Physics-Informed Learning Under Mixing: How Physical Knowledge Speeds up Learning
Abstract
A major challenge in physics-informed machine learning is to understand how the incorporation of prior domain knowledge affects learning rates when data are dependent. Focusing on empirical risk minimization with physics-informed regularization, we derive complexity-dependent bounds on the excess risk in probability and in expectation. We prove that, when the physical prior information is aligned, the learning rate improves from the (slow) Sobolev minimax rate to the (fast) optimal i.i.d. one without sample-size deflation due to data dependence.
Cite
Text
Scampicchio et al. "Physics-Informed Learning Under Mixing: How Physical Knowledge Speeds up Learning." International Conference on Learning Representations, 2026.Markdown
[Scampicchio et al. "Physics-Informed Learning Under Mixing: How Physical Knowledge Speeds up Learning." International Conference on Learning Representations, 2026.](https://mlanthology.org/iclr/2026/scampicchio2026iclr-physicsinformed/)BibTeX
@inproceedings{scampicchio2026iclr-physicsinformed,
title = {{Physics-Informed Learning Under Mixing: How Physical Knowledge Speeds up Learning}},
author = {Scampicchio, Anna and Toso, Leonardo Felipe and Rickenbach, Rahel and Anderson, James and Zeilinger, Melanie},
booktitle = {International Conference on Learning Representations},
year = {2026},
url = {https://mlanthology.org/iclr/2026/scampicchio2026iclr-physicsinformed/}
}