Some of the variables, some of the parameters, some of the times, with some physics known: Identification with partial information

Understand

Experimental data is often comprised of variables measured independently, at different sampling rates (non-uniform ${\Delta}$t between successive measurements); and at a specific time point only a subset of all variables may be sampled.

• Approaches to identifying dynamical systems from such data typically use interpolation, imputation or subsampling to reorganize or modify the training data $\textit{prior}$ to learning.
• Partial physical knowledge may also be available $\textit{a priori}$ (accurately or approximately), and data-driven techniques can complement this knowledge.
• Here we exploit neural network architectures based on numerical integration methods and $\textit{a priori}$ physical knowledge to identify the right-hand side of the underlying governing differential equations.