## Abstract

Experimental data is often comprised of variables measured independently, at different sampling rates (non-uniform Δt 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 prior to learning. Partial physical knowledge may also be available 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 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 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.

Original language | English (US) |
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Article number | 108343 |

Journal | Computers and Chemical Engineering |

Volume | 178 |

DOIs | |

State | Published - Oct 2023 |

## All Science Journal Classification (ASJC) codes

- General Chemical Engineering
- Computer Science Applications

## Keywords

- Dynamical systems
- Gray boxes
- Partial information
- Recurrent neural networks
- System identification