Affine transformations accelerate the training of physics-informed neural networks of a one-dimensional consolidation problem.

ABSTRACT: Physics-informed neural networks (PINNs) leverage data and knowledge about a problem. They provide a nonnumerical pathway to solving partial differential equations by expressing the field solution as an artificial neural network. This approach has been applied successfully to various types of differential equations. A major area of research on PINNs is the application to coupled partial differential equations in particular, and a general breakthrough is still lacking. In coupled equations, the optimization operates in a critical conflict between boundary conditions and the underlying equations, which often requires either many iterations or complex schemes to avoid trivial solutions and to achieve convergence. We provide empirical evidence for the mitigation of bad initial conditioning in

SUBMITTER: Mandl L 

PROVIDER: S-EPMC10511457 | biostudies-literature | 2023 Sep

REPOSITORIES: biostudies-literature