributed to the methodological framework and revision. D.W., N.W., and N.Z. assisted with data, forms, and revision. C.C., Z.R., and L.T. provided supervision and revision. S.H., S.K., W.G., and Z.W. provided conceptual guidance and revision. All authors reviewed the manuscript and approved the authorship.
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Cai, G., Zou, Z., Ma, D. et al. Earth analog priors for deployable Mars habitats.
npj Space Explor. 2, 24 (2026). https://doi.org/10.1038/s44453-026-00034-z
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DOI: https://doi.org/10.1038/s44453-026-00034-z
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