Neural Vector Field Transformations: Learning the Flow of Autonomous Systems by Conjugation to Explicitly Integrable Reference Flows

Andrew Qing He

We represent the flow map of an autonomous ODE $\dot{x}=f(x)$ as a conjugate ${\Phi }_t=F_{\theta }^{-1}\circ {\Psi }_t\circ F_{\theta }$ of an explicitly integrable reference flow ${\Psi }_t$ by an invertible neural…