AI RESEARCH
Meta-Learned Basis Adaptation for Parametric Linear PDEs
arXiv CS.LG
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ArXi:2604.09289v1 Announce Type: new We propose a hybrid physics-informed framework for solving families of parametric linear partial differential equations (PDEs) by combining a meta-learned predictor with a least-squares corrector. The predictor, termed \textbf{KAPI} (Kernel-Adaptive Physics-Informed meta-learner), is a shallow task-conditioned model that maps query coordinates and PDE parameters to solution values while internally generating an interpretable, task-adaptive Gaussian basis geometry.