Learning Nonlinear Continuous-Time Systems for Formal Uncertainty Propagation and Probabilistic Evaluation
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910012189704192 |
|---|---|
| author | Amorese, Peter Lahijanian, Morteza |
| author_facet | Amorese, Peter Lahijanian, Morteza |
| contents | Nonlinear ordinary differential equations (ODEs) are powerful tools for modeling real-world dynamical systems. However, propagating initial state uncertainty through nonlinear dynamics, especially when the ODE is unknown and learned from data, remains a major challenge. This paper introduces a novel continuum dynamics perspective for model learning that enables formal uncertainty propagation by constructing Taylor series approximations of probabilistic events. We establish sufficient conditions for the soundness of the approach and prove its asymptotic convergence. Empirical results demonstrate the framework's effectiveness, particularly when predicting rare events. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05103 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Learning Nonlinear Continuous-Time Systems for Formal Uncertainty Propagation and Probabilistic Evaluation Amorese, Peter Lahijanian, Morteza Systems and Control Dynamical Systems Nonlinear ordinary differential equations (ODEs) are powerful tools for modeling real-world dynamical systems. However, propagating initial state uncertainty through nonlinear dynamics, especially when the ODE is unknown and learned from data, remains a major challenge. This paper introduces a novel continuum dynamics perspective for model learning that enables formal uncertainty propagation by constructing Taylor series approximations of probabilistic events. We establish sufficient conditions for the soundness of the approach and prove its asymptotic convergence. Empirical results demonstrate the framework's effectiveness, particularly when predicting rare events. |
| title | Learning Nonlinear Continuous-Time Systems for Formal Uncertainty Propagation and Probabilistic Evaluation |
| topic | Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2602.05103 |