INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities
arXiv:2606.18032v1 Announce Type: cross Abstract: We propose a new weak-form Physics-Informed Neural Network approach (named INI-VPINN). INI-VPINN naturally incorporates Neumann boundary and interface conditions into the variational formulation. It removes the need for additional loss terms or multiple subdomain networks. This framework employs compact support weighting functions and integration by parts to implicitly impose flux and continuity constraints. In this way, it implicitly ensures physical consistency across material boundaries. The proposed method is tested on Poisson and Laplace p
The continuous evolution of AI and machine learning techniques is pushing the boundaries of scientific computing, making this a natural progression in physics-informed neural networks.
This development offers a more robust and physically consistent method for solving complex engineering and physics problems, potentially accelerating simulations and design in various domains.
The explicit handling of Neumann boundary and interface conditions within a weak-form Physics-Informed Neural Network simplifies problem setup and improves accuracy for multi-material domains.
- · Engineering R&D
- · Material science
- · Computational fluid dynamics
- · AI/ML researchers
- · Traditional numerical solvers
- · Companies reliant on overly complex simulation pipelines
Improved accuracy and efficiency in simulating complex physical phenomena, especially across different materials.
Faster innovation cycles in industries like aerospace, automotive, and semiconductor manufacturing due to reduced simulation time.
New engineering capabilities for designing materials and structures previously difficult or impossible to model effectively.
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Read at arXiv cs.LG