We are a research group on Scientific Machine Learning (SciML) and Uncertainty Quantification (UQ) at the School of Computational Science and Engineering (CSE), Georgia Tech. Our research is driven by grand challenge problems in scientific and engineering fields that involve data-driven modeling, learning, and optimization of complex systems under uncertainty.
Examples of such problems include (1) how to quantify the system predictive accuracy of simulation-based or machine learning-based models under uncertain system and/or model parameters; (2) how to best learn and mitigate infectious diseases like COVID-19 from heterogeneous models, incomplete data, and uncertain track of disease spread; (3) how to robustly design new materials, such as nanoscale self-assembly materials in semiconductor and artificially engineered metamaterials in acoustic and electromagnetic devices under the uncertainty arising from material properties and manufacturing errors; (4) how to optimally design magnetic confinement devices and control coil currents for plasma fusion to harness fusion energy under the imprecision of the device shape and current control; (5) how to better characterize the sensitivity of cardiovascular diseases such as heart attack, stroke, aneurysms, etc., with respect to different physiological abnormalities and to better quantify the risk or reliability of corresponding treatments under large and uncertain variation of personalized physiological conditions; (6) how to optimally place sea-floor sensors to detect undersea earthquakes for tsunami early warning under the uncertainty of where, when, and how large the earthquake may happen.
These problems brings significant challenges in high-fidelity modeling, large-scale simulation, high-dimensional Bayesian inference and data assimilation, optimal data acquisition and experimental design, as well as stochastic optimization for system design and control, all under various uncertainties. We tackle these challenges by developing fast, scalable, and parallel computational methods, which exploit the structure of the problems, including geometry, sparsity, intrinsic low-dimensionality, smoothness, derivative information, etc. Specific methods we have been developing include projected neural networks/operators, weighted/adaptive/goal-oriented reduced basis, high-order functional Taylor approximation, randomized low-rank tensor/operator decompositions, adaptive sparse grid interpolation/integration, derivative-based scalable optimization methods using high-order adjoints, symbolic differentiation, or automatic differentiation, etc.
Our vision is to build real-time digital twins of real-world complex systems in, e.g., materials, energy, health, natural hazard, and use them to learn, simulate, and optimize the systems, while quantifying uncertainties that may bring significant impact such as the butterfly effect on the system performance.
Office: CODA E1350B
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Address: 756 West Peachtree Street Northwest, Atlanta, GA 30308