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 kernels directly from spatiotemporal observations. Within the solver, the unknown kernel is represented using a constrained Kolmogorov--Arnold Network (KAN) parameterization, with the physical constraints...
| Authors | Aruzhan Tleubek, Salah A Faroughi |
|---|---|
| Primary category | cs.LG |
| Published | 13 July 2026 |
| Last updated at source | 13 July 2026 |
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