A PAC-Bayesian View of Generalisation for Physics-Informed Machine Learning

arXiv:2605.26341v1 Announce Type: new Abstract: Physics-informed machine learning (PIML) integrates mechanistic knowledge, typically in the form of partial differential equations (PDE), into data-driven models. Despite strong empirical performance, its statistical generalisation properties remain poorly understood, particularly in the regression setting with unbounded losses. Existing analyses rely on approximation or stability arguments and do not fully capture how physical structure influences generalisation from finite data. In this work, we develop a PAC-Bayesian framework for PIML that pr

Source: arXiv cs.LG — read the full report at the original publisher.

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