Error estimates for physics-informed neural networks approximating the Navier–Stokes equations
Tim De Ryck, Ameya D. Jagtap, Siddhartha Kumar Mishra
Abstract
Abstract We prove rigorous bounds on the errors resulting from the approximation of the incompressible Navier–Stokes equations with (extended) physics-informed neural networks. We show that the underlying partial differential equation residual can be made arbitrarily small for tanh neural networks with two hidden layers. Moreover, the total error can be estimated in terms of the training error, network size and number of quadrature points. The theory is illustrated with numerical experiments.
Topics & Concepts
Artificial neural networkCompressibilityQuadrature (astronomy)ResidualApplied mathematicsComputer scienceMathematicsAlgorithmArtificial intelligencePhysicsThermodynamicsOpticsModel Reduction and Neural NetworksControl and Stability of Dynamical SystemsMachine Learning in Materials Science