Adversarial Sampling for Solving Differential Equations with Neural NetworksDownload PDF

27 Sept 2021, 22:32 (modified: 20 Nov 2021, 02:33)DLDE Workshop -- NeurIPS 2021 PosterReaders: Everyone
Keywords: Adversarial methods, Differential Equations, Sampling
Abstract: Neural network-based methods for solving differential equations have been gaining traction. They work by improving the differential equation residuals of a neural network on a sample of points in each iteration. However, most of them employ standard sampling schemes like uniform or perturbing equally spaced points. We present a novel sampling scheme which samples points adversarially to maximize the loss of the current solution estimate. A sampler architecture is described along with the loss terms used for training. Finally, we demonstrate that this scheme outperforms pre-existing schemes by comparing both on a number of problems.
Publication Status: This work is unpublished.
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