Robin-Neumann Coupling of PINN and FEM Solvers: A Steklov-Poincar\'e View, with Application to Fluid-Structure Interaction with Contact
arXiv:2606.14181v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) are meshless and carry moving geometry and topology change through resampling of collocation points; the finite-element method (FEM) is the workhorse for boundary-fitted discretisations. Coupling the two across a shared interface promises the best of both, yet existing PINN-FEM schemes are validated only empirically. We put the coupling on a domain-decomposition footing: viewing each solver as a Steklov-Poincar\'e (trace-to-flux) operator, we transfer the classical Dirichlet-Neumann (DN) divergence diagn
This research addresses a critical limitation in the practical application of PINNs by providing a robust theoretical framework for their coupling with established FEM solvers, rather than relying solely on empirical validation, which is common in early-stage AI integration.
A validated method for combining the strengths of PINNs and FEM could significantly accelerate simulations in complex physics, especially for problems involving moving geometries where traditional methods struggle.
The ability to reliably couple meshless PINNs with meshed FEM methods creates a hybrid approach that potentially offers greater accuracy and efficiency for advanced engineering and scientific simulations, expanding the applicability of AI in complex physics.
- · AI research institutions
- · Engineering simulation software developers
- · Aerospace and automotive R&D
- · Fluid dynamics researchers
- · Developers of less adaptable simulation tools
This theoretical advancement simplifies and improves the accuracy of multi-physics simulations, especially for fluid-structure interaction.
Faster and more reliable simulations could lead to accelerated design cycles and innovation in fields like materials science and engineering.
The increased fidelity and speed of simulation might reduce physical prototyping, shifting R&D costs and timelines significantly across major industries.
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Read at arXiv cs.LG