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

• URL: http://arxiv.org/abs/2304.14214v1
• Date: Thu, 27 Apr 2023 14:21:05 GMT
• Title: Some of the variables, some of the parameters, some of the times, with some physics known: Identification with partial information
• Authors: Saurabh Malani, Tom S. Bertalan, Tianqi Cui, Jose L. Avalos, Michael Betenbaugh, Ioannis G. Kevrekidis
• Abstract summary: We exploit neural network architectures based on numerical integration methods and $textita priori$ physical knowledge. Iterates such neural-network models allow for learning from data sampled at arbitrary time points. This enables learning unknown kinetic rates or microbial growth functions while simultaneously estimating experimental parameters.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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. 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.

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