# PILA: Physics-Informed Low Rank Augmentation for Interpretable Earth Observation

arXiv: https://arxiv.org/abs/2405.18953 · HTML: https://mlsanity.com/paper/2405.18953/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 51 references that are in the map.
- First posted on arXiv 29 May 2024.

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

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Learning to Estimate 3D Human Pose and Shape from a Single Color Image](https://mlsanity.com/paper/1805.04092/) (2018)
- [A Survey on Self-supervised Learning: Algorithms, Applications, and Future Trends](https://mlsanity.com/paper/2301.05712/) (2023)
- [Differentiable Rendering: A Survey](https://mlsanity.com/paper/2006.12057/) (2020)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling](https://mlsanity.com/paper/2102.13156/) (2021)
- [Learning View Priors for Single-view 3D Reconstruction](https://mlsanity.com/paper/1811.10719/) (2018)
- [Robust Hybrid Learning With Expert Augmentation](https://mlsanity.com/paper/2202.03881/) (2022)
- [Deep Grey-Box Modeling With Adaptive Data-Driven Models Toward Trustworthy Estimation of Theory-Driven Models](https://mlsanity.com/paper/2210.13103/) (2022)
- [Denoising of Geodetic Time Series Using Spatiotemporal Graph Neural Networks: Application to Slow Slip Event Extraction](https://mlsanity.com/paper/2405.03320/) (2024)

## Built on by (most cited first, 1 of 1)

- [DFF: Decision-Focused Fine-tuning for Smarter Predict-then-Optimize with Limited Data](https://mlsanity.com/paper/2501.01874/) (2025)

## Abstract (arXiv)

Physically meaningful representations are essential for Earth Observation (EO), yet existing physical models are often simplified and incomplete. This leads to discrepancies between simulation and observations that hinder reliable forward model inversion. Common approaches to EO inversion either ignored this incompleteness or relied on case-specific preprocessing. More recent methods use physics-informed autoencoders but depend on auxiliary variables that are difficult to interpret and multiple regularizers that are difficult to balance. We propose Physics-Informed Low-Rank Augmentation (PILA), a framework that augments incomplete physical models using a learnable low-rank residual to improve flexibility, while remaining close to the governing physics. We evaluate PILA on two EO inverse problems involving diverse physical processes: forest radiative transfer inversion from optical remote sensing; and volcanic deformation inversion from Global Navigation Satellite Systems (GNSS) displacement data. Across different domains, PILA yields more accurate and interpretable physical variables. For forest spectral inversion, it improves the separation of tree species and, compared to ground measurements, reduces prediction errors by 40-71% relative to the state-of-the-art. For volcanic deformation, PILA's recovery of variables captures a major inflation event at the Akutan volcano in 2008, and estimates source depth, volume change, and displacement patterns that are consistent with prior studies that however required substantial additional preprocessing. Finally, we analyse the effects of model rank, observability, and physical priors, and suggest that PILA may offer an effective general pathway for inverting incomplete physical models even beyond the domain of Earth Observation. The code is available at https://github.com/yihshe/PILA.git.