A metalearning approach for Physics-Informed Neural Networks (PINNs): Application to parameterized PDEs

Michael Penwarden, Shandian Zhe, Akil Narayan, Robert M. Kirby

Abstract: Highlights•Metalearning approach for PINNs with application to parameterized PDEs using weighted interpolation.•Exploiting the assumed smoothness of neural network weights for parameterized PDEs over the parametric domain.•Theoretical and implementation considerations to guide tuning and set up.•Accelerated optimization on four canonical and two higher-dimensional forward problems with a survey of predictive methods.