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Physics-Informed Multi-Task Surrogate Model for the Martian Nightside Thermosphere
Sergey Nikiforov
TL;DR
Sparse nightside observations make thermospheric reconstruction difficult and can cause purely data-driven models to produce density inversions. The paper develops a multi-task physics-informed neural network with a weak vertical monotonicity prior, finding that λ = 0.50 gives the best reported balance of predictive performance and vertical consistency while providing a fast surrogate. Its scope is limited to nightside neutral densities from 140–350 km and does not impose full thermospheric self-consistency.
Problem
Sparse nightside sampling limits reconstruction and can cause purely data-driven models to produce non-physical density inversions in poorly sampled altitude regimes.
Method
The paper trains a multi-task neural network on MAVEN observations with a composite data-and-physics loss that penalizes positive vertical log-density gradients.
Results
At λ = 0.50, the model achieves the lowest macro-averaged RMSE and MAE, the highest R2, and substantially reduced inversion rates for O and N2.
Takeaways & Limitations
MT-PINN provides a fast observational surrogate for nightside reconstruction and profile-by-profile comparison with physics-based models without repeated GCM runs.
Takeaways & Limitations
The model is restricted to nightside neutral densities from 140–350 km and does not enforce hydrostatic balance, energy conservation, or self-consistent momentum coupling.
Abstract
from arXiv · showhide
Modeling the Martian nightside thermosphere remains challenging due to sparse in situ sampling and strong coupling among transport, magnetic, and seasonal processes. Purely data-driven models can produce non-physical artifacts, such as density inversions, in poorly sampled altitude regimes. We present a multi-task physics-informed neural network that simultaneously predicts the base-10 logarithmic densities of four neutral species (O, CO$_2$, N$_2$, and Ar) using more than a decade of MAVEN/NGIMS observations (MY 32-38, 2014-2025). A shared backbone learns a common representation of the nightside thermospheric state and branches into species-specific output heads. A weak monotonicity prior is incorporated via automatic differentiation by penalizing positive vertical gradients in logarithmic density. Experiments using an orbit-disjoint train/validation/test split show that physics-informed regularization substantially reduces non-physical inversions while preserving predictive skill and slightly improving it in the best-performing configuration, as measured by RMSE, MAE, and $R^2$. The resulting model provides a computationally efficient surrogate for nightside thermospheric reconstruction with improved vertical consistency.
1 Introduction
The study introduces MT-PINN to address sparse nightside MAVEN coverage and reduce non-physical density inversions while complementing existing thermospheric models. Its fast surrogate supports trajectory reconstruction, sensitivity studies, and direct model–data comparison.
- 1 Introduction: GCMs capture large-scale dynamics but are computationally intensive, while Mars-GRAM offers efficient average profiles but struggles with localized short-lived space-weather variability.These trade-offs motivate an observationally constrained surrogate for rapid evaluation.
- 1 Introduction: Sparse nightside sampling can make purely data-driven models extrapolate poorly, producing non-physical density inversions.The proposed MT-PINN adds a weak monotonicity constraint on the vertical density gradient.
- 1 Introduction: MT-PINN is designed as an observationally constrained complement where global simulations and empirical climatologies can deviate from in situ measurements.It is intended for sparsely sampled nightside conditions rather than as a replacement for physics-based GCMs.
- 1 Introduction: The surrogate enables profile reconstruction along arbitrary trajectories, seasonal and space-weather sensitivity studies, and model–data comparison without repeated GCM runs.Its differentiable output supports profile-by-profile comparison with GCM results under matched environmental conditions.
2 Data and Parameter Formulation
The study combines MAVEN and complementary geophysical observations spanning MY 32–38 with spatial, temporal, seasonal, and external energy drivers. Nightside conditions are identified using solar zenith angle and supplemented with modeled upstream solar-wind inputs.
- 2 Data and Parameter Formulation: The dataset spans late MY 32 to early MY 38, covering a complete solar cycle and the MY 34 global dust storm.It combines NGIMS neutral densities, MAG magnetic fields, SWEA and SEP particle fluxes, SPICE geometry, and reconstructed dust climatology.
- 2 Data and Parameter Formulation: Inputs include altitude, latitude, longitude, solar zenith angle, local solar time, seasonal parameter Ls, and external energy-related drivers.The formulation accounts for particle precipitation and day-to-night circulation when direct local nightside solar forcing is absent.
- 2 Data and Parameter Formulation: Upstream solar-wind density, velocity, temperature, and dynamic pressure are estimated with an external Gaussian-process model when direct local measurements are unavailable.Nightside conditions are defined by solar zenith angle exceeding 90°.
3 Multi-Task Physics-Informed Neural Network
The MT-PINN jointly predicts log-densities for four species through a shared representation and species-specific heads, while combining measurement fidelity with a weak vertical monotonicity prior. Orbit-disjoint evaluation is designed to test generalization without leakage across correlated MAVEN trajectories.
- 3.1 Neural Network Architecture: The model jointly predicts base-10 logarithmic densities for O, CO2, N2, and Ar using a shared backbone with species-specific output heads.The shared representation captures common responses to altitude, solar zenith angle, season, magnetic structure, and particle precipitation.
- 3.1 Neural Network Architecture: Log-density targets improve numerical stability and represent the approximately exponential altitude dependence across species whose densities span several orders of magnitude.The target is yi = log10(ρi), and regression is performed in log-density space.
- 3.2 Loss Function: The total objective combines uncertainty-weighted agreement with valid measurements and a physics-informed structural penalty for positive vertical log-density gradients.The validity mask excludes invalid NGIMS measurements, while per-sample normalization prevents samples with multiple valid species from dominating the batch loss.
- 3.2 Loss Function: The monotonicity regularizer selectively penalizes positive vertical gradients while leaving negative gradients unconstrained, allowing localized deviations from transient heating or measurement noise.Gradients are obtained by automatic differentiation with respect to normalized altitude and rescaled using the altitude standard deviation.
- 3.3 Data Partitioning and Evaluation: Orbit-disjoint splitting assigns complete MAVEN orbits to training, validation, or test sets to avoid leakage from strongly correlated measurements along individual trajectories.Approximately 80% of data are used for training, with the remainder divided evenly between validation and test subsets.
4 Results
On held-out test data, MT-PINN is evaluated for unseen-orbit generalization, vertical consistency, and calibration of the physics-weight trade-off. The λ = 0.50 configuration achieves the strongest combined predictive and structural performance while retaining differentiable profiles for gradient-based diagnostics.
- 4 Results: The held-out evaluation measures generalization to unseen orbital passes and consistency of predicted vertical structure.Metrics are reported on the held-out test set unless stated otherwise, with inversion rates evaluated across all held-out inputs.
- 4.1 Calibration of Physical Regularization: The physics weight λ is treated as a calibration parameter balancing statistical fidelity against physical structure rather than as a fixed hyperparameter.The study explores a range of λ values to characterize this trade-off.
- 4.1 Calibration of Physical Regularization: λ = 0.50 achieves the lowest macro-averaged RMSE and MAE and highest R2, while reducing inversion rates for O and N2 and maintaining a very low rate for Ar.Increasing λ to 0.75 or 1.00 worsens predictive performance and increases inversion rates relative to λ = 0.50.
- 4.2 Differentiable Profile Diagnostics: MT-PINN produces continuous, differentiable vertical profiles that support diagnostics of ∂ŷ_i/∂z and integration with physics-based workflows.The selected λ therefore affects both statistical fit and the reliability of gradient-based interpretation in sparsely sampled regimes.
- 4.1 Calibration of Physical Regularization: Figure 1 compares macro-averaged RMSE with mean inversion rate across O, CO2, N2, and Ar for tested physics weights λ.Marker color encodes λ, and the star identifies λ = 0.50.
- 4.3 Reference Benchmark: An XGBoost reference achieves RMSE ≈0.207 and R2 ≈0.911 for O, but its reduced features and different split make this contextual rather than strictly controlled benchmarking.Tree ensembles do not naturally provide smooth differentiable vertical structure for gradient-based diagnostics.
5 Discussion and Outlook
The model offers a fast, observationally constrained surrogate with improved vertical consistency, but its scope and physical guarantees remain limited. Shared multi-species representations and soft regularization also leave unresolved questions about bias propagation and broader model intercomparison.
- Limitations and Scope: The model is limited to nightside neutral densities from 140–350 km and is not a globally self-consistent thermospheric model.Its constraint does not enforce hydrostatic balance, energy conservation, or self-consistent momentum coupling.
- Limitations and Scope: Shared latent representations may propagate systematic biases between species, requiring further controlled investigation of their specific contribution to multi-species prediction.This limitation concerns the multi-task representation rather than the monotonicity regularization itself.
- Computational Efficiency and Model Intercomparison: The surrogate supports rapid profile reconstruction, sensitivity studies, and model–data comparison without repeated full circulation-model runs.Once trained, the network enables rapid pointwise evaluation compared with running a full three-dimensional circulation model.
- Computational Efficiency and Model Intercomparison: Systematic quantitative intercomparison with classical thermospheric models remains outside the present study’s scope, with broader comparisons and model extensions left for future work.Future work includes intercomparison across seasons, magnetic configurations, and extreme solar events, plus hydrostatic constraints and ionospheric constituents.
- Implications: A weak structural prior reduces non-physical vertical gradients without reducing predictive skill, while retaining accurate multi-species density predictions.The shared representation is combined with weak physical regularization rather than a full dynamical solver.