Noise-Aware System Identification for High-Dimensional Stochastic Dynamics

Ziheng Guo; Igor Cialenco; Ming Zhong

Home/Archive/arXiv

arXiv · 2411.00002

Noise-Aware System Identification for High-Dimensional Stochastic Dynamics

Ziheng Guo·Igor Cialenco·Ming Zhong

View original source ↗Read source document ↗Export metadata ↓

Abstract

Stochastic dynamical systems are ubiquitous in physics, biology, and engineering, where both deterministic drifts and random fluctuations govern system behavior. Learning these dynamics from data is particularly challenging in high-dimensional settings with complex, correlated, or state-dependent noise. We introduce a noise-aware system identification framework that jointly recovers the deterministic drift and full noise structure directly from the trajectory data, without requiring prior assumptions on the noise model. Our method accommodates a broad class of stochastic dynamics, including colored and multiplicative noise, that scales efficiently to high-dimensional systems, and accurately reconstructs the underlying dynamics. Numerical experiments on diverse systems validate the approach and highlight its potential for data-driven modeling in complex stochastic environments.

Explore related subjects

math.NA cs.NA

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Ziheng Guo, Igor Cialenco, Ming Zhong. 2026-03-08. Noise-Aware System Identification for High-Dimensional Stochastic Dynamics. https://arxiv.org/abs/2411.00002

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

$L^{p}$-convergence of Kantorovich-type Max-Min Neural Network Operators

In this work, we study the Kantorovich variant of max-min neural network operators, in which the operator kernel is defined in terms of sigmoidal functions. Our main aim is to demonstrate the $L^{p}$-convergence of these nonlinear operators for $1\leq p<\infty$, which makes it possible to obtain approximation results for functions that are not necessarily continuous. In addition, we will derive quantitative estimates for the rate of approximation in the $L^{p}$-norm. We will provide some explicit examples, studying the approximation of discontinuous functions with the max-min operator, and varying additionally the underlying sigmoidal function of the kernel. Further, we numerically compare the $L^{p}$-approximation error with the respective error of the Kantorovich variants of other popular neural network operators. As a final application, we show that the Kantorovich variant has advantages compared to the sampling variant of the max-min operator and Kantorovich variant of the max-product operator when it comes to approximate noisy functions as for instance biomedical ECG signals.

math.NA↗

arXiv2026

Quotient geometry of tensor ring decomposition

Differential geometries derived from tensor decompositions have been extensively studied and provided the foundations for a variety of efficient numerical methods. Despite the practical success of the tensor ring (TR) decomposition, its intrinsic geometry remains less understood, primarily due to the underlying ring structure and the resulting nontrivial gauge invariance. We establish the quotient geometry and immersed-submanifold structure of TR decomposition by imposing full-rank conditions on all unfolding matrices of the core tensors and capturing the gauge invariance. The intrinsic ring structure of TR leads to an analysis that is substantially different from other tensor formats. Additionally, for the uniform TR decomposition, where all core tensors are identical and the manifold structure is known, we derive explicit parameterizations for the vertical and horizontal spaces, which enable Riemannian optimization. Numerical experiments validate the developed geometries via tensor ring completion tasks.

math.NA↗

arXiv2026

Boundary elements for clamped Kirchhoff--Love plates

We present a Galerkin boundary element method for clamped Kirchhoff--Love plates with piecewise smooth boundary. It is a direct method based on the representation formula and requires the inversion of the single-layer operator, an application of the double-layer operator to the Dirichlet data, and, in the presence of a vertical load, an application of the Dirichlet trace of the Newton potential to that load. We present trace approximation spaces of arbitrary order, required for both the Dirichlet data and the unknown Neumann trace. Our boundary element method is quasi-optimal with respect to the natural trace norm and achieves optimal convergence order under minimal regularity assumptions. We provide explicit representations of all three integral operators and discuss the implementation of the appearing integrals. Numerical experiments for smooth and non-smooth domains confirm predicted convergence rates.

math.NA↗