Credit: UC San Diego Publications | Copyright Regents of the University of California
I am broadly interested in computational methods and numerical analysis for control, optimization, design and uncertainty quantification of complex and large-scale systems. I work on using reduced-order models in the context of multifidelity and data-driven modeling, optimization and control, uncertainty quantification, reliability-based design, and design under uncertainty. More information can be found on my CV.
I am affiliated with the Center for Extreme Events Research (CEER) as well as the Center for Computational Mathematics (CCoM). Interested graduate students in the Graduate Program in Computational Science, Mathematics and Engineering can contact me to dicuss opportunities.
Department of Mechanical and Aerospace Engineering
University of California San Diego
Jacobs Hall (EBU1) | Room 3113
9500 Gilman Drive | La Jolla | CA 92093-0411
Sept. 2021: The IACM Conference on Mechanistic Machine Learning and Digital Twins for Computational Science, Engineering & Technology will be hosted here in San Diego from September 26-29, 2021, and I am excited to be on the local organizing committee. Stay tuned for updates.
Oct. 2020: Welcome to Stephen Chen and Nate Linden, who joined our group as PhD students in Fall 2020.
Oct. 2020: Our paper Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms (with Peter Benner, Pawan Goyal, Benjamin Peherstorfer and Karen Willcox) appeared in Computer Methods for Applied Mechanics and Engineering. The paper shows that non-polynomial nonlinear systems can be learned directly from data and additional knowledge about the nonlinear function.
Sept. 2020: Just posted our paper Stability Domains for Quadratic-Bilinear Reduced-Order Models. The paper considers a computational approach to estimate the stability domain of quadratic-bilinear reduced-order models, yielding qualitative information about stability. Applications on several different test problems and model reduction techniques show that while still conservative, the approach yields stability domains that are several orders of magnitude larger than analytic estimates in the literature.
Sept. 2020: With a great team of collaborators at MIT and the University of Michigan, we obtained an award for SWQU: Composable Next Generation Software Framework for Space Weather Data Assimilation and Uncertainty Quantification, where we will be integrating data-driven and projection-based model reduction for space weather applications, and use them in the context of uncertainty quantification. Refer to the UCSD news article Making space weather forecasts faster and better for more info.
Jul. 2020: Excited to receive the DoD Newton award to work with Prof. Melvin Leok on structure-preserving model reduction, see the news release: Mathematician, Engineer receive Newton Award for Transformative Ideas during COVID-19 Pandemic, and also the DoD announcement.
Jul. 2020: I am excited to partner with Confluency LLC, Chicago on an NSF Grant 2004275 SBIR Phase I: Human-Centered, Augmented Intelligence Software for Water and Wastewater. This Small Business Innovation Research (SBIR) Phase I project will develop methods for combining multi-fidelity simulation models and data-driven models to support decision-making for both long-term planning needs and real-time operational decision support for water and wastewater systems.
Apr. 2020: Over the last two years, we have developed new methods to learn nonlinear dynamical systems from data as part of the Air Force Center of Excellence Multi-Fidelity Modeling of Rocket Combustion Dynamics. In collaboration with Renee Swischuk, Elizabeth Qian, Benjamin Peherstorfer, Cheng Huang and Karen Willcox, we published those results in Learning Physics-Based Reduced-Order Models for a Single-Injector Combustion Process and Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems (see the Publications page for dowload and Codes for the source code and data.) Some recent media coverage:
Mar. 2020: Due to the COVID-19 outbreak, several upcoming conferences that I would have attended got cancelled: The SIAM Conference on Mathematics of Data Science, the SIAM Annual Meeting 2020, the Southern California Applied Mathematics Symposium and the 2020 Center for Extreme Events Research (CEER) Research Summit at UC San Diego. In the absense of those venues, I'll be posting more research updates here and feel free to reach out.
Mar. 2020: Our paper Learning Physics-Based Reduced-Order Models for a Single-Injector Combustion Process (with Renee Swischuk, Cheng Huang, Karen Willcox) finally appeared in AIAA Journal. This paper learns a data-driven reduced-order model from simulated combustion data of over 300,000 degrees of freedom.
Feb. 2020: Our paper Adaptive reduced-order model construction for conditional value-at-risk estimation (with Matthias Heinkenschloss and Timur Takhtaganov) got accepted to SIAM/ASA Journal on Uncertainty Quantification.
Feb. 2020: Our paper Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems (with Elizabeth Qian, Benjamin Peherstorfer, Karen Willcox) appeared in Physica D: Nonlinear Phenomena.
Feb. 2020: I attended the ICERM Workshop on Mathematics of Reduced Order Models at Brown University and presented work on Operator Inference for non-polynomial systems & control.
Jan. 2020: Our paper Information reuse for importance sampling in reliability-based design optimization got accepted in Reliability Engineering & System Saftey, and was mentioned in the Aerospace America: 2019 Year in Review.
Jan. 2020: Our paper Learning physics-based reduced-order models for a single-injector combustion process (with Renee Swischuk, Cheng Huang, Karen Willcox) appeared in the conference proceedings of the AIAA SciTech 2020 Forum.
Jan. 2020: Our paper Risk-based design optimization via probability of failure, conditional value-at-risk, and buffered probability of failure (with Anirban Chaudhuri and Matthew Norton) appeared in the conference proceedings of the AIAA SciTech 2020 Forum.
Nov. 2019: I attended the Workshop on Feedback control and gave a talk on "LQR control for systems with uncertain parameters via online‐adaptive reduced models." The workshop was part of an excellent Special Semester on Optimization at the Johann-Radon Institute for Computational and Applied Mathematics (RICAM), JKU Linz.
Oct. 2019: At the ENUMATH 2019 conference, I presented Lifting transformations and model reduction as well as Reduced order models for risk measure estimation in robust design..
Jul. 2019: Our paper Balanced truncation model reduction for lifted nonlinear systems (with Karen Willcox) is now posted on arxiv, see arXiv:1907.12084.
Jul. 2019: I attended the 15th U.S. National Congress on Computational Mechanics in Austin, TX presented Multifidelity Estimation of Risk Measures in Robust Design on July 31 from 3:40pm-4:00pm in MS#205 Multilevel/Multifidelity Strategies for Uncertainty Quantification.
Jun. 2019: Two papers that I co-authored are on the most-cited list of SIAM Journal of Uncertainty Quantification (accessed 06/17/2019), see Conditional-Value-at-Risk Estimation via Reduced-Order Models (with Matthias Heinkenschloss, Timur Takhtaganov, Karen Willcox) and Multifidelity Preconditioning of the Cross-Entropy Method for Rare Event Simulation and Failure Probability Estimation (with Benjamin Peherstorfer, Karen Willcox).
Jun. 2019: Our conference paper Transform & Learn: A data-driven approach to nonlinear model reduction. (with Elizabeth Qian, Alexandre Marques and Karen Willcox) appeared in the proceedings of the AIAA Aviation 2019 Forum. Software for this publication available under https://github.com/elizqian/transform-and-learn and we have also made a more general operator inference code available at https://github.com/elizqian/operator-inference .
May 2019: Our paper Multifidelity probability estimation via fusion of estimators (with Alexandre Marques, Umberto Villa, Benjamin Peherstorfer and Karen Willcox) is now published at the Journal of Computational Physics, link.
Apr. 2019: Our paper Nonlinear Model Order Reduction via Lifting Transformations and Proper Orthogonal Decomposition (with Karen Willcox) appeared online at AIAA Journal, link.
Dec. 2018: After 3.5 years of review, our patent finally got granted: US10145576B2: System and method for controlling operations of air-conditioning system.
04/04 - 04/05/2019: I attended the East Coast Optimization Meeting 2019 at George Mason University and presenting recent results on conditional-value-at-risk estimation via reduced models.
02/25 - 03/01/2019: I attended the SIAM CSE 2019 conference. There, together with Dr. Kevin Carlberg, we are organized the minisymposium MS343: Data-augmented Reduced-order Modeling: Operator Learning and Closure/error Modeling. I also gave a talk about Lifting Nonlinear Systems: More Structure, More Opportunities for ROM? at MS60 organized by Troy Butler and Steve Matthis.
11/16/2018: I presented work on "Lifting transformations for dynamical systems and model reduction" as part of the Kolchin seminar at the City University of New York (CUNY)".
11/06/2018: I gave a talk about "Nonlinear model reduction for complex systems" at the University of Washington Mechanical Engineering Graduate seminar.
10/23/2018: Our paper Conditional-Value-at-Risk Estimation via Reduced-Order Models (with Matthias Heinkenschloss, Timur Takhtaganov, Karen Willcox) just appeared online at SIAM/ASA Journal of Uncertainty Quantification.
07/27/2018: I presented at WCCM 2018 conference about "Stabilization of reduced-order flow models through learning-based closure modeling".
After three years, our patent finally got granted on May 22, 2018: US9976765B2: System and method for controlling operations of air-conditioning system.
05/30 – 06/01: Karen Willcox organized a workshop on Data to Decisions: Computational Methods for Design of Next-Generation Engineered Systems Workshop. where I presented recent work.
04/23/2018: I gave a talk at the Tufts Computational and Applied Math Seminar about "Conditional-Value-at-Risk Estimation with Reduced-Order Models".
04/10-13/2018: I presented at the MoRePaS IV conference (Model Reduction of Paramatrized Systems) in Nantes, France.
03/15/2018: Our paper System identification via CUR-factored Hankel approximation (with Alex A. Gorodetsky) appeared online in SIAM Journal of Scientific Computing.
03/6-9/2018: The workshop Reducing Dimensions and Cost for UQ in Complex Systems was a great opportunity to connect with other researchers, and I am happy that I could present recent results on Conditional-Value-at-Risk estimation there.
03/02/2018: I presented work on "Conditional-Value-at-Risk Estimation with Reduced-Order Models" at our in-house Aerospace Computational Design Lab (ACDL) seminar series.
02/03/2018: I gave a colloquium talk on "Reduced-order models for data-driven modeling and uncertainty quantification" at the Department of Mathematics at Dartmouth College, Hanover, NH.
11/21/2017: I gave a presentation about "Model reduction for uncertainty quantification of high-dimensional systems" at the Department of Mathematics at the Johannes Gutenberg University Mainz.
10/9-13/2017, I visited Professor Matthias Heinkenschloss at Rice University to work on efficient computation of risk measures in optimization.
07/10/2017: During the SIAM Conference on Control and its Applications in Pittsburgh I presented work on "Data-Driven Reduced-Order Models for Control of PDEs with Uncertain Parameters".
06/26/2017: I presented work on "Stabilization of reduced-order flow models through learning-based closure modeling" at the Conference on Classical and Geophysical Fluid Dynamics: Modeling, Reduction and Simulation at Virginia Tech.
05/23/17: At the SIAM Optimization conference in Vancouver, I presented our work on "Data-Driven Model Reduction via CUR-Factored Hankel Approximation".
04/18/2017: I gave a talk at the Sibley School of Mechanical and Aerospace Engineering at Cornell about "Exploiting Low-Dimensional Structures for Sensing and Control of Fluids via Data-Driven Reduced-Order Modeling".
04/03/17: We organized a minisymposium on "Uncertainty Quantification and Model Inadequacy in Combustion Simulations" at the 2017 SIAM International Conference on Numerical Combustion (with Todd Oliver). There, I presented "Multifidelity Failure Probability Estimation in Combustion Modeling".
03/30-31/17: I visited Professor Karthik Duraisamy at the University of Michigan.
03/17/17: I gave a presentation at the Department of Mathematics Colloquium at Virginia Tech.
03/15/17: I gave a talk on "Data-driven low-dimensional modeling for analysis and decision-making" at Sandia National Laboratories in Livermore, CA.
03/02/2017 I presented our work on "Multifidelity Computation of Failure Probabilities" at the SIAM CSE 2017 in Atlanta, GA.
02/28/2017 We co-organized a minisymposium on "Model Order Reduction: Perspectives from Junior Researchers" at SIAM CSE 2017 (with Alessandro Alla ).
02/15/2017: I gave a presentation about "Exploiting low-dimensional structures for sensing and control of fluids via data-driven reduced-order modeling at the "Computational Science Seminar", Department of Mathematics, University of Massachusetts Dartmouth, February 15, 2017.
02/02/2017: I presented our work on "Data-driven modeling for control of systems with time-varying and uncertain parameters" at the workshop on "Data-Driven Methods for Reduced-Order Modeling and Stochastic Partial Differential Equations" at the Banff International Research Station in Canada.
Jan 16-20,2017: I visited Professor Matthias Heinkenschloss at Rice University to work on risk measure estimation and computation.