Scholarlink

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.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Constructing Neural Forms for Hard-Constraint PINNs with Complex Dirichlet Boundaries

  • 会议论文

  • 发表日期：

    2025年

查看全文
  • Frank Ehebrecht,
  • Toni Scharle,
  • Martin Atzmueller

摘要

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.