José L. Avalos‬

Saurabh Malani, Tom S. Bertalan, Tianqi Cui et al.

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.

Sebastián Espinel-Ríos, José Montaño López, José L. Avalos

This work presents an omics-driven modeling pipeline that integrates machine-learning tools to facilitate the dynamic modeling of multiscale biological systems. Random forests and permutation feature importance are proposed to mine omics datasets, guiding feature selection and dimensionality reduction for dynamic modeling. Continuous and differentiable machine-learning functions can be trained to link the reduced omics feature set to key components of the dynamic model, resulting in a hybrid model. As proof of concept, we apply this framework to a high-dimensional proteomics dataset of $\textit{Saccharomyces cerevisiae}$. After identifying key intracellular proteins that correlate with cell growth, targeted dynamic experiments are designed, and key model parameters are captured as functions of the selected proteins using Gaussian processes. This approach captures the dynamic behavior of yeast strains under varying proteome profiles while estimating the uncertainty in the hybrid model's predictions. The outlined modeling framework is adaptable to other scenarios, such as integrating additional layers of omics data for more advanced multiscale biological systems, or employing alternative machine-learning methods to handle larger datasets. Overall, this study outlines a strategy for leveraging omics data to inform multiscale dynamic modeling in systems biology and bioprocess engineering.