(8h) Physics-Informed Neural Networks for Kinetic Parameter Estimation and Uncertainty Quantification

Top-down kinetics has mainly relied on the laborious acquisition and assessment of steady-state kinetic data obtained through standard design-of-experiments. In this work, we demonstrate that kinetic parameters can be retrieved from a reduced number of transient experiments given prior knowledge of the underlying mechanism and its associated kinetic model. Furthermore, we outline the structural limitation for information retrieval from surface experiments latent dynamics based on an algebraic indeterminacy criterion governed by stoichiometry. We utilize the mean-field approximation as a general surrogate for chemical kinetics, and artificial neural networks (ANNs) as basis functions for the solution of time-dependent ordinary differential equations (ODEs) by adapting the physics-informed artificial neural network (PINN) approach [1,2] to chemical systems' dynamics. Based on the PINN structure, we formulate the inverse chemical kinetics problem as physics-regularized regression problems (or data-regularized solution of ODEs) [3], and we extend the analysis to maximum-likelihood estimators (MLEs). MLEs provide the statistical structure for the estimation of confidence intervals for regressed model parameters through Hessian-based uncertainty quantification. This neural network-assisted framework for the analysis of chemical kinetics ODEs can be employed in the estimation of kinetic parameters and preliminary reaction mechanism discrimination based on transient data.

[1] Lagaris, I. E., Likas, A., & Fotiadis, D. I. (1997). Artificial Neural Networks for Solving Ordinary and Partial Differential Equations. IEEE Transactions on Neural Networks, 9(5), 987–1000.

[2] Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686–707.

[3] Gusmão, G. S., Retnanto, A. P., da Cunha, S. C. & Medford, A. J. (2020). Kinetics-Informed Neural Networks. ArXiv ID: 2011.14473