AI RESEARCH
Stochastic Dimension-Free Zeroth-Order Estimator for High-Dimensional and High-Order PINNs
arXiv CS.LG
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ArXi:2603.24002v1 Announce Type: new Physics-Informed Neural Networks (PINNs) for high-dimensional and high-order partial differential equations (PDEs) are primarily constrained by the $\mathcal{O}(d^k)$ spatial derivative complexity and the $\mathcal{O}(P)$ memory overhead of backpropagation (BP). While randomized spatial estimators successfully reduce the spatial complexity to $\mathcal{O}(1)$, their reliance on first-order optimization still leads to prohibitive memory consumption at scale.