PINNs for parametrized problems
F.N.P. van Ruiten (TU Delft - Electrical Engineering, Mathematics and Computer Science)
M. Möller – Mentor (TU Delft - Numerical Analysis)
D. Toshniwal – Graduation committee member (TU Delft - Numerical Analysis)
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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.