Angan Mukherjee

Poulomi Das, Angan Mukherjee, Debangsu Bhattacharyya

This paper proposes Variational Inference-based Bayesian Estimation with Sobol screening (VIBES), a two-stage scalable framework for Bayesian uncertainty quantification (UQ). The proposed approach combines Sobol global sensitivity analysis (GSA) for screening and dimensionality reduction, followed by variational inference (VI) for UQ of kinetic, design/operational, and economic parameters. In the first stage, Sobol GSA is performed to identify dominant variables and parameters governing uncertainty in process outputs. In the second stage, Bayesian inference is performed only on the reduced dimensional space using VI, thus reducing computational burden and enhancing scalability. The framework is demonstrated on a process for bioadhesive production through base-catalyzed depolymerization of kraft lignin and subsequent crosslinking with isolated soy protein. A Python-Aspen interface is developed for automated simulation and parameter estimation, enabling Bayesian calibration through stochastic gradient-based optimization and automatic-differentiation. The methodology is generic and readily generalizable to other biomass conversion pathways. The results show that application of VIBES consistently reduces predictive uncertainty bounds across all model outputs by more than 80%, even when only the reduced-space input variables and parameters are optimized during Bayesian estimation. The framework can be potentially applied for scalable, uncertainty-aware decision-making in high-dimensional, complex chemical process systems.

Angan Mukherjee, Tyler A. Soderstrom, Michael J. Kurtz et al.

Real-time process monitoring requires methods that extract actionable information from high-dimensional time-series data. In this work, we present a new approach for process monitoring that combines tools of topological data analysis (TDA) and machine learning. In the proposed approach, we represent multivariate time-series data as manifolds and use topological descriptors to summarize the structure of such data; we then use a neural ordinary differential equation to learn the dynamic evolution of the topological structure of the system. Using real data from an industrial process, we show that this trajectory-based event detection approach is effective at detecting diverse types of events. We contrast this approach against reconstruction-based approaches such as principal component analysis and autoencoders and against a trajectory-based approach that uses Koopman autoencoders.

Angan Mukherjee, Victor M. Zavala

Physics-constrained machine learning (PCML) combines physical models with data-driven approaches to improve reliability, generalizability, and interpretability. Although PCML has shown significant benefits in diverse scientific and engineering domains, technical and intellectual challenges hinder its applicability in complex chemical engineering applications. Key difficulties include determining the amount and type of physical knowledge to embed, designing effective fusion strategies with ML, scaling models to large datasets and simulators, and quantifying predictive uncertainty. This perspective summarizes recent developments and highlights challenges/opportunities in applying PCML to chemical engineering, emphasizing on closed-loop experimental design, real-time dynamics and control, and handling of multi-scale phenomena.