Neural oscillators for generalizing parametric PDEs

Taniya Kapoor, Abhishek Chandra, Daniel Tartakovsky, Hongrui Wang, Alfredo Núñez, Rolf Dollevoet

Keywords: Parametric PDEs, Neural Oscillator, Generalization, Extrapolation

Abstract: Parametric partial differential equations (PDEs) are ubiquitous in various scientific and engineering fields, manifesting the behavior of systems under varying parameters. Predicting solutions over a parametric space is desirable but prohibitively costly and challenging. In addition, recent neural PDE solvers are usually limited to interpolation scenarios, where solutions are predicted for inputs within the support of the training set. This work proposes to utilize neural oscillators to extend predictions for parameters beyond the trained regime, effectively extrapolating the parametric space. The proposed methodology is validated on three parametric PDEs: linear advection, viscous burgers, and nonlinear heat. The results underscore the promising potential of neural oscillators in extrapolation scenarios for both linear and nonlinear parametric PDEs.

Submission Number: 22