arXiv:2505.11638v4 Announce Type: replace-cross Abstract: Natural Gradient Descent (NGD) has emerged as a promising optimization algorithm for training neural network-based solvers for partial differential equations (PDEs), such as Physics-Informed Neural Networks (PINNs). However, its practical use is often limited by the high computational cost of solving linear systems involving the Gramian matrix. While matrix-free NGD methods based on the conjugate gradient (CG) method avoid explicit matrix inversion, the ill-conditioning of the Gramian significantly slows the convergence of CG. In this w
The increasing complexity and scale of AI models for scientific computing, particularly PINNs, necessitate more efficient optimization methods to overcome existing computational bottlenecks.
Improved optimization techniques for PINNs can significantly accelerate scientific discovery, engineering design, and simulation across various industries by enabling faster and more accurate PDE solutions.
The proposed method offers a path to reduce the computational cost of training PINNs, making advanced physics-informed AI models more accessible and practical for real-world applications.
- · AI researchers in scientific computing
- · Engineering simulation software companies
- · Pharmaceutical and materials science R&D
- · High-performance computing (HPC) providers
- · Traditional numerical solvers for PDEs (in some applications)
- · Organizations heavily reliant on slow iterative simulation processes
More complex and accurate physics-informed AI models become feasible to train and deploy.
Accelerated design cycles for new materials, drugs, and industrial processes emerge as AI-driven simulations improve.
The development of 'digital twins' for complex physical systems could be significantly advanced, leading to new forms of predictive maintenance and operational optimization.
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Read at arXiv cs.LG