AI RESEARCH
A PAC-Bayesian View of Generalisation for Physics-Informed Machine Learning
arXiv CS.LG
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ArXi:2605.26341v1 Announce Type: new 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.