Data-driven discovery and control of multistable nonlinear systems and hysteresis via structured Neural ODEs
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917365566930944 |
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| author | Salas, Ike Griss King, Ethan |
| author_facet | Salas, Ike Griss King, Ethan |
| contents | Many engineered physical processes exhibit nonlinear but asymptotically stable dynamics that converge to a finite set of equilibria determined by control inputs. Identifying such systems from data is challenging: stable dynamics provide limited excitation and model discovery is often non-unique. We propose a minimally structured Neural Ordinary Differential Equation (NODE) architecture that enforces trajectory stability and provides a tractable parameterization for multistable systems, by learning a vector field in the form $F(x,u) = f(x)\,(x - g(x,u))$, where $f(x) < 0$ elementwise ensures contraction and $g(x,u)$ determines the multi-attractor locations. Across several nonlinear benchmarks, the proposed structure is efficient on short time horizon training, captures multiple basins of attraction, and enables efficient gradient-based feedback control through the implicit equilibrium map $g$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27024 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Data-driven discovery and control of multistable nonlinear systems and hysteresis via structured Neural ODEs Salas, Ike Griss King, Ethan Systems and Control Mathematical Physics Dynamical Systems Many engineered physical processes exhibit nonlinear but asymptotically stable dynamics that converge to a finite set of equilibria determined by control inputs. Identifying such systems from data is challenging: stable dynamics provide limited excitation and model discovery is often non-unique. We propose a minimally structured Neural Ordinary Differential Equation (NODE) architecture that enforces trajectory stability and provides a tractable parameterization for multistable systems, by learning a vector field in the form $F(x,u) = f(x)\,(x - g(x,u))$, where $f(x) < 0$ elementwise ensures contraction and $g(x,u)$ determines the multi-attractor locations. Across several nonlinear benchmarks, the proposed structure is efficient on short time horizon training, captures multiple basins of attraction, and enables efficient gradient-based feedback control through the implicit equilibrium map $g$. |
| title | Data-driven discovery and control of multistable nonlinear systems and hysteresis via structured Neural ODEs |
| topic | Systems and Control Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2603.27024 |