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. I am affiliated with the Center for Extreme Events Research (CEER) as well as the Center for Computational Mathematics (CCoM).
Department of Mechanical and Aerospace Engineering
University of California San Diego
Jacobs Hall (EBU1) | Room 3113
9500 Gilman Drive | La Jolla | CA 92093-0411
September 19-23, 2022: I am very honored to be an invited speaker at the Model Reduction and Surrogate Modeling (MORE) conference in Berlin. The MORE is merger of the triannual MoRePaS and MODRED conferences, and the leading conference of the model reduction community. Always gret to see new and old faces and learn about new research directions at such a well-run conference.
August 18-19, 2022: Our Postdocs Harsh Sharma and Dongjin Lee will attend the USACM Thematic Conference on Uncertainty Quantification for Machine Learning Integrated Physics Modeling (UQ-MLIP) and present posters on Bayesian Identification of Nonseparable Hamiltonian Systems Using Stochastic Dynamic Models (H. Sharma) and A Bi-Fidelity Method for Coherent Risk Assessment of Non-Linear Systems Under Dependent and High-Dimensional Random Variables (D. Lee).
August 13, 2022: I wrote a short News & Views article for Nature Computational Science about Learning state variables for physical systems. The problem of automatically determining state variables for physical systems is challenging, but essential in the modeling process of almost all scientific and engineering processes. That short perspective/discussion article reviews recent work and highlights a few interesting directions.
August 13, 2022: In our third science outreach event this year, we are hosting a science booth themed "Space Research at UCSD" at the Southeast San Diego Science & Art Expo, an inclusive science, art, and culture event that welcomes families from around San Diego County. This event features the Southeast San Diego STEM Ecosystem, UC San Diego, and other community partners to highlight science, art, and culture in the world around us.
August 10, 2022: Welcome to our new PhD students Hyeonghun Kim and Boyang Li. Hyeonghun is interested in data-driven reduced-order modeling methods to better understand high-dimensional dynamical systems and to control them. He joins us with a B.S. in Mechanical & Electrical Control Engineering from Handong Global University in South Korea. Boyang is co-advised with Prof. Sylvia Herbert and is interested in developing control methodologies that possess both mathematical formality and versatility in application to various robotics systems, drawing ideas from optimization theory, dynamical systems, and machine learning. Boyang just graduated with a B.Sc. in Mathematics and Physics from William & Mary.
June 19 - July 02, 2022: Opal Issan and Boris Kramer attended the back-to-back Geospace Environment Modeling (GEM) workshop and the Solar Heliospheric and INterplanetary Environment (SHINE) workshop and present their work on reduced-order modeling for solar physics applications there. This is a new research direction for our group and is funded through the NSF SWQU: Composable Next Generation Software Framework for Space Weather Data Assimilation and Uncertainty Quantification. We learned a good deal about this application and saw some really exciting research.
July 31-August 5, 2022: The WCCM was moved to fully virtual. We organized a minisymposium together with Yuto Miyatake on Structure-preserving model reduction for nonlinear systems.
June 1-3, 2022: To honor Prof. Terry Herdman's retirement from Virginia Tech, there was a conference on Applied and Computational Mathematics. where I could give a talk on "Learning reduced-order models via structure-preserving operator inference". It was great to be back to Virginia Tech and see all the great things the ``ICAMlers" have done through the decades..
May 31, 2022: Our research group attended the Southern California Applied Mathematics Symposium (SOCAMS) sponsored by SIAM and hosted by Harvey Mudd. They presented their most recent research as follows: Dr. Harsh Sharma ("Preserving Lagrangian Structure in Data-Driven Reduced-Order Modeling of Large-Scale Mechanical Systems"), Opal Issan ("Predicting Solar Wind Streams from the Inner-Heliosphere to Earth via Shifted Operator Inference"), Dr. Dongjin Lee ("A bi-fidelity method for conditional-value-at-risk estimation under dependent and high-dimensional random variables"), Nate Linden ("A Bayesian Framework for Parameter Estimation from Sparse and Noisy Measurement Data in Systems Biology"). This was a great opportunity to meet researchers and graduate students in the Southern California region working on similar problems.
May 23-June 01, 2022: The Institute for Computational and Experimental Research in Mathematics (ICERM) at Brown University is doing a fantastic job of hosting the Spring 2020 Reunion Event. This event gets researchers from the winter/spring 2020 workshops back together in person. It was a great time to see many of my colleagues again and to work together on publications, proposals, and just to discuss research.
April 12-15, 2022: It was great to attend the SIAM UQ 2022 conference in Atlanta in person again and seeing so many familiar faces. Together with Prof. Rebecca Morrison, we organized a minisymposium with seven speakers on Uncertainty quantification and data assimilation for space weather applications, which highlighted research on our project SWQU: Composable Next Generation Software Framework for Space Weather Data Assimilation and Uncertainty Quantification. Postdoc Dr. Dongjin Lee presented his recent work Coherent Risk Assessment for Nonlinear Structural Analysis via Reduced-Order Models and graduate student Nate Linden presented his work on Bayesian Parameter Estimation from Sparse and Noisy Measurement Data in Systems Biology.
April 12, 2022: Nate Linden's first paper since joining UCSD just posted. Its title is Bayesian Parameter Estimation for Dynamical Models in Systems Biology. The paper is addressing the challenges that one faces with UQ in systems biology models, which are low-dimensional (few states) but have a much higher number of parameters that enter nonlinearly into the ODEs. Plus, one is almost never able to sense all state variables, and the measurements are sparse in time and corrupted with noise. Nate proposes a comprehensive framework that starts with identifiability and sensitivity analysis to reduce the number of parameters to be learned, and then uses the unscented Kalman filter Markov chain Monte Carlo algorithm to learn the posterior distribtions of the parameters.
April 7, 2022: Postdoc Dongjin Lee posted his recent work Bi-fidelity conditional-value-at-risk estimation by dimensionally decomposed generalized polynomial chaos expansion. on arxiv. Risk measure estimation has been an interest of our group for a few years now, and this work addresses a specific challenge of high-dimensional and dependent input random variables. Most existing methods make an independence assumption, yet Dongjin's dynamically decomposed generalized polynomial chaos expansion (DD-GPCE) can handle arbitrary and dependent input RVs. Moreover, we suggest an additional approximation of the output quantity of interest via a Fourier polynomial expansion, reducing computational cost of the estimation process when we are dealing with complex systems with large state spaces.
Mar 28, 2022: Opal Issan's paper Predicting solar wind streams from the inner-Heliosphere to Earth via shifted operator inference. is up on arxiv. The work derives novel ROMs to predict solar wind from the heliosphere to Earth and compares the derived models to reduced-physics approximations, finding that the latter are less accurate. Along the way, Opal derived a new shifted operator inference framework to learn polynomial dynamical systems models directly from data by incorporating translational symmetries into the model learning method.
Mar 12, 2022: Harsh Sharma's paper Preserving Lagrangian structure in data-driven reduced-order modeling of large-scale mechanical systems. is up on arxiv. This work presents a nonintrusive physics-preserving method to learn reduced-order models for Lagrangian mechanical systems. The numerical results demonstrate Lagrangian operator inference on an Euler-Bernoulli beam model and a soft-robotic fishtail model with 779,232 degrees of freedom.
Feb 4, 2022: Upon placing 49 new Starlink satellites in low-earth orbit, the following day 40 of those were lost due to a geomagnetic storm that caused atmospheric drag to increase by as much as 50%, see some references here and at space.com. This shows the importance of predicting space weather events and atmospheric drag. Our project SWQU: Composable Next Generation Software Framework for Space Weather Data Assimilation and Uncertainty Quantification is working on exactly that, as are integrating data-driven and projection-based model reduction for space weather and use them in the context of uncertainty quantification.
Jan 18, 2022: I am giving a talk about Learning dynamics of nonlinear fluid models via structure-preserving operator inference at the fluid mechanics seminar at Stanford University.
Jan 11, 2022: I gave a virtual talk about Learning dynamics of nonlinear fluid models via structure-preserving operator inference at the numerical optimization seminar at University of Konstanz, Germany.
Jan 05, 2022: Very honored to have won an NSF CAREER award for my project Goal-Oriented Variable Transformations for Efficient Reduced-Order and Data-Driven Modeling.
Jan 01, 2022: I am very excited to have been awarded a new NSF project on Nonlinear Balancing: Reduced Models and Control together with my colleagues Serkan Gugercin and Jeff Borggaard at Virginia Tech.
Dec 2021: Postdoc Harsh Sharma's paper Hamiltonian operator inference: physics-preserving learning of reduced-order models for Hamiltonian systems. (in collaboration with Zhu Wang) posted online at Physica D: Nonlinear Phenomena. The paper shows how to learn reduced-order models for Hamiltonian systems from data only, and demonstrates this on a variety of nonlinear Hamiltonian models..
Dec 2021: Our paper Certifiable risk-based engineering design optimization (with Anirban Chaudhuri, Matthew Norton, Johannes Royset and Karen Willcox) posted online at AIAA Journal. The paper shows that coherent and regular risk measures have many advantages compared to using reliability in design optimization, such as they preserve convexity of the limit state function, and provide data-driven conservativeness for the ensuing designs.
Nov 15, 2021: I gave a talk on "Multifidelity modeling for engineering design with coherent risk measures" at Sandia National Labs UQ semniar series.
July 2021: Our paper Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference. (Nihar Sawant and Benjamin Peherstorfer) just posted on arxiv. The paper shows how to enforce stability of ROMs in the operator inference procedure, and uses key results from Stability Domains for Quadratic-Bilinear Reduced-Order Models..
Feb. 2021: Science News published an article on Solar storms can wreak havoc. We need better space weather forecasts which mentiones our work in space weather modeling.
Sept. 26-29, 2021: The IACM Conference on Mechanistic Machine Learning and Digital Twins for Computational Science, Engineering & Technology was held as a hybrid conference in San Diego, where I served on the local organizing committee. Together with Wayne Uy and Benjamin Peherstorfer we organized a minisymposium MS 4.5: Data-driven reduced-order methods for system control.
Aug. 9-11, 2021: I attended the virtual AIAA Propulsion and Energy 2021 Forum where I presented Performance comparison of data-driven reduced models for a single-injector combustion process which is joined work with MS student Parikshit Jain and Shane McQuarrie (UT Austin).
July 19-21, 2021: At the SIAM Conference on Control and Its Applications we organized (with Jeff Borggaard and Serkan Gugercin) a 12-speaker minisymposium on Model Reduction for Control of High-Dimensional Nonlinear Systems. I presented our ongoing work on "Balanced truncation model reduction via nonlinear energy functions."
June 28-30, 2021: I gave a talk on "Adaptive Reduced-Order Model Construction for Conditional Value-at-Risk Estimation" (joint work with M. Heinkenschloss and T. Takhtaganov at the 4th International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP21) which was conducted virtual, June 28-30, 2021.
May 2021: I presented Balanced reduced-order models for iterative nonlinear control of large-scale systems at the 2021 American Control Conference (virtual), which is work with former MS student Yizhe Huang. The paper proposes a control strategy for large-scale nonlinear systems that combines balancing-based model reduction with the iterative linear quadratic regular method for nonlinear systems.
May 2021: Our paper Stability Domains for Quadratic-Bilinear Reduced-Order Models. was published in SIAM Journal on Applied Dynamical Systems. 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.
Dec. 2020: Aerospace America wrote an article on the Progress toward the 2030 vision of CFD as part of their 2020 Year In Review Series, where our work on Information reuse for importance sampling in reliability-based design optimization (with Anirban Chaudhuri, Karen Willcox) got highlighted as a way to do multifidelity design optimization under uncertainty.
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: 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.