Self-induced stochastic resonance: A physics-informed machine learning approach

• URL: http://arxiv.org/abs/2510.22848v1
• Date: Sun, 26 Oct 2025 21:49:20 GMT
• Title: Self-induced stochastic resonance: A physics-informed machine learning approach
• Authors: Divyesh Savaliya, Marius E. Yamakou,
• Abstract summary: Self-induced resonance (SISR) is the emergence of coherent oscillations in excitable systems driven solely by noise.<n>This work presents a physics-informed machine learning framework for modeling and predicting SISR in the FitzHugh neuron.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Self-induced stochastic resonance (SISR) is the emergence of coherent oscillations in slow-fast excitable systems driven solely by noise, without external periodic forcing or proximity to a bifurcation. This work presents a physics-informed machine learning framework for modeling and predicting SISR in the stochastic FitzHugh-Nagumo neuron. We embed the governing stochastic differential equations and SISR-asymptotic timescale-matching constraints directly into a Physics-Informed Neural Network (PINN) based on a Noise-Augmented State Predictor architecture. The composite loss integrates data fidelity, dynamical residuals, and barrier-based physical constraints derived from Kramers' escape theory. The trained PINN accurately predicts the dependence of spike-train coherence on noise intensity, excitability, and timescale separation, matching results from direct stochastic simulations with substantial improvements in accuracy and generalization compared with purely data-driven methods, while requiring significantly less computation. The framework provides a data-efficient and interpretable surrogate model for simulating and analyzing noise-induced coherence in multiscale stochastic systems.

Related papers

• Nonlocal Kramers-Moyal formulas and data-driven discovery of stochastic dynamical systems with multiplicative Lévy noise [2.3951444869691594]
  We develop novel data-driven algorithms capable of simultaneously identifying all governing components from data.<n>This work provides a principled and practical toolbox for discovering interpretable SDE models governing complex systems.
  arXiv  Detail & Related papers  (2026-01-27T05:44:50Z)
• 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)
• Disordered Dynamics in High Dimensions: Connections to Random Matrices and Machine Learning [52.26396748560348]
  We provide an overview of high dimensional dynamical systems driven by random matrices.<n>We focus on applications to simple models of learning and generalization in machine learning theory.
  arXiv  Detail & Related papers  (2026-01-03T00:12:32Z)
• Physics-Informed Neural ODEs with Scale-Aware Residuals for Learning Stiff Biophysical Dynamics [4.285464959472458]
  We introduce PhysicsInformed Neural ODEs with Scale-Aware Residuals (PI-NODE-SR)<n>This framework combines a low-order explicit solver (Heun method) residual normalisation to balance contributions between state variables evolving on disparate timescales.<n>It learns from a single oscillation simulated with a stiff solver (Rodas5P) and extrapolates beyond 100 ms, capturing both oscillation frequency and near-correct amplitudes.
  arXiv  Detail & Related papers  (2025-11-13T06:52:11Z)
• Reframing Generative Models for Physical Systems using Stochastic Interpolants [45.16806809746592]
  Generative models have emerged as powerful surrogates for physical systems, demonstrating increased accuracy, stability, and/or statistical fidelity.<n>Most approaches rely on iteratively denoising a Gaussian, a choice that may not be the most effective for autoregressive prediction tasks in PDEs and dynamical systems such as climate.<n>In this work, we benchmark generative models across diverse physical domains and tasks, and highlight the role of interpolants.
  arXiv  Detail & Related papers  (2025-09-30T14:02:00Z)
• Discovering Governing Equations in the Presence of Uncertainty [11.752763800308276]
  In this work, we theorize that accounting for system variability together with measurement noise is the key to consistently discover the governing equations underlying dynamical systems.<n>We show that SIP consistently identifies the correct equations by an average of 82% relative to the Sparse Identification Dynamics (SINDy) approach and its variant.
  arXiv  Detail & Related papers  (2025-07-13T18:31:25Z)
• Data-Driven Reconstruction and Characterization of Stochastic Dynamics via Dynamical Mode Decomposition [0.0]
  Noise limits the performance and predictive capabilities of classical and quantum dynamical systems.<n>We introduce a general, data-driven framework based on Dynamical Mode Decomposition (DMD) to analyze system dynamics under noise.<n>This methodology provides a broadly applicable tool for diagnostic, predictive, noise mitigation analyses, and control in complex systems.
  arXiv  Detail & Related papers  (2025-07-08T08:59:06Z)
• Flow Matching Meets PDEs: A Unified Framework for Physics-Constrained Generation [21.321570407292263]
  We propose Physics-Based Flow Matching, a generative framework that embeds physical constraints, both PDE residuals and algebraic relations, into the flow matching objective.<n>We show that our approach yields up to an $8times$ more accurate physical residuals compared to FM, while clearly outperforming existing algorithms in terms of distributional accuracy.
  arXiv  Detail & Related papers  (2025-06-10T09:13:37Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Stabilizing Machine Learning Prediction of Dynamics: Noise and Noise-inspired Regularization [58.720142291102135]
  Recent has shown that machine learning (ML) models can be trained to accurately forecast the dynamics of chaotic dynamical systems. In the absence of mitigating techniques, this technique can result in artificially rapid error growth, leading to inaccurate predictions and/or climate instability. We introduce Linearized Multi-Noise Training (LMNT), a regularization technique that deterministically approximates the effect of many small, independent noise realizations added to the model input during training.
  arXiv  Detail & Related papers  (2022-11-09T23:40:52Z)
• A Causality-Based Learning Approach for Discovering the Underlying Dynamics of Complex Systems from Partial Observations with Stochastic Parameterization [1.2882319878552302]
  This paper develops a new iterative learning algorithm for complex turbulent systems with partial observations. It alternates between identifying model structures, recovering unobserved variables, and estimating parameters. Numerical experiments show that the new algorithm succeeds in identifying the model structure and providing suitable parameterizations for many complex nonlinear systems.
  arXiv  Detail & Related papers  (2022-08-19T00:35:03Z)
• Noisy Recurrent Neural Networks [45.94390701863504]
  We study recurrent neural networks (RNNs) trained by injecting noise into hidden states as discretizations of differential equations driven by input data. We find that, under reasonable assumptions, this implicit regularization promotes flatter minima; it biases towards models with more stable dynamics; and, in classification tasks, it favors models with larger classification margin. Our theory is supported by empirical results which demonstrate improved robustness with respect to various input perturbations, while maintaining state-of-the-art performance.
  arXiv  Detail & Related papers  (2021-02-09T15:20:50Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)
• Multiplicative noise and heavy tails in stochastic optimization [62.993432503309485]
  empirical optimization is central to modern machine learning, but its role in its success is still unclear. We show that it commonly arises in parameters of discrete multiplicative noise due to variance. A detailed analysis is conducted in which we describe on key factors, including recent step size, and data, all exhibit similar results on state-of-the-art neural network models.
  arXiv  Detail & Related papers  (2020-06-11T09:58:01Z)

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.