Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.

Area of Science:

• Chemical kinetics
• Statistical modeling
• Inverse problems

Background:

• Extracting nonlinear dynamics from time-series data is crucial in natural sciences.
• Surface heterogeneous reactions exhibit inherent nonlinearity due to multi-phase interactions and surface-area effects.
• Sparse and noisy data present significant challenges in accurately modeling these dynamics.

Purpose of the Study:

• To develop a Bayesian statistical framework for extracting nonlinear dynamics from sparse, noisy time-series data of surface heterogeneous reactions.
• To simultaneously estimate hidden variables and kinetic parameters governing these complex chemical processes.
• To demonstrate the framework's efficacy on typical surface heterogeneous reactions like dissolution and precipitation.

Main Methods:

• Adaptation of belief propagation and expectation-maximization (EM) algorithms for partial observation problems.
• Utilizing sequential Monte Carlo (SMC) algorithms within the belief propagation method to estimate nonlinear dynamical systems.
• Applying the framework to time-series data of observable intermediate product concentrations.

Main Results:

• Successfully estimated rate constants for dissolution and precipitation reactions.
• Accurately determined the temporal evolution of solid reactants and products.
• Demonstrated effective extraction of underlying nonlinear dynamics from limited observable data.

Conclusions:

• The proposed Bayesian framework provides a robust method for analyzing nonlinear dynamics in surface heterogeneous reactions.
• The approach is effective even with sparse and noisy observational data, enabling accurate parameter and state estimation.
• This work offers a powerful tool for understanding complex chemical processes in various scientific domains.