AI RESEARCH
Physics-Informed Residuals for Adaptive Mesh Refinement in Finite-Difference PDE Solvers
arXiv CS.LG
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ArXi:2606.02475v1 Announce Type: cross 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.