Data-driven discovery and control of multistable nonlinear systems and hysteresis via structured Neural ODEs
For engineers modeling multistable physical systems with limited excitation data, this provides a tractable and stable identification method with control capabilities.
The paper proposes a structured Neural ODE architecture that enforces trajectory stability and parameterizes multistable systems by learning a vector field with contraction and attractor location terms. The method efficiently captures multiple basins of attraction from short training data and enables gradient-based feedback control.
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 $g$.