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

Experimental data is often comprised of variables measured independently, at different sampling rates (non-uniform Δt between successive measurements); and a specific time point only subset all may be sampled. Approaches to identifying dynamical systems from such typically use interpolation, imputation or subsampling reorganize modify the training prior learning. Partial physical knowledge also available priori (accurately approximately), data-driven techniques can complement this knowledge. Here we exploit neural network architectures based on numerical integration methods identify right-hand side underlying governing differential equations. Iterates neural-network models allow for learning sampled arbitrary points without modification. Importantly, integrate with partial in “physics informed gray-boxes”; enables unknown kinetic microbial growth functions while simultaneously estimating experimental parameters.