[2512.03290] ASPEN: An Adaptive Spectral Physics-Enabled Network for Ginzburg-Landau Dynamics

Computer Science > Machine Learning arXiv:2512.03290 (cs) [Submitted on 2 Dec 2025 (v1), last revised 23 Mar 2026 (this version, v4)] Title:ASPEN: An Adaptive Spectral Physics-Enabled Network for Ginzburg-Landau Dynamics Authors:Julian Evan Chrisnanto, Nurfauzi Fadillah, Yulison Herry Chrisnanto View a PDF of the paper titled ASPEN: An Adaptive Spectral Physics-Enabled Network for Ginzburg-Landau Dynamics, by Julian Evan Chrisnanto and 2 other authors View PDF HTML (experimental) Abstract:Physics-Informed Neural Networks (PINNs) have emerged as a powerful, mesh-free paradigm for solving partial differential equations (PDEs). However, they notoriously struggle with stiff, multi-scale, and nonlinear systems due to the inherent spectral bias of standard multilayer perceptron (MLP) architectures, which prevents them from adequately representing high-frequency components. In this work, we introduce the Adaptive Spectral Physics-Enabled Network (ASPEN), a novel architecture designed to overcome this critical limitation. ASPEN integrates an adaptive spectral layer with learnable Fourier features directly into the network's input stage. This mechanism allows the model to dynamically tune its own spectral basis during training, enabling it to efficiently learn and represent the precise frequency content required by the solution. We demonstrate the efficacy of ASPEN by applying it to the complex Ginzburg-Landau equation (CGLE), a canonical and challenging benchmark for nonlinear, st...