Coupling-Robust Accuracy in Multiphysics Physics Informed Neural Networks via Kronecker-Preconditioned Optimization
arXiv:2605.23391v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) for coupled multiphysics systems suffer systematic accuracy degradation as inter-equation coupling strengthens. We provide a theoretical explanation for this phenomenon through neural tangent kernel (NTK) analysis: for linearly coupled systems, we prove that the standard NTK's spectral radius grows as $\Omega(\gamma^2)$ with coupling strength $\gamma$, shrinking the stable learning rate, while block-diagonal Gauss--Newton (GN) preconditioning yields a preconditioned NTK $K_P = J H^{+} J^\top$ (where $H$ is
This research addresses a known limitation in Physics-Informed Neural Networks (PINNs) as their application scales to more complex, real-world multiphysics problems, offering a theoretical explanation and a preconditioning solution.
Improving the accuracy and stability of PINNs in complex simulations is critical for their practical adoption across scientific and engineering domains, accelerating discovery and design cycles.
The proposed Kronecker-Preconditioned Optimization method could make PINNs significantly more robust and reliable for modeling strongly coupled multiphysics systems, expanding their applicability.
- · AI/ML researchers in scientific computing
- · Engineering simulation software developers
- · Industries relying on complex multi-physics modeling (e.g., aerospace, automotiv
- · Traditional numerical solvers (gradual displacement for specific tasks)
- · Researchers using un-preconditioned PINNs for coupled systems
More accurate and stable AI models for complex physical simulations become feasible.
Accelerated design and optimization processes across various engineering and scientific fields due to improved simulation capabilities.
Enhanced ability to model and predict behavior in systems where traditional methods struggle, potentially leading to new material discoveries or more efficient industrial processes.
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Read at arXiv cs.LG