Print Email Facebook Twitter PINNs for parametrized problems Title PINNs for parametrized problems Author van Ruiten, Frank (TU Delft Electrical Engineering, Mathematics and Computer Science) Contributor Möller, M. (mentor) Toshniwal, D. (graduation committee) Degree granting institution Delft University of Technology Programme Applied Mathematics Date 2022-12-19 Abstract Physics Informed Neural Networks are a relatively new subject of study in the area of numerical mathematics. In this thesis, we take a look at part of the work that has been done in this area up until now, with the ultimate goal to develop a new type of PINN that improves upon the old concept. We introduce the concept of parameterized PINNs, which allow a single trained network to solve multiple partial differential equations for multiple boundary conditions and geometries by parametrizing these variables as an input for the network. Two methods are tested: one using global basis functions, and one using B-splines. The proposed methods are tested for Laplace’s equation and Poisson’s equation in multiple dimensions, most of which show that these methods are viable alternatives for the current style of collocation-based PINNs. Subject PINNsNeural Networks To reference this document use: http://resolver.tudelft.nl/uuid:6c1da590-3ea8-43d5-aba4-90da1c941c48 Part of collection Student theses Document type master thesis Rights © 2022 Frank van Ruiten Files PDF PINNs_for_parametrized_problems.pdf 4.5 MB Close viewer /islandora/object/uuid:6c1da590-3ea8-43d5-aba4-90da1c941c48/datastream/OBJ/view