(261a) Data-Driven Dynamic Modeling and Uncertainty Quantification Using Variational Inference: Applications to Microkinetic Modeling

Variational inference (VI) has emerged as a powerful framework for scalable Bayesian inference. This approach enables efficient probabilistic modeling and uncertainty quantification of complex dynamical systems [1]. Unlike traditional Markov Chain Monte Carlo (MCMC) approaches, which can lead to significant computational overhead for high dimensional systems, VI formulates the estimation of the posterior parameter density as an optimization problem, thus making the approach scalable and flexible [2]. VI has been applied in deep learning, reinforcement learning, and probabilistic programming, but its application to physics-constrained machine learning (PCML) remains underexplored, particularly for dynamic chemical processes where predictive uncertainty and physical consistency is ndeed.

In this work, we propose a VI-PCML framework for dynamic data-driven modeling and uncertainty quantification. We focus our developments to applications to microkinetic modeling (MKM), which is a widely used modeling technique used in heterogeneous catalysis. Specifically, MKM aims to elucidate detailed reaction mechanisms from data, which is essential for catalyst design [3]. However, MKM often involves large sets of kinetic parameters, which can introduce significant model uncertainty due to data sparsity. By leveraging VI, we reformulate the kinetic parameters as probability distributions rather than fixed values [4], thus improving model reliability, interpretability, and robustness. The approach integrates neural ordinary differential equations (NODEs) with VI to approximate the posterior distribution of kinetic parameters while incorporating observational data to generate physically consistent predictions. This formulation also accommodates hybrid modeling approaches [5] to capture the dynamics of process variables that are either partially observed or inaccurately modeled by the mechanistic model.

A key advantage of the proposed VI-PCML framework is its ability to account for unknown phenomena such as catalyst degradation, mass transfer limitations, and other latent effects that traditional MKM approaches fail to capture explicitly. By learning optimal parameters from data while satisfying physical constraints, we show that our approach enhances both generalizability and predictive reliability. We demonstrate that the proposed framework significantly reduces predictive uncertainty compared to standard ML models that lack physical constraints. This work highlights the potential of VI as a key enabler for PCML, paving the way for robust, interpretable data-driven dynamic modeling and uncertainty quantification in chemical process systems.

References

1. Bacsa, K., Lai, Z., Liu, W., Todd, M. & Chatzi, E. Symplectic encoders for physics-constrained variational dynamics inference. Sci Rep 13, 2643 (2023).

2. Glyn-Davies, A., Vadeboncoeur, A., Akyildiz, O. D., Kazlauskaite, I. & Girolami, M. A Primer on Variational Inference for Physics-Informed Deep Generative Modelling. arXiv preprint arXiv: 2409.06560 (2024).

3. Motagamwala, A. H. & Dumesic, J. A. Microkinetic Modeling: A Tool for Rational Catalyst Design. Chem Rev 121, 1049–1076 (2021).

4. Thompson, J. C., Zavala, V. M. & Venturelli, O. S. Integrating a tailored recurrent neural network with Bayesian experimental design to optimize microbial community functions. PLoS Comput Biol 19, e1011436 (2023).

5. Mukherjee, A. et al. Development of hybrid first principles – artificial intelligence models for transient modeling of power plant superheaters under load-following operation. Appl Therm Eng 262, 124795 (2025).