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
The rapid advancement of AI necessitates a deeper theoretical understanding of its generalisation properties, particularly as it integrates with established scientific domains like physics.
Improved theoretical understanding of Physics-Informed Machine Learning can lead to more robust, reliable, and interpretable AI models crucial for scientific discovery and engineering applications.
This work introduces a new theoretical framework (PAC-Bayesian) to rigorously analyze the generalisation of PIML, moving beyond empirical observations to foundational principles.
- · AI researchers
- · Scientific computing
- · Engineering design
- · Theoretical machine learning
- · Ad-hoc PIML model development
- · Empirical-only AI development
The new PAC-Bayesian framework provides a formal mathematical tool to analyze and improve PIML models.
Better theoretical guarantees for PIML could accelerate its adoption in safety-critical applications where reliability and interpretability are paramount.
A deeper understanding of integrated AI-science models could lead to new forms of scientific discovery and autonomous research agents.
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