Interpretability and Generalization Bounds for Learning Spatial Physics

ArXi:2506.15199v3 Announce Type: replace 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.