To this end, we use concepts from constructive solid geometry (R-functions) and generalized barycentric coordinates (mean value potential fields) to construct an approximate distance function to the boundary of a domain. We introduce geometry-aware trial functions in artifical neural networks to improve the training in deep learning to solve partial differential equations. This issue is also pertinent in the development of physics informed neural networks (PINN) for the meshfree solution of partial differential equations. The challenges in satisfying Dirichlet boundary conditions in meshfree and particle methods are well-known. In this presentation, I will introduce a new approach based on distance fields to exactly impose boundary conditions in physics-informed deep neural networks. Talk at IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Lisbon Meshfree analysis on complex geometries using physics-informed deep neural networksįriday, 14th January 2022, 09:00 PST, 10:00 MT, 11:00 CST, 12:00 EST, 17:00 GMT
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