Publikation
Constructing Neural Forms for Hard-Constraint PINNs with Complex Dirichlet Boundaries
Frank Ehebrecht; Toni Scharle; Martin Atzmueller
In: Rosa Meo; Fabrizio Silvestri (Hrsg.). Machine Learning and Principles and Practice of Knowledge Discovery in Databases. European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD-WS), Cham, Pages 501-510, ISBN 978-3-031-74633-8, Springer Nature Switzerland, 2025.
Zusammenfassung
This paper presents an approach to construct neural forms for hard constraint PINNs with complex Dirichlet boundaries. We show how to construct hard-constraints (1) when the geometry can be represented by a set of implicit functions, or (2) otherwise by solving Poisson's equation with a soft-constraint PINN. For these methods, it is neither necessary to check if points are within the geometry, nor to calculate some distance measure to its boundary. Our evaluation demonstrates our approach by solving the p-Laplace equation on a set of complex geometries, each exemplifying a certain aspect of our proposed approach, showing its impact by comparing our results to an FEM ground truth.