Neural ordinary differential equations (neural ODEs) are effective priors for modeling continuous time dynamical systems, being neural network analogues of the differential equation-based modeling paradigm of the physical sciences. However, training these models can be difficult in practice, especially for long or chaotic time series data.

In this talk, I will first provide an overview of neural ODEs, followed by a discussion of their unstable training problem. After presenting two methods to effectively train neural ODEs - homotopy-based training, and neighborhood-based training - I will close with a brief showcase of an experimental physics application: inverting atomic force microscope measurements with neural ODEs to infer unknown tip-sample interaction forces.