Noise-Aware System Identification for High-Dimensional Stochastic Dynamics
Ziheng Guo, Igor Cialenco, Ming Zhong
TL;DR
This paper presents a noise-aware system identification method that accurately recovers both deterministic and stochastic components of high-dimensional dynamical systems directly from data, without prior noise assumptions.
Contribution
It introduces a scalable framework capable of handling complex noise structures like colored and multiplicative noise in high-dimensional stochastic systems.
Findings
Successfully reconstructs dynamics in diverse systems
Handles complex noise structures without prior assumptions
Scales efficiently to high-dimensional data
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.
Peer Reviews
Decision·Submitted to ICLR 2026
- Clearly written and motivated paper - Theoretical guarantees: convergence results
- Lack of scalability - Validation only on synthetic data - No numerical comparison against the state-of-the-art in learning SDEs - Numerical evaluation limited to relatively small dimension not matching the claim of scalability - No evaluation on real-world data
1. The paper provides a solid derivation of the drift loss based on stochastic process theory, which is different from the existing methods. 2. Demonstrations on both finite-dimensional and PDE-type stochastic systems show good performance of the proposed method.
1. The paper does not compare with established SDE inference methods such as [R1],[R2],[R3] . Without such benchmarks, it is difficult to assess how much improvement the proposed method offers beyond the existing works. 2. Although the introduction mentions physics, biology, and finance, the experiments are purely toy models. It would be useful to explore whether the method could be applied to financial time series or stock dynamics, where stochastic modeling is central, or to other real data d
* The general idea is easy to follow * The proposed method is theoretically grounded and is novel
* The "Related Works" section (1.1) should be moved to a later part of the paper. Currently, it discusses specific methods and loss functions before the core model and notation have been introduced in Section 2. This disrupts the logical flow and may confuse readers. Positioning it as an independent section after the methodology would provide the necessary context for the comparisons made. * The theoretical derivation assumes continuous-time observation. In practice, data is discrete, and the m
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Taxonomy
TopicsModel Reduction and Neural Networks