dorsal/arxiv
View SchemaHigh-Fidelity Modeling of Stochastic Chemical Dynamics on Complex Manifolds: A Multi-Scale SIREN-PINN Framework for the Curvature-Perturbed Ginzburg-Landau Equation
| Authors | Julian Evan Chrisnanto, Salsabila Rahma Alia, Nurfauzi Fadillah, Yulison Herry Chrisnanto |
|---|---|
| Categories | |
| ArXiv ID | 2601.08104vv1 |
| URL | https://arxiv.org/abs/2601.08104 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
The accurate identification and control of spatiotemporal chaos in reaction-diffusion systems remains a grand challenge in chemical engineering, particularly when the underlying catalytic surface possesses complex, unknown topography. In the \textit{Defect Turbulence} regime, system dynamics are governed by topological phase singularities (spiral waves) whose motion couples to manifold curvature via geometric pinning. Conventional Physics-Informed Neural Networks (PINNs) using ReLU or Tanh activations suffer from fundamental \textit{spectral bias}, failing to resolve high-frequency gradients and causing amplitude collapse or phase drift. We propose a Multi-Scale SIREN-PINN architecture leveraging periodic sinusoidal activations with frequency-diverse initialization, embedding the appropriate inductive bias for wave-like physics directly into the network structure. This enables simultaneous resolution of macroscopic wave envelopes and microscopic defect cores. Validated on the complex Ginzburg-Landau equation evolving on latent Riemannian manifolds, our architecture achieves relative state prediction error $\epsilon_{L_2} \approx 1.92 \times 10^{-2}$, outperforming standard baselines by an order of magnitude while preserving topological invariants ($|\Delta N_{defects}| < 1$). We solve the ill-posed \textit{inverse pinning problem}, reconstructing hidden Gaussian curvature fields solely from partial observations of chaotic wave dynamics (Pearson correlation $\rho = 0.965$). Training dynamics reveal a distinctive Spectral Phase Transition at epoch $\sim 2,100$, where cooperative minimization of physics and geometry losses drives the solver to Pareto-optimal solutions. This work establishes a new paradigm for Geometric Catalyst Design, offering a mesh-free, data-driven tool for identifying surface heterogeneity and engineering passive control strategies in turbulent chemical reactors.
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"abstract": "The accurate identification and control of spatiotemporal chaos in reaction-diffusion systems remains a grand challenge in chemical engineering, particularly when the underlying catalytic surface possesses complex, unknown topography. In the \\textit{Defect Turbulence} regime, system dynamics are governed by topological phase singularities (spiral waves) whose motion couples to manifold curvature via geometric pinning. Conventional Physics-Informed Neural Networks (PINNs) using ReLU or Tanh activations suffer from fundamental \\textit{spectral bias}, failing to resolve high-frequency gradients and causing amplitude collapse or phase drift. We propose a Multi-Scale SIREN-PINN architecture leveraging periodic sinusoidal activations with frequency-diverse initialization, embedding the appropriate inductive bias for wave-like physics directly into the network structure. This enables simultaneous resolution of macroscopic wave envelopes and microscopic defect cores. Validated on the complex Ginzburg-Landau equation evolving on latent Riemannian manifolds, our architecture achieves relative state prediction error $\\epsilon_{L_2} \\approx 1.92 \\times 10^{-2}$, outperforming standard baselines by an order of magnitude while preserving topological invariants ($|\\Delta N_{defects}| \u003c 1$). We solve the ill-posed \\textit{inverse pinning problem}, reconstructing hidden Gaussian curvature fields solely from partial observations of chaotic wave dynamics (Pearson correlation $\\rho = 0.965$). Training dynamics reveal a distinctive Spectral Phase Transition at epoch $\\sim 2,100$, where cooperative minimization of physics and geometry losses drives the solver to Pareto-optimal solutions. This work establishes a new paradigm for Geometric Catalyst Design, offering a mesh-free, data-driven tool for identifying surface heterogeneity and engineering passive control strategies in turbulent chemical reactors.",
"arxiv_id": "2601.08104",
"authors": [
"Julian Evan Chrisnanto",
"Salsabila Rahma Alia",
"Nurfauzi Fadillah",
"Yulison Herry Chrisnanto"
],
"categories": [
"nlin.CD",
"cs.AI"
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"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "High-Fidelity Modeling of Stochastic Chemical Dynamics on Complex Manifolds: A Multi-Scale SIREN-PINN Framework for the Curvature-Perturbed Ginzburg-Landau Equation",
"url": "https://arxiv.org/abs/2601.08104",
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