High-Fidelity Modeling of Stochastic Chemical Dynamics on Complex Manifolds: A Multi-Scale SIREN-PINN Framework for the Curvature-Perturbed Ginzburg-Landau Equation

• URL: http://arxiv.org/abs/2601.08104v1
• Date: Tue, 13 Jan 2026 00:52:23 GMT
• Title: High-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,
• Abstract summary: 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.
• Score: 0.0
• 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 $ε_{L_2} \approx 1.92 \times 10^{-2}$, outperforming standard baselines by an order of magnitude while preserving topological invariants ($|ΔN_{defects}| < 1$). We solve the ill-posed \textit{inverse pinning problem}, reconstructing hidden Gaussian curvature fields solely from partial observations of chaotic wave dynamics (Pearson correlation $ρ= 0.965$). 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.

Related papers

• Improved Grid-Based Simulation of Coulombic Dynamics [0.8602553195689513]
  We propose two complementary correction schemes that consistently outperform the uncorrected counterparts.<n>The proposed framework aligns naturally with quantum computing architectures.<n>This study thus establishes practical strategies toward high-accuracy Coulombic dynamics on both classical and emerging quantum platforms.
  arXiv  Detail & Related papers  (2026-03-03T13:07:09Z)
• On the Mechanism and Dynamics of Modular Addition: Fourier Features, Lottery Ticket, and Grokking [49.1352577985191]
  We present a comprehensive analysis of how two-layer neural networks learn features to solve the modular addition task.<n>Our work provides a full mechanistic interpretation of the learned model and a theoretical explanation of its training dynamics.
  arXiv  Detail & Related papers  (2026-02-18T20:25:13Z)
• 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)
• Latent Object Permanence: Topological Phase Transitions, Free-Energy Principles, and Renormalization Group Flows in Deep Transformer Manifolds [0.5729426778193398]
  We study the emergence of multi-step reasoning in deep Transformer language models through a geometric and statistical-physics lens.<n>We formalize the forward pass as a discrete coarse-graining map and relate the appearance of stable "concept basins" to fixed points of this renormalization-like dynamics.<n>The resulting low-entropy regime is characterized by a spectral tail collapse and by the formation of transient, reusable object-like structures in representation space.
  arXiv  Detail & Related papers  (2026-01-16T23:11:02Z)
• Intrinsic-Metric Physics-Informed Neural Networks (IM-PINN) for Reaction-Diffusion Dynamics on Complex Riemannian Manifolds [0.0]
  This study introduces the Intrinsic-Metric Physics-Informed Neural Network (IM-PINN)<n>It is a mesh-free geometric deep learning framework that solves partial differential equations directly in the continuous parametric domain.<n>The framework offers a memory-efficient, resolution-independent paradigm for simulating biological pattern formation on evolving surfaces.
  arXiv  Detail & Related papers  (2025-12-26T12:41:05Z)
• Learning vertical coordinates via automatic differentiation of a dynamical core [39.817742239477255]
  We propose a framework to define a parametric vertical coordinate system as a learnable component within a differentiable dynamical core.<n>We develop an end-to-end differentiable numerical solver for the two-dimensional non-hydrostatic equations on an Arakawa C-grid.<n>We demonstrate that these learned coordinates reduce the mean squared error by a factor of 1.4 to 2 in non-linear statistical benchmarks.
  arXiv  Detail & Related papers  (2025-12-19T18:31:07Z)
• Reconstructing Multi-Scale Physical Fields from Extremely Sparse Measurements with an Autoencoder-Diffusion Cascade [38.28865883904372]
  Cascaded Sensing (Cas-Sensing) is a hierarchical reconstruction framework that integrates an autoencoder-diffusion cascade.<n>A conditional diffusion model, trained with a mask-cascade strategy, generates fine-scale details conditioned on large-scale structures.<n>Experiments on both simulation and real-world datasets demonstrate that Cas-Sensing generalizes well across varying sensor configurations and geometric boundaries.
  arXiv  Detail & Related papers  (2025-12-01T11:46:14Z)
• Observation of non-Hermitian topology in cold Rydberg quantum gases [42.41909362660157]
  We experimentally demonstrate non-Hermitian spectra topology in a dissipative Rydberg atomic gas.<n>By increasing the interaction strength, the system evolves from Hermitian to non-Hermitian regime.<n>This work establishes cold Rydberg gases as a versatile platform for exploring the rich interplay between non-Hermitian topology, strong interactions, and dissipative quantum dynamics.
  arXiv  Detail & Related papers  (2025-09-30T13:44:43Z)
• Differential-Integral Neural Operator for Long-Term Turbulence Forecasting [43.04613533979613]
  textbfunderlineDifferential-textbfunderlineIntegral textbfunderlineNeural textbfunderlineOperator (method)<n>method explicitly models the turbulent evolution through parallel branches that learn distinct physical operators.<n>It successfully suppresses error accumulation over hundreds of timesteps, maintains high fidelity in both the vorticity fields and energy spectra, and establishes a new benchmark for physically consistent, long-range turbulence forecast.
  arXiv  Detail & Related papers  (2025-09-25T14:08:26Z)
• Entanglement and optimization within autoregressive neural quantum states [3.318269729347296]
  Neural quantum states (NQS) are powerful variational ans"atze capable of representing highly entangled quantum many-body wavefunctions.<n>We perform large-scale simulations of ensembles of random autoregressive wavefunctions for chains of up to $256$ spins.<n>We uncover signatures of transitions in their average entanglement scaling, entanglement spectra, and correlation functions.
  arXiv  Detail & Related papers  (2025-09-15T18:59:19Z)
• PIORF: Physics-Informed Ollivier-Ricci Flow for Long-Range Interactions in Mesh Graph Neural Networks [23.97389618896843]
  We propose Physics-Informed Ollivier-Ricci Flow (PIORF), a novel rewiring method that combines physical correlations with graph topology.<n>We show that PIORF consistently outperforms baseline models and existing rewiring methods, achieving up to 26.2 improvement.
  arXiv  Detail & Related papers  (2025-04-05T04:14:05Z)
• Graph Fourier Neural ODEs: Modeling Spatial-temporal Multi-scales in Molecular Dynamics [38.53044197103943]
  GF-NODE integrates a graph Fourier transform for spatial frequency decomposition with a Neural ODE framework for continuous-time evolution.<n>We show that GF-NODE achieves state-of-the-art accuracy while preserving essential geometrical features over extended simulations.<n>These findings highlight the promise of bridging spectral decomposition with continuous-time modeling to improve the robustness and predictive power of MD simulations.
  arXiv  Detail & Related papers  (2024-11-03T15:10:48Z)
• The Limiting Dynamics of SGD: Modified Loss, Phase Space Oscillations, and Anomalous Diffusion [29.489737359897312]
  We study the limiting dynamics of deep neural networks trained with gradient descent (SGD) We show that the key ingredient driving these dynamics is not the original training loss, but rather the combination of a modified loss, which implicitly regularizes the velocity and probability currents, which cause oscillations in phase space.
  arXiv  Detail & Related papers  (2021-07-19T20:18:57Z)

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.