# Learning Robust Satellite Attitude Dynamics with Physics-Informed Normalising Flow

arXiv: https://arxiv.org/abs/2508.07841 · HTML: https://mlsanity.com/paper/2508.07841/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 36 references that are in the map.
- First posted on arXiv 11 Aug 2025.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [A Structured Self-attentive Sentence Embedding](https://mlsanity.com/paper/1703.03130/) (2017)
- [Long Short-Term Memory-Networks for Machine Reading](https://mlsanity.com/paper/1601.06733/) (2016)
- [Lagrangian Duality for Constrained Deep Learning](https://mlsanity.com/paper/2001.09394/) (2020)
- [Physics-Informed Neural Nets for Control of Dynamical Systems](https://mlsanity.com/paper/2104.02556/) (2021)
- [Large Scale Model Predictive Control with Neural Networks and Primal Active Sets](https://mlsanity.com/paper/1910.10835/) (2019)
- [Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators](https://mlsanity.com/paper/2109.10793/) (2021)
- [Transformer-based Model Predictive Control: Trajectory Optimization via Sequence Modeling](https://mlsanity.com/paper/2410.23916/) (2024)
- [Neural representation of a time optimal, constant acceleration rendezvous](https://mlsanity.com/paper/2203.15490/) (2022)
- [Physics-Informed Neural Networks for Satellite State Estimation](https://mlsanity.com/paper/2403.19736/) (2024)
- [Robust Power System State Estimation using Physics-Informed Neural Networks](https://mlsanity.com/paper/2507.05874/) (2025)
- [VNN: Verification-Friendly Neural Networks with Hard Robustness Guarantees](https://mlsanity.com/paper/2312.09748/) (2023)

## Abstract (arXiv)

Attitude control is a fundamental aspect of spacecraft operations. Model Predictive Control (MPC) has emerged as a powerful strategy for these tasks, relying on accurate models of the system dynamics to optimize control actions over a prediction horizon. In scenarios where physics models are incomplete, difficult to derive, or computationally expensive, machine learning offers a flexible alternative by learning the system behavior directly from data. However, purely data-driven models often struggle with generalization and stability, especially when applied to inputs outside their training domain. To address these limitations, we investigate the benefits of incorporating Physics-Informed Neural Networks (PINNs) into the learning of spacecraft attitude dynamics, comparing their performance with that of purely data-driven approaches. Using a Real-valued Non-Volume Preserving (Real NVP) neural network architecture with a self-attention mechanism, we trained several models on simulated data generated with the Basilisk simulator. Two training strategies were considered: a purely data-driven baseline and a physics-informed variant to improve robustness and stability. Our results demonstrate that the inclusion of physics-based information significantly enhances the performance in terms of the mean relative error with the best architectures found by 27.08%. These advantages are particularly evident when the learned models are integrated into an MPC framework, where PINN-based models consistently outperform their purely data-driven counterparts in terms of control accuracy and robustness, and achieve improved settling times when compared to traditional MPC approaches, yielding improvements of up to 62%, when subject to observation noise and RWs friction.