Minimum-Action Learning achieves a 10,000x reduction in noise variance for symbolic physical law identification from observational data.
arXiv · March 19, 2026 · 2603.16951
The Takeaway
It enables the recovery of exact physical laws (like Kepler's gravity) from extremely noisy datasets (SNR ~0.02) that were previously considered intractable. The framework's use of energy-conservation as a selection criterion allows it to discriminate true physics from 'near-miss' mathematical confounders.
From the abstract
Identifying physical laws from noisy observational data is a central challenge in scientific machine learning. We present Minimum-Action Learning (MAL), a framework that selects symbolic force laws from a pre-specified basis library by minimizing a Triple-Action functional combining trajectory reconstruction, architectural sparsity, and energy-conservation enforcement. A wide-stencil acceleration-matching technique reduces noise variance by 10,000x, transforming an intractable problem (SNR ~0.02