Approximation Theory of Laplacian-Based Neural Operators for Reaction-Diffusion System
Neural operators provide a framework for learning solution operators of partial differential equations (PDEs), enabling efficient surrogate modeling for complex systems. While universal approximation results are now well understood, approximation analysis specific to nonlinear reaction-diffusion systems remains limited. In this paper, we study neural operators applied to the solution mapping from initial conditions to time-dependent solutions of a generalized Gierer-Meinhardt reaction-diffusion system, a prototypical model of nonlinear pattern formation. Our main results establish explicit approximation error bounds in terms of network depth, width, and spectral rank by exploiting the Lap...
| Authors | Takashi Furuya, Ryo Ozawa, Jenn-Nan Wang |
|---|---|
| Primary category | cs.LG |
| Published | 12 May 2026 |
| Last updated at source | 12 May 2026 |
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