# Faster Thermal Profiling of a Lunar Rover with Machine Learning Adapted Finite Difference Model

arXiv: https://arxiv.org/abs/2605.27651 · HTML: https://mlsanity.com/paper/2605.27651/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 46 references that are in the map.
- First posted on arXiv 26 May 2026.

## Builds on (most cited first, 7 of 7)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Improved Training of Physics-Informed Neural Networks with Model Ensembles](https://mlsanity.com/paper/2204.05108/) (2022)
- [Known Operator Learning and Hybrid Machine Learning in Medical Imaging -- A Review of the Past, the Present, and the Future](https://mlsanity.com/paper/2108.04543/) (2021)
- [Physics-driven Deep Learning for PET/MRI](https://mlsanity.com/paper/2206.06788/) (2022)
- [Physics-Informed Machine Learning Towards A Real-Time Spacecraft Thermal Simulator](https://mlsanity.com/paper/2407.06099/) (2024)
- [Exploring Efficient Quantification of Modeling Uncertainties with Differentiable Physics-Informed Machine Learning Architectures](https://mlsanity.com/paper/2506.18247/) (2025)

## Abstract (arXiv)

Autonomous space systems operating in extreme thermal environments require accurate and efficient thermal modeling to support both pre-mission system design and onboard autonomy. For lunar rovers, large temperature gradients, radiative heat transfer, and variable surface conditions make reliable thermal prediction especially challenging. High-fidelity physics-based simulations provide accurate results but are computationally expensive, while simplified models and lookup-table approach often lack sufficient accuracy. Physics-informed machine learning (PIML) offers a promising alternative by combining data-driven models with embedded physical knowledge. This paper presents a PIML framework for thermal analysis of a simplified lunar rover with internal heat sources, where machine learning enables environment-adaptive coarse meshing. The proposed architecture integrates a transfer neural network (TNN) that adaptively determines 3D finite-difference nodalization based on thermal loads and initial conditions, enabling more accurate coarse-mesh calculations. A differentiable finite-difference thermal simulator is embedded within the framework to enforce physical consistency and support efficient training, while an upscaling layer reconstructs high-resolution temperature fields from the coarse-grid solution. The proposed PIML approach is evaluated against high-fidelity fine-mesh simulations, low-fidelity fixed coarse-mesh models, and a purely data-driven artificial neural network (ANN). Results show that the PIML framework improves prediction accuracy by 50% and 39% relative to the coarse-mesh physics model and ANN model, respectively, while maintaining physically consistent thermal distributions. Computationally, the framework is also 3x faster than high-fidelity simulations, demonstrating an effective balance between accuracy and efficiency for thermal modeling of lunar rover systems.