arXiv:2506.15199v3 Announce Type: replace Abstract: While there are many applications of ML to scientific problems that look promising, visuals can be deceiving. Using numerical analysis techniques, we rigorously quantify the accuracy, convergence rates, and generalization bounds of certain ML models applied to linear differential equations for parameter discovery or solution finding. Beyond the quantity and discretization of data, we identify that the function space of the data is critical to the generalization of the model. A similar lack of generalization is empirically demonstrated for com
The proliferation of ML applications in scientific problems necessitates a rigorous quantification of their accuracy and limitations to ensure reliable deployment.
Understanding the interpretability and generalization bounds of ML models for scientific problems is crucial for their responsible and effective integration, particularly in high-stakes fields.
This research provides a more rigorous framework for evaluating the reliability and applicability of ML in scientific discovery, shifting the focus beyond promising visuals to quantifiable performance.
- · AI model developers for scientific applications
- · Scientific research institutions
- · Fields relying on differential equations
- · Developers of unquantified 'black-box' ML models
Increased scrutiny and demand for explainable AI in scientific domains.
Development of new ML architectures specifically designed for better interpretability and generalization in physics applications.
Accelerated pace of scientific discovery in areas where ML can be rigorously validated and trusted.
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Read at arXiv cs.LG