Probabilistic function-on-function nonlinear autoregressive model for emulation and reliability analysis of dynamical systems

• URL: http://arxiv.org/abs/2602.01929v1
• Date: Mon, 02 Feb 2026 10:29:30 GMT
• Title: Probabilistic function-on-function nonlinear autoregressive model for emulation and reliability analysis of dynamical systems
• Abstract summary: This work introduces a novel Function-on-Function AutoRegressive model with eXogenous inputs (F2NARX)<n>It substantially improves predictive efficiency while maintaining high accuracy.<n>Results show that F2NARX outperforms state-of-the-art NARX model by orders of magnitude in efficiency.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Constructing accurate and computationally efficient surrogate models (or emulators) for predicting dynamical system responses is critical in many engineering domains, yet remains challenging due to the strongly nonlinear and high-dimensional mapping from external excitations and system parameters to system responses. This work introduces a novel Function-on-Function Nonlinear AutoRegressive model with eXogenous inputs (F2NARX), which reformulates the conventional NARX model from a function-on-function regression perspective, inspired by the recently proposed $\mathcal{F}$-NARX method. The proposed framework substantially improves predictive efficiency while maintaining high accuracy. By combining principal component analysis with Gaussian process regression, F2NARX further enables probabilistic predictions of dynamical responses via the unscented transform in an autoregressive manner. The effectiveness of the method is demonstrated through case studies of varying complexity. Results show that F2NARX outperforms state-of-the-art NARX model by orders of magnitude in efficiency while achieving higher accuracy in general. Moreover, its probabilistic prediction capabilities facilitate active learning, enabling accurate estimation of first-passage failure probabilities of dynamical systems using only a small number of training time histories.

Related papers

• mNARX+: A surrogate model for complex dynamical systems using manifold-NARX and automatic feature selection [0.0]
  We propose an automatic approach for nonlinear autoregressive modeling that leverages the feature-based structure of functional-NARX (F-NARX) modeling.<n>We show that the mNARX+ algorithm provides a systematic, data-driven method for creating accurate and stable surrogate models for complex dynamical systems.
  arXiv  Detail & Related papers  (2025-07-17T17:11:07Z)
• Learning Optical Flow Field via Neural Ordinary Differential Equation [44.16275288019991]
  Recent works on optical flow estimation use neural networks to predict the flow field that maps positions of one image to positions of the other.<n>We introduce a novel approach for predicting the derivative of the flow using a continuous model, namely neural ordinary differential equations (ODE)
  arXiv  Detail & Related papers  (2025-06-03T18:30:14Z)
• Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems [49.819436680336786]
  We propose an efficient transformed Gaussian process state-space model (ETGPSSM) for scalable and flexible modeling of high-dimensional, non-stationary dynamical systems.<n>Specifically, our ETGPSSM integrates a single shared GP with input-dependent normalizing flows, yielding an expressive implicit process prior that captures complex, non-stationary transition dynamics.<n>Our ETGPSSM outperforms existing GPSSMs and neural network-based SSMs in terms of computational efficiency and accuracy.
  arXiv  Detail & Related papers  (2025-03-24T03:19:45Z)
• Bayesian Kernel Regression for Functional Data [1.4501446815590895]
  In supervised learning, the output variable to be predicted is often represented as a function.<n>We propose a novel functional output regression model based on kernel methods.
  arXiv  Detail & Related papers  (2025-03-17T19:28:27Z)
• No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs [56.78271181959529]
  This paper proposes a conceptual shift to modeling low-dimensional dynamical systems by departing from the traditional two-step modeling process.<n>Instead of first discovering a closed-form equation and then analyzing it, our approach, direct semantic modeling, predicts the semantic representation of the dynamical system.<n>Our approach not only simplifies the modeling pipeline but also enhances the transparency and flexibility of the resulting models.
  arXiv  Detail & Related papers  (2025-01-30T18:36:48Z)
• Recurrent Stochastic Configuration Networks with Hybrid Regularization for Nonlinear Dynamics Modelling [3.8719670789415925]
  Recurrent configuration networks (RSCNs) have shown great potential in modelling nonlinear dynamic systems with uncertainties.<n>This paper presents an RSCN with hybrid regularization to enhance both the learning capacity and generalization performance of the network.
  arXiv  Detail & Related papers  (2024-11-26T03:06:39Z)
• Scaling and renormalization in high-dimensional regression [72.59731158970894]
  We present a unifying perspective on recent results on ridge regression.<n>We use the basic tools of random matrix theory and free probability, aimed at readers with backgrounds in physics and deep learning.<n>Our results extend and provide a unifying perspective on earlier models of scaling laws.
  arXiv  Detail & Related papers  (2024-05-01T15:59:00Z)
• CGNSDE: Conditional Gaussian Neural Stochastic Differential Equation for Modeling Complex Systems and Data Assimilation [1.4322470793889193]
  A new knowledge-based and machine learning hybrid modeling approach, called conditional neural differential equation (CGNSDE), is developed. In contrast to the standard neural network predictive models, the CGNSDE is designed to effectively tackle both forward prediction tasks and inverse state estimation problems.
  arXiv  Detail & Related papers  (2024-04-10T05:32:03Z)
• FAStEN: An Efficient Adaptive Method for Feature Selection and Estimation in High-Dimensional Functional Regressions [7.674715791336311]
  We propose a new, flexible and ultra-efficient approach to perform feature selection in a sparse function-on-function regression problem. We show how to extend it to the scalar-on-function framework. We present an application to brain fMRI data from the AOMIC PIOP1 study.
  arXiv  Detail & Related papers  (2023-03-26T19:41:17Z)
• Adaptive LASSO estimation for functional hidden dynamic geostatistical model [69.10717733870575]
  We propose a novel model selection algorithm based on a penalized maximum likelihood estimator (PMLE) for functional hiddenstatistical models (f-HD) The algorithm is based on iterative optimisation and uses an adaptive least absolute shrinkage and selector operator (GMSOLAS) penalty function, wherein the weights are obtained by the unpenalised f-HD maximum-likelihood estimators.
  arXiv  Detail & Related papers  (2022-08-10T19:17:45Z)
• Neural Dynamic Mode Decomposition for End-to-End Modeling of Nonlinear Dynamics [49.41640137945938]
  We propose a neural dynamic mode decomposition for estimating a lift function based on neural networks. With our proposed method, the forecast error is backpropagated through the neural networks and the spectral decomposition. Our experiments demonstrate the effectiveness of our proposed method in terms of eigenvalue estimation and forecast performance.
  arXiv  Detail & Related papers  (2020-12-11T08:34:26Z)
• 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.