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Investigating Guiding Information for Adaptive Collocation Point Sampling in PINNs
April 19, 2024, 4:41 a.m. | Jose Florido, He Wang, Amirul Khan, Peter K. Jimack
cs.LG updates on arXiv.org arxiv.org
Abstract: Physics-informed neural networks (PINNs) provide a means of obtaining approximate solutions of partial differential equations and systems through the minimisation of an objective function which includes the evaluation of a residual function at a set of collocation points within the domain. The quality of a PINNs solution depends upon numerous parameters, including the number and distribution of these collocation points. In this paper we consider a number of strategies for selecting these points and investigate …
abstract arxiv cs.lg differential domain evaluation function information networks neural networks physics physics-informed quality residual sampling set solutions systems through type
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