Many engineering inverse problems are inherently ill-posed, meaning that multiple parameter combinations may explain the same experimental observations. Traditional optimization methods often provide only a single best-fit solution without quantifying the associated uncertainty. This project aims to develop Bayesian deep learning frameworks capable of efficiently approximating posterior probability distributions while providing reliable uncertainty estimates.
The research combines probabilistic machine learning, information geometry, and deep generative models to accelerate Bayesian inference for computationally expensive engineering systems. Particular emphasis is placed on understanding how the geometry of the posterior distribution influences learning dynamics, uncertainty estimation, and model robustness.
The research integrates several probabilistic learning approaches, including:
The developed frameworks are evaluated on benchmark inverse problems and engineering applications with varying levels of ill-conditioning.
This project establishes a unified probabilistic framework for solving inverse problems in computational science and engineering. By combining Bayesian inference, deep generative models, and uncertainty quantification, the research aims to enable reliable parameter estimation, uncertainty-aware prediction, and accelerated scientific discovery. The methodologies developed are applicable to computational mechanics, fluid dynamics, materials science, geophysics, and other domains requiring trustworthy Scientific Machine Learning.
Under review at Probabilistic Engineering Mechanics
Conditioning-dependent variational inference for uncertainty quantification in physics-based inverse problems — A. Srivastava, A. Hazra, R. Dubaku. arXiv:2609.25145