Some of the variables, some of the parameters, some of the times, with some physics known: Identification with partial information
This addresses the challenge of system identification from incomplete and irregularly sampled data for researchers in fields like physics and biology, but it appears incremental as it builds on existing neural network and physics-informed approaches.
The paper tackles the problem of identifying dynamical systems from experimental data with non-uniform sampling and partial variable measurements, using neural networks based on numerical integration and partial physical knowledge to learn governing differential equations without data modification. The result is a method that enables learning unknown functions like kinetic rates or microbial growth while estimating experimental parameters, though no concrete numbers are provided.
Experimental data is often comprised of variables measured independently, at different sampling rates (non-uniform $Δ$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. Iterates of such neural-network models allow for learning from data sampled at arbitrary time points $\textit{without}$ data modification. Importantly, we integrate the network with available partial physical knowledge in "physics informed gray-boxes"; this enables learning unknown kinetic rates or microbial growth functions while simultaneously estimating experimental parameters.