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Overview
Overview
Over the past seven decades, advances in computational methods for simulating physical processes have reshaped science and engineering. Today, we increasingly rely on simulation-based predictions to guide critical decisions, from evaluating engineered systems to mitigating natural hazards. With such high stakes, we must insist that the predictions be trustworthy and include quantified uncertainty to support risk-aware decision-making.
My research seeks to achieve this objective through a multifaceted approach that integrates theory, data, and experiments utilizing advanced computational methods for multiscale modeling, uncertainty quantification, and scientific machine learning.
Select from a research theme, a methodological innovation, or a specific engineering and science application listed below to learn more.
Theme
Theme
(T1)
Multiscale Modeling
and Analysis
(T1)
Multiscale Modeling
and Analysis
Macroscopic physical models often arise from the coarse-graining of microscopic processes and exhibit trade-offs between fidelity and computational feasibility. I study this trade-off for coarse-graining methods in statistical and solid mechanics. I design machine learning methods to construct macroscale models from microscale data, grounded in approximation theory and physical laws.
(T2)
Fusion of Models, Data, and Experiments
(T2)
Fusion of Models, Data, and Experiments
Acknowledging that no model is perfect, I systematically assimilate scientific data into computational models with uncertainty quantification to assess their validity and enhance reliability. This includes Bayesian approaches to parameter and state estimation, model validation, and optimal experimental design, which are empowered by probabilistic and machine learning methods tailored to specific applications.
(T3)
Algorithms for Simulation, Inference, and Control
(T3)
Algorithms for Simulation, Inference, and Control
Risk-aware prediction and control of physical systems often require repeated solutions of computational models, thus demanding efficient algorithms. I develop derivative-based algorithms for PDE-constrained optimization, dimension reduction, operator learning, and statistical sampling with theoretical certification. These algorithms enable efficient, scalable uncertainty quantification and control for large-scale computational models that would otherwise be intractable.
Methodology
Methodology
(M1)
Derivative-Informed Operator Learning
For Bayesian Inverse Problems
(M1)
Derivative-Informed Operator Learning
For Bayesian Inverse Problems
I study DINO (Derivative-Informed Neural Operator), a supervised learning method for building ML surrogates of parametric PDEs. Unlike black-box approaches, DINO integrates sensitivity information (e.g., Frechet derivative) into the neural operator architecture and training. This improves surrogate construction efficiency by orders of magnitude and enhances the performance of surrogate-driven optimization and uncertainty quantification. We demonstrate DINO's ability to solve high-dimensional Bayesian inverse problems: it accelerates geometric MCMC by 2–9x and powers LazyDINO, an amortized inference method that is orders of magnitude more cost-efficient than competing approaches.
(M2)
Sequantial Bayesian Inference and
Optimal Experimental Design
(M2)
Sequantial Bayesian Inference and
Optimal Experimental Design
Sequential Bayesian inference involves recursively updating the probability distribution of the uncertain parameter in a model based on a stream of noisy observations of the environment. It plays a central role in problems cast as partially observed Markov decision processes, e.g., in predictive digital twins and sequential Bayesian experimental design. I develop advanced algorithms for sequential Bayesian inference and experimental design, particularly algorithms that enable real-time filtering and optimization using probabilistic and machine-learning methods, such as flow-based generative models and deep-learning surrogate models.
Applications
Applications
(A1)
Block Copolymers and Nanofabrication
(A1)
Block Copolymers and Nanofabrication
Block copolymer (BCP) melts undergo microphase separation upon quenching, forming a rich set of nanostructures. This process is amenable to external guidance, making BCP a promising building block for nanofabrication. However, the at-scale deployment of BCP directed self-assembly (DSA) in nanofabrication is hindered by a high risk of defect formation. My work aims to enable simulations of DSA with quantified uncertainty and risk-aware DSA design.
(A2)
Data-Driven Multiscale Inelasticity
(A2)
Data-Driven Multiscale Inelasticity
Complex, history-dependent material behaviors arise from microscale mechanisms that are costly to resolve, and their constitutive models are often weakly identifiable from macroscale experiments due to unobserved and uncontrolled microscale physics. I develop theory and computational methods for learning macroscale constitutive models using data obtained from microscale simulations and designed experiments.
(A3)
Natural Hazard Prediction
and Mitigation
(A3)
Natural Hazard Prediction
and Mitigation
Coming soon...
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