Neural ODEs constrained by the gradient of a jointly learned maximal Lyapunov function universally approximate locally exponentially stable dynamics within a region of attraction exactly given by the Lyapunov 1-sublevel set.
Dissipative symoden: Encoding hamiltonian dynamics with dissipation and control into deep learning,
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NEXUS introduces a graph-based neural energy-field model that derives forces from scalar energy and dissipation terms to achieve physically consistent contact-rich 3D dynamics.
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Locally Stable Neural ODEs with Characterized Region of Attraction
Neural ODEs constrained by the gradient of a jointly learned maximal Lyapunov function universally approximate locally exponentially stable dynamics within a region of attraction exactly given by the Lyapunov 1-sublevel set.