Analyzing the Impact of Adaptive Weighting in Self-Adaptive Physics-Informed Neural Networks for Solving PDEs
J.P. Mańkowski (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Jing Sun (TU Delft - Pattern Recognition and Bioinformatics)
A. Heinlein (TU Delft - Numerical Analysis)
Tiexing Wang (Shearwater GeoServices)
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Abstract
Self-Adaptive Physics-Informed Neural Networks
(SA-PINNs) are a variation of traditional Physics-Informed Neural Networks (PINNs) designed to
solve the challenges of solving ”stiff” partial differential equations (PDEs). By using adaptive weighting, SA-PINNs are able to focus their attention on areas of the domain with higher errors, therefore improving accuracy. This work investigates the
roles of individual loss components, namely residuals, boundary conditions, and initial conditions, in the performance of SA-PINNs.