A PAC-Bayesian View of Generalisation for Physics-Informed Machine Learning
This work develops a PAC-Bayesian framework for Physics-Informed Machine Learning (PIML) to provide strong generalization guarantees, especially for regression with unbounded losses. By treating data fidelity and PDE residuals as a single risk, the authors show that model complexity scales with input-gradient norms of the losses. This links physical regularity directly to better generalization bounds.