Physics-informed learning under mixing: How physical knowledge speeds up learning

2025/09/29 by Anna Scampicchio, Scampicchio, Anna, Leonardo F. Toso +7 · 1 citation
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Mechanical and Optical Resonators #Neural Networks and Applications #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2509.24801

openalex publication_date 2025/09/29 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

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 any sample-size deflation due to data dependence.

Cited by

• Complexity Dependent Error Rates for Physics-informed Statistical Learning via the Small-ball Method

Related

• Physics-informed machine learning as a kernel method
• Complexity Dependent Error Rates for Physics-informed Statistical Learning via the Small-ball Method
• Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications
• Physics-Augmented Learning: A New Paradigm Beyond Physics-Informed Learning
• Deep Learning with Physics Priors as Generalized Regularizers