Identifying parameter couplings and uncertainties of mixed-noise stochastic systems via full-covariance Gaussian mixture network

[2608.15198] Identifying parameter couplings and uncertainties of mixed-noise stochastic systems via full-covariance Gaussian mixture network Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Machine Learning arXiv:2608.15198 (stat) [Submitted on 15 Aug 2026] Title: Identifying parameter couplings and uncertainties of mixed-noise stochastic systems via full-covariance Gaussian mixture network Authors: Xiaolong Wang , Xiangwen Hao , Jing Feng , Yuanyuan Liu , Yong Xu View a PDF of the paper titled Identifying parameter couplings and uncertainties of mixed-noise stochastic systems via full-covariance Gaussian mixture network, by Xiaolong Wang and 4 other authors View PDF HTML (experimental) Abstract: Parameter identification of stochastic dynamical systems driven by mixed noises is challenging due to intractable likelihood functions. We propose PENN-GMD, a parameter estimation neural network that maps partially observed trajectories to a Gaussian mixture distribution (GMD) over the system parameters. Unlike conventional uncertainty estimates, the GMD employs full covariance matrices to explicitly reveal parameter couplings and multi-modal likelihood structures. The network is trained by minimizing the negative log-likelihood via a surjective parameterization that hard-encodes all GMD constraints, thereby approximating the true likelihood. We validate the method on five numerical examples with increasing complexity, including systems driven by fractional Gaussian and Lévy noises, oscillators with colored noise, coupled neurons under different observability, and an aeroelastic airfoil with unidentifiable stochastic disturbances. Results demonstrate that PENN-GMD accurately recovers likelihood distributions, captures parameter couplings, and naturally diagnoses non-identifiability through variance broadening or mode splitting. These capabilities establish PENN-GMD as a practical tool for uncertainty-aware parameter identification in complex stochastic systems where conventional likelihood-based methods are infeasible. Subjects: Machine Learning (stat.ML) ; Machine Learning (cs.LG); Computational Physics (physics.comp-ph) Cite as: arXiv:2608.15198 [stat.ML] (or arXiv:2608.15198v1 [stat.ML] for this version) https://doi.org/10.48550/arXiv.2608.15198 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Xiaolong Wang [ view email ] [v1] Sat, 15 Aug 2026 12:30:10 UTC (7,829 KB) Full-text links: Access Paper: View a PDF of the paper titled Identifying parameter couplings and uncertainties of mixed-noise stochastic systems via full-covariance Gaussian mixture network, by Xiaolong Wang and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: stat.ML < prev | next > new | recent | 2026-08 Change to browse by: cs cs.LG physics physics.comp-ph stat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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