Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs

Abstract Physics-informed neural networks approximate solutions of PDEs by minimizing pointwise residuals. We derive rigorous bounds on the error, incurred PINNs in approximating a large class linear parabolic PDEs, namely Kolmogorov equations that include heat equation and Black-Scholes option pricing, as examples. construct networks, whose PINN residual (generalization error) can be made small desired. also prove total L 2 -error bounded generalization which turn is terms training provided sufficient number randomly chosen (collocation) points used. Moreover, we size samples only grow polynomially with underlying dimension, enabling to overcome curse dimensionality this context. These results enable us provide comprehensive error analysis for PDEs.