arXiv:2606.02475v1 Announce Type: cross Abstract: Classical finite-difference solvers remain reliable tools for partial differential equations, but their efficiency depends on where mesh resolution is placed. Uniform refinement can waste degrees of freedom when solution difficulty is localised near sharp gradients, fronts, oscillations, or constraint-sensitive regions. This paper studies a hybrid strategy in which a physics-informed neural network (PINN) is used not as the final solver, but as an off-grid residual probe for adaptive mesh refinement. The PINN residual is sampled over the domain
The paper leverages recent advancements in physics-informed neural networks to address long-standing computational efficiency challenges in PDE solvers, reflecting increasing integration of AI into scientific computing.
This development can significantly improve the efficiency and accuracy of simulating complex physical systems, accelerating research and development in fields from engineering to climate science.
The conventional approach to adaptive mesh refinement in finite-difference solvers is enhanced by using PINNs as an intelligent, off-grid residual probe, optimizing computational resource allocation.
- · Computational fluid dynamics sector
- · Materials science research
- · Climate modeling institutions
- · AI/ML frameworks for scientific computing
- · Legacy uniform mesh refinement techniques
- · Computational science reliant solely on traditional numerical methods
Improved simulation speeds and accuracy for various scientific and engineering problems.
Reduced computational costs for R&D, potentially democratizing access to high-fidelity simulations.
Acceleration of discovery in fields requiring extensive PDE solving, such as drug design or advanced materials development.
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Read at arXiv cs.LG