新闻 · arXiv cs.LG

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks

Discovering the memory or nonlocal kernel governing an integro-differential equation (IDE) from sparse and noisy observations is an ill-posed inverse problem. Existing identification methods often rely on problem-specific analytical derivations, specialized observation requirements, or restrictive assumptions about the kernel, limiting their applicability across different classes of IDEs. In this work, we propose a differentiable-solver-based framework for discovering memory and nonlocal…