Convergence rates for ansatz‐free data‐driven inference in physically constrained problems

We study a Data-Driven approach to inference in physical systems measure-theoretic framework. The under consideration are characterized by two measures defined over the phase space: (i) A likelihood measure expressing that state of system be admissible, sense satisfying all governing laws; (ii) material local observed laboratory. assume deterministic loading, which means first is supported on linear subspace. additionally second only known approximately through sequence empirical (discrete) measures. develop method for quantitative analysis convergence based flat metric and obtain error bounds both annealing discretization or sampling procedure, leading determination appropriate rates. Finally, we provide an example illustrating application theory transportation networks.