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

• URL: http://arxiv.org/abs/2512.03290v1
• Date: Tue, 02 Dec 2025 22:58:06 GMT
• Title: ASPEN: An Adaptive Spectral Physics-Enabled Network for Ginzburg-Landau Dynamics
• Authors: Julian Evan Chrisnanto, Nurfauzi Fadillah, Yulison Herry Chrisnanto,
• Abstract summary: Physics-Informed Neural Networks (PINs) have emerged as a powerful, mesh-free paradigm for solving partial differential equations (PDEs)<n>They notoriously struggle with stiff, multi-scale, and nonlinear systems due to the inherent spectral bias of standard multilayer perceptron (MLP) architectures.<n>We introduce the Adaptive Spectral-Enabled Network (ASPEN), a novel architecture designed to overcome this limitation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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, stiff spatio-temporal dynamics. Our results show that a standard PINN architecture catastrophically fails on this problem, diverging into non-physical oscillations. In contrast, ASPEN successfully solves the CGLE with exceptional accuracy. The predicted solution is visually indistinguishable from the high-resolution ground truth, achieving a low median physics residual of 5.10 x 10^-3. Furthermore, we validate that ASPEN's solution is not only pointwise accurate but also physically consistent, correctly capturing emergent physical properties, including the rapid free energy relaxation and the long-term stability of the domain wall front. This work demonstrates that by incorporating an adaptive spectral basis, our framework provides a robust and physically-consistent solver for complex dynamical systems where standard PINNs fail, opening new options for machine learning in challenging physical domains.

Related papers

• Supervised Metric Regularization Through Alternating Optimization for Multi-Regime Physics-Informed Neural Networks [0.0]
  PINNs often face challenges when modeling dynamical systems with sharp regime transitions, such as bifurcations.<n>We propose a Topology-Aware PINN (TAPINN) that aims to mitigate this challenge by the latent space via Supervised Metric Regularization.<n>Preliminary experiments on the Duffing demonstrate that while standard baselines suffer from spectral bias and high-capacity gradient networks overfit, our approach achieves stable convergence with 2.18x lower variance than a multi-output Sobolev Error baseline, and 5x fewer parameters than a hypernetwork-based alternative.
  arXiv  Detail & Related papers  (2026-02-10T17:06:57Z)
• PhyG-MoE: A Physics-Guided Mixture-of-Experts Framework for Energy-Efficient GNSS Interference Recognition [49.955269674859004]
  This paper introduces PhyG-MoE (Physics-Guided Mixture-of-Experts), a framework designed to align model capacity with signal complexity.<n>Unlike static architectures, the proposed system employs a spectrum-based gating mechanism that routes signals based on their spectral feature entanglement.<n>A high-capacity TransNeXt expert is activated on-demand to disentangle complex features in saturated scenarios, while lightweight experts handle fundamental signals to minimize latency.
  arXiv  Detail & Related papers  (2026-01-19T07:57:52Z)
• Soft Partition-based KAPI-ELM for Multi-Scale PDEs [0.0]
  This work introduces a soft partition-based Kernel-Adaptive Physics-Informed Extreme Learning Machine.<n>A signed-distance-based weighting stabilizes least-squares learning on irregular frequencies.<n>Although demonstrated on steady linear PDEs, the results show that soft-partition kernel adaptation provides a fast, architecture-free approach for multiscale PDEs.
  arXiv  Detail & Related papers  (2026-01-13T16:43:38Z)
• Adaptive Mesh-Quantization for Neural PDE Solvers [51.26961483962011]
  Graph Neural Networks can handle the irregular meshes required for complex geometries and boundary conditions, but still apply uniform computational effort across all nodes.<n>We propose Adaptive Mesh Quantization: spatially adaptive quantization across mesh node, edge, and cluster features, dynamically adjusting the bit-width used by a quantized model.<n>We demonstrate our framework's effectiveness by integrating it with two state-of-the-art models, MP-PDE and GraphViT, to evaluate performance across multiple tasks.
  arXiv  Detail & Related papers  (2025-11-23T14:47:24Z)
• PHASE-Net: Physics-Grounded Harmonic Attention System for Efficient Remote Photoplethysmography Measurement [63.007237197267834]
  Existing deep learning methods are mostly physiological monitoring and lack theoretical robustness.<n>We propose a physics-informed r paradigm derived from the Navier-Stokes equations of hemodynamics, showing that the pulse signal follows a second-order system.<n>This provides a theoretical justification for using a Temporal Conal Network (TCN)<n>Phase-Net achieves state-of-the-art performance with strong efficiency, offering a theoretically grounded and deployment-ready r solution.
  arXiv  Detail & Related papers  (2025-09-29T14:36:45Z)
• BridgeNet: A Hybrid, Physics-Informed Machine Learning Framework for Solving High-Dimensional Fokker-Planck Equations [0.0]
  BridgeNet is a novel framework that integrates convolutional neural networks with physics-informed neural networks to efficiently solve non-linear, high-dimensional Fokker-Planck equations (FPEs)<n>This work represents a substantial advancement in computational physics, offering a scalable and accurate solution methodology with promising applications in fields ranging from financial mathematics to complex system dynamics.
  arXiv  Detail & Related papers  (2025-06-04T18:12:59Z)
• Physics-embedded Fourier Neural Network for Partial Differential Equations [35.41134465442465]
  We introduce Physics-embedded Fourier Neural Networks (PeFNN) with flexible and explainable error. PeFNN is designed to enforce momentum conservation and yields interpretable nonlinear expressions. We demonstrate its outstanding performance for challenging real-world applications such as large-scale flood simulations.
  arXiv  Detail & Related papers  (2024-07-15T18:30:39Z)
• NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition [67.46012350241969]
  This paper proposes a general acceleration methodology called NeuralStagger. It decomposing the original learning tasks into several coarser-resolution subtasks. We demonstrate the successful application of NeuralStagger on 2D and 3D fluid dynamics simulations.
  arXiv  Detail & Related papers  (2023-02-20T19:36:52Z)
• Momentum Diminishes the Effect of Spectral Bias in Physics-Informed Neural Networks [72.09574528342732]
  Physics-informed neural network (PINN) algorithms have shown promising results in solving a wide range of problems involving partial differential equations (PDEs) They often fail to converge to desirable solutions when the target function contains high-frequency features, due to a phenomenon known as spectral bias. In the present work, we exploit neural tangent kernels (NTKs) to investigate the training dynamics of PINNs evolving under gradient descent with momentum (SGDM)
  arXiv  Detail & Related papers  (2022-06-29T19:03:10Z)
• Message Passing Neural PDE Solvers [60.77761603258397]
  We build a neural message passing solver, replacing allally designed components in the graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.
  arXiv  Detail & Related papers  (2022-02-07T17:47:46Z)
• Optimal Transport Based Refinement of Physics-Informed Neural Networks [0.0]
  We propose a refinement strategy to the well-known Physics-Informed Neural Networks (PINNs) for solving partial differential equations (PDEs) based on the concept of Optimal Transport (OT) PINNs solvers have been found to suffer from a host of issues: spectral bias in fully-connected pathologies, unstable gradient, and difficulties with convergence and accuracy. We present a novel training strategy for solving the Fokker-Planck-Kolmogorov Equation (FPKE) using OT-based sampling to supplement the existing PINNs framework.
  arXiv  Detail & Related papers  (2021-05-26T02:51:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.