AEGIS: Differentiable Mars Climate Model with Neural Closures

• Dust and CO2 radiative heating, surface exchange, and seasonal polar-cap condensation jointly shape Martian circulation, pressure, and frost.Source: §1 · p. 1
• Uncertain coupled parameterizations, expensive ensemble calibration, limited gradient access, and the effort of separate adjoints motivate a shared differentiable implementation.Source: §1 · p. 1
• Automatic differentiation through a simulation's computational graph supports calibration, sensitivity analysis, inverse problems, and training across multiple time steps.Source: §1 · p. 1
• AEGIS shares the Dinosaur backbone with JCM and NeuralGCM but adds Mars-specific state variables and operators for a different physical regime.Unlike Earth-focused configurations, it uses Mars planetary scales and evolves frost and regolith alongside the atmosphere, with CO2 phase change and inventory projection in the differentiated trajectory.Source: §1 · p. 2
• The contributions include extending the core for coupled atmosphere-surface-frost-regolith physics, providing modular physical and neural interfaces, and evaluating gradients, fields, calibration, and integrations.Source: §1 · p. 2

2.1 ATMOSPHERIC CONFIGURATIONS AND THE DYNAMICAL FRAMEWORK

• Planetary constants and boundary conditions configure atmospheric, physically forced, or hybrid simulations, with planetary scaling removing dependence on Earth-specific default scales.The coupled state includes surface temperature, CO2 frost, and regolith temperature alongside atmospheric variables.Source: §2.1 · pp. 2–3
• Mars operators represent CO2 and dust radiation, surface and regolith exchange, mixing, convection, and condensation, with phase change updating pressure and conserving atmosphere-plus-frost inventory.Per-step projection preserves the combined inventory while allowing seasonal exchange.Source: §2.1 · p. 3

2.2 DIFFERENTIATION AND NEURAL COMPONENTS

• Automatic differentiation follows repeated coupled time steps to support trajectory objectives, using forward mode for a few physical controls and reverse mode for neural weights.Reverse-mode training uses step rematerialization to reduce memory use by recomputing selected forward intermediates.Source: §2.2 · p. 3
• Neural components enter through a shared interface as bounded residuals or component replacements, with flux constraints that preserve the radiative energy budget for any network weights.The residual adapter leaves surface reservoirs under physical control; the replacement adapter imposes flux boundary conditions and computes heating from flux convergence.Source: §2.2 · p. 4, Figure 1 · p. 4

3.1 VERIFIED GRADIENTS THROUGH THE COUPLED MARS MODEL

• All 54 physical-sensitivity checks pass; at 44,400 s the largest discrepancy is 3.56 × 10−7, while nine β derivatives through five sols agree with finite differences within 3.99 × 10−6 relative discrepancy.Across the β rollout, pressure and frost derivatives are equal and opposite, with their sum at most 9.3 × 10−11 Pa.Source: §3.1 · pp. 4–5, Table 1 · p. 5, Figure 2 · p. 5

3.2 COMPUTATIONAL PERFORMANCE AND LONG INTEGRATIONS

• Under the same configuration (Δt = 450 s, float64), ten Mars years (6,686 sols; 1,319,003 steps) completed in 11.4 h on one GPU; all 670 saved states were finite, maximum relative CO2 inventory drift was 2.9 × 10−8, and year-ten pressure and temperature differed from year nine by 0.16 Pa and 0.20 K.Source: §3.2 · p. 6

3.3 SEASONAL COMPARISONS WITH MOLA TOPOGRAPHY

• Surface-pressure pattern correlations range from 0.975 to 0.989 across twelve season–reference comparisons, and the model reproduces terrain-driven pressure structure across four seasons and three reference products.Surface-temperature pattern correlations are 0.732–0.821; product sampling conventions differ, so these are model and reanalysis comparisons.Source: §3.3 · p. 6, Table 3 · p. 7, Figure 3 · p. 7

3.4 PHYSICS ABLATIONS: PROCESS SENSITIVITY

• Regolith conduction and boundary-layer mixing dominate the short-horizon process-sensitivity ranking, followed by dry convection and surface-exchange multipliers; radiative opacity multipliers produce smaller but resolved changes.All thirteen configurations remain finite; freely evolving trajectories reach chaotic saturation at long horizons, so RMS separations are interpreted at short horizons.Source: §3.4 · pp. 6–7, Figure 4 · p. 8

3.5 NEURAL COMPONENTS AS COUPLED EXPERIMENTS

• AEGIS lets neural modules enter a coupled step as bounded additive residuals or full component replacements, with training based on the resulting trajectory.Source: §3.5 · p. 7

3.5.1 LEARNING RADIATIVE FLUXES

• Continued local fitting gives the lowest 48-step temperature error, reducing interpolation RMSE from 0.620 to 0.416 K and higher-dust extrapolation RMSE from 1.799 to 0.979 K.The learned flux representation retains the discrete radiative budget, with maximum held-out local closure residual of 1.42 × 10−14 W m−2.Source: §3.5.1 · pp. 7–8, Table 4 · p. 8, Figure 5 · p. 8

3.5.2 RECOVERING A PHYSICAL PARAMETER THROUGH A TRAJECTORY

• After 120 updates through 24-step trajectories, initial multipliers of 0.5, 1.0, and 3.0 converge to 1.59950, 1.59901, and 1.59696, all within 0.20% of the prescribed 1.6 target.The controlled column experiment fixes illumination, dust, and pressure per column; derivative checks agree with finite differences to relative discrepancies below 3.41 × 10−10.Source: §3.5.2 · p. 9, Figure 6 · p. 9

4 FUTURE EXTENSIONS

• The next studies can use existing coupled operators and trajectory objectives for broader observational comparison, repeated neural experiments across seeds, and multi-year equilibration.These are described as natural next steps building on the present coarse-resolution physical simulations, coupled-heating seed, and structured neural component replacement.Source: §4 · p. 9
• Planetary, radiation, and reservoir interfaces allow altered albedo, imposed heating, or volatile inventories to be evaluated with spatial climate diagnostics.Differentiable objectives could connect intervention parameters to regional temperature, frost persistence, or atmospheric pressure.Source: §4 · p. 9
• Larger changes in atmospheric composition or mass require extending body thermodynamics, opacity data, condensable processes, and applicable dynamical assumptions together.Source: §4 · p. 9

5 CONCLUSION

• Integrations of up to ten Mars years remain stable, reproduce the seasonal CO2 cycle and terrain-driven surface-pressure structure, and conserve total CO2 inventory.A Mars year completes in under 1.5 hours on a single GPU.Source: §5 · p. 9
• AEGIS couples modular Mars physics to the Dinosaur core and exposes learned-component interfaces within a differentiated trajectory.The trajectory represents terrain, radiative forcing, surface and subsurface heat exchange, vertical transport, and seasonal CO2 exchange between atmosphere and frost.Source: §5 · pp. 9–10
• Gradients agree with finite differences through coupled trajectories, while gradient-based calibration lowers held-out reanalysis temperature error in every test window.Neural heating and radiation interfaces also support training and comparison of learned components.Source: §5 · pp. 9–10

A MARS PHYSICS OPERATORS

• MOLA elevation is regridded to the transform grid and converted into spectral orography, while prescribed dust fields enter through seasonal or per-window adapters.Keeping these data separate from numerical operators makes boundary-condition experiments straightforward.Source: A MARS PHYSICS OPERATORS · p. 12
• Radiation combines CO2 absorption and dust optical properties in column flux calculations, with atmospheric heating derived from flux convergence.The main configuration uses Ames-derived 12-band correlated-k tables, temperature and log-pressure interpolation, and two-stream transfer; common interface fluxes make column energy exchanges telescope to the top-of-atmosphere balance, including for neural radiation.Source: A MARS PHYSICS OPERATORS · p. 12
• Surface temperature responds to radiative, sensible, conductive, and latent exchange, while vertical diffusion mixes momentum, heat, and tracers.A 12-layer regolith conducts heat beneath the surface and supplies thermal memory across daily and seasonal forcing.Source: A MARS PHYSICS OPERATORS · p. 12
• CO2 condensation and sublimation exchange mass between atmosphere and frost, and a post-step projection repairs negative frost and rescales pressure to preserve their total inventory.The frost temperature follows a pressure-dependent saturation relation; an energy-limited option ties exchange to the surface energy budget, while seasonal atmospheric pressure can still change as mass shifts to the surface reservoir.Source: A MARS PHYSICS OPERATORS · pp. 12–13

B CALIBRATION AND NEURAL-TRAINING PROTOCOL

• Twelve prespecified reanalysis windows span Mars years 24–35, with four each for training, validation, and testing and each split sampling four seasonal quarters.Initial conditions use reference temperature, winds, and pressure; surface and frost use start-time fields, while soil uses preceding surface history.Source: B CALIBRATION AND NEURAL-TRAINING… · p. 13
• The training loss averages squared errors in temperature, zonal wind, and meridional wind after scaling each by its training-target standard deviation, using horizontal-area, equal sigma-layer, and equal-window weights.Source: B CALIBRATION AND NEURAL-TRAINING… · p. 13
• Both fitting experiments perform 50 Adam updates at learning rate 10^-3 with gradient-norm clipping at one, and validation selects the checkpoint.Physical calibration adjusts bounded CO2 longwave opacity, dust longwave opacity, and surface exchange multipliers; neural fitting retains all three physical multipliers at one.Source: B CALIBRATION AND NEURAL-TRAINING… · p. 13

C ADDITIONAL SEASONAL REFERENCE COMPARISONS

• Surface pressure reproduces the shared terrain-driven structure, with low-lying basins as pressure maxima and elevated terrain as minima.Surface temperature shows daytime-weighted seasonal heating and a cold winter pole.Source: C ADDITIONAL SEASONAL REFERENCE… · p. 13
• Near-surface wind is the most reference-dependent field because products differ in reported level and averaging, complicating direct comparison with the model’s organized jets.The wind-speed spread remains the largest between reference products across evaluated seasons.Source: C ADDITIONAL SEASONAL REFERENCE… · p. 13
• Surface CO2 frost concentrates near the seasonal winter cap and serves as a sensitive diagnostic of atmosphere–surface mass exchange.The winter-cap frost pattern remains consistent across evaluated seasons.Source: C ADDITIONAL SEASONAL REFERENCE… · p. 13
• Across all three evaluated seasons, terrain-driven surface pressure, seasonal temperature, and winter-cap CO2 frost patterns remain consistent, while near-surface wind shows the largest reference-product spread.The seasonal maps compare AEGIS with NASA Ames, MCD 6.1, and ARCO-MACDA.Source: C ADDITIONAL SEASONAL REFERENCE… · p. 13, Figure 7 · p. 14, Figure 8 · p. 14