Credit: UC San Diego Publications | Copyright Regents of the University of California

Research Interests

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).

Upcoming events

We have an opening for a postdoctoral position, please check the "Openings" tab for more information.

September 15, 2023: I am giving a talk at the Computational Mathematics and Scientific Computing seminar at the Courant Institute on the topic of "Scalable computations for nonlinear balanced truncation model reduction".

September, 2023: Welcome to our new graduate students! Elle Lavichant starts her M.S. in MAE and continues the research she has done as a B.S. student on biomass combustion with us, Steven Nguyen (co-advised with Prof. Jorge Cortes) is joining us from UC Santa Barbara, and Dylan Hirsch (co-advised with Prof. Sylvia Herbert) will be joining us from MIT.

News

September 8, 2023: Postdoc Harsh Sharma's article on Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifolds got accepted at CMAME. The workcombines the expressivness of quadratic approximation manifolds with projection-based model reduction that enforces symplecticity. This was a large collaboration (with Silke Glas and Hongliang Mu, University of Twente, Patrick Buchfink, U. Stuttgart, Rudy Geelen, UT Austin) and combined expertises in multiple areas.

August 20-25, 2023: Opal Issan and I presented at the 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023) in Tokyo. Together with Yuto Miyatake (Kyoto), we organized a session on Learning Dynamical Systems by Preserving Symmetries, Energies, and Variational Principles and together with Enrico Camporeale (NOAA and UC Boulder) we organized a session on Space Weather: Modeling, Surrogates and Uncertainty Quantification.

August 2-4, 2023: Dongjin Lee and Nate Linden attended the UQ Summer School at USC.

July 24-26, 2023: Nick Corbin and I attended the biannual SIAM Conference on Control and Its Applications in Philadelphia. Together with Jeff Borggaard and Serkan Gugercin, I organized a two-part minisymposium on Nonlinear Model Order Reduction for Control Applications where both Nick and I presented recent work.

July 23-27, 2023: Postdoc Dongjin Lee presented his work at the 17th U. S. National Congress on Computational Mechanics in Albuquerque, NM.

July, 2023: Congratulations to Postdoc Dongjin Lee, who will be starting an Assistant Professor position at Hanyang University (Seoul, Sout Korea) in the Department of Automotive Engineering. Dongjin has research interests in design optimization, uncertainty quantification, and significant work experience with Hyundai Motors.

July 16-21, 2023: Nate Linden presented his work on "Multimodel modeling for blood glucose and insulin measurements in diabetes" at the 2023 Society of Mathematical Biology Annual Meeting at Ohio State University.

July 14, 2023: Postdoc Dongjin Lee and undergraduate student Elle Lavichant posted their article on Global sensitivity analysis in the limited data setting with application to char combustion on arxiv. Therein, they present a new method that can effectively learn surrogate models from very limited high-fidelity simulations. Those models are then used for Sobol sensitivity analysis to determine influential parameters for design optimization.

July 5, 2023: We collaborated with Ruijian Han, Akil Narayan and Yiming Xu on the paper An approximate control variates approach to multifidelity distribution estimation, which just posted on arxiv. The suggested method can effectively estimate cumulative distribution functions of quantities of interest, which we demonstrated on a two-dimensional fibre-composite material model.

June 24, 2023: Congratulations to PhD student Nate Linden for publishing his second journal paper, this time on Bayesian parameter estimation for the inclusion of uncertainty in progressive damage simulation of composites in the Journal of Composite Structures.

June, 2023: Congratulations to our undergraduate researchers Elle Lavichant (ME) and Hannah Haider (AE) for earning their BS degrees from the Jacobs School of Engineering. Elle will continue in our group in the MS program and Hannah is moving on to Columbia University to start her PhD.

May 22-26, 2023: Together with Profs. Jeff Borggaard and Serkan Gugercin we organized a Workshop and Conference: Nonlinear Model Reduction for Control at Virginia Tech. We had a great week of tutorials and research talks. Participants particularly enjoyed that there was plenty of time for discussion and seeding future collaborations. Thanks also to the NSF-CMMI program for giving us a presentation.

May 13, 2023: Graduate student Opal Issan just posted her second paper Bayesian Inference and Global Sensitivity Analysis for Ambient Solar Wind Prediction on arxiv. In collaboration with Pete Riley (Predictive Sciences) and Enrico Camporeale (NOAA/CU Boulder) Opal proposed a comprehensive uncertainty quantification (UQ) framework that is able to successfully quantify and reduce parametric uncertainties in a chain of models that maps GONG magnetograms to ambient solar wind near Earth. The work involved global sensitivity analysis, Markov chain Monte Carlo methods and in-depth analysis of the model chain. She will present this work at the Geospace Environment Modeling Summer Workshop in San Diego, June 11-16.

May 10, 2023: Congratulations to Opal Issan for having her work appear in a SIAM News Blog post on Speeding Up Solar Wind Forecasts with Reduced-order Modeling.

April 22, 2023: Our group attended the Southern California Applied Mathematics Symposium at UC Irvine. Nate Linden, Dongjin Lee and Harsh Sharma presented their recent research.

April 15, 2023: We participated with a science booth themed "Space Research at Barrio Logan 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. Thanks to Opal Issan, Nate Linden and Nick Corbin for volunteering for the event. As always, it is great to partner with our two UCSD student clubs Students for the Exploration and Development of Space (SEDS) and the Rocket Propulsion Laboratory for this event.

April 6-7, 2023: Opal Issan and Dongjin Lee attended the USACM workshop on establishing benchmarks for data-driven modeling of physical systems at USC. Opal is presenting "Predicting solar wind streams from the inner-heliosphere to earth via shifted operator inference" and Dongjin is presenting "Multifidelity risk assessment for nonlinear systems under high-dimensional dependent random variables."

March 30, 2023: I gave a seminar talk at the School of Aerospace Engineering Seminar Series at Georgia Tech.

March 27-29, 2023: I attended the AAAI Spring Symposium on Computational Approaches to Scientific Discovery in San Francisco, and present a talk on "Learning Exact and Optimal Quadratic Forms for Nonlinear Non-Autonomous ODEs". This was a great way to meet people from different communities working on a central problem in computational science.

March 14, 2023: Congratulations to Nate Linden whose SIAM News Blog post on Identifiability and Sensitivity Analysis for Bayesian Parameter Estimation in Systems Biology appeared today.

March 9-10, 2023: The Space Weather with Quantified Uncertainties Spring Meeting 2023 took place at MIT with a full 2-day program and a trip to MIT Haystack observatory. Graduate student Opal Issan, undergraduate student Hannah Haider, and I attended this well-run NSF program workhop. Opal presented a poster on ``Parameter Estimation of Ambient Solar Wind Models using ACE Observations".

March 4, 2023: As our first science outreach event this year, we hosted a science booth themed "Space Research at UCSD" at the Comienza con un Sueno on UCSD's campus. Thanks to Opal Issan, Nate Linden and Nick Corbin for volunteering for the event. As always, it is great to partner with our two UCSD student clubs Students for the Exploration and Development of Space (SEDS) and the Rocket Propulsion Laboratory for this event.

February 26-March 3, 2023: Postdoc Harsh Sharma and I attended the SIAM Conference on Computational Science and Engineering (CSE23) in Amsterdam. Together with Prof. Gleb Pogudin, we organized an 8-speaker minisymposium on Exact Polynomialization and Quadratization of Nonlinear Dynamics; together with Prof. Silke Glas and Harsh Sharma we organized an 8-speaker minisymposium on Structure-Preserving Model Reduction for Lagrangian and Hamiltonian Systems; and I presented work (with Opal Issan) on The Shifted Operator Inference Method for Learning Solar Wind Models. SIAM CSE was a well-run and once again fantastic event for our community.

February 6-February 24, 2023: I was in residence at the Isaac Newton Institute at the University of Cambridge, UK, for the semester program on The mathematical and statistical foundation of future data-driven engineering, specifically the deep-dive session on Optimal Control and Inference organized by Susana Gomes and Sebastian Reich. It was a productive three weeks with many interesting discussions.

February 7, 2023: At long last, the second part to our paper series, Nonlinear Balanced Truncation: Part 2-Model Reduction on Manifolds. (with Jeff Borggaard and Serkan Gugercin) posted on arxiv. In the work, we leverage the energy functions of nonlinear dynamical systems (computed in Nonlinear Balanced Truncation: Part 1-Computing Energy Functions) and proposes a strategy to simulataneously balance and reduce the nonlinear systems. The nonlinear coordinate transformation to achieve this is of polynomial form and defines a balanced approximate nonlinear manifold where the system is reduced on. .

February 1, 2023: Our paper Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference. (with Nihar Sawant and Benjamin Peherstorfer) appeared in CMAME. 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..

February 1, 2023: Congratulations to Postdoc Dongjin Lee for publishing his first article as a member of my group: Bi-fidelity conditional value-at-risk estimation by dimensionally decomposed generalized polynomial chaos expansion in Structural and Multidisciplinary Optimization. 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.

February 1, 2023: I gave a seminar talk at the School of Nuclear Science & Engineering at Oregon State University.

December 8, 2022: I gave a talk at the SimTech Seminar on Model Reduction and Data Techniques for Surrogate Modelling at the the University of Stuttgart, Germany, about "Learning dynamics of nonlinear systems via structure-preserving operator inference".

December 6-9, 2022: Postdoc Harsh Sharma attended the 61st IEEE Conference on Decision and Control and presented his paper Bayesian Identification of Nonseparable Hamiltonian Systems Using Stochastic Dynamic Models (joint work with collaborators Nicholas Galioto and Alex A. Gorodetsky at University of Michigan). In this paper, we propose a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models.

November 7, 2022: Congratulations to graduate student Opal Issan for having her first journal paper appear at the Journal of Computational Physics (free link until Dec 27). With a passion for space weather models, Opal focuses on a background solar wind model and proposed shifted Operator Inference (sOPINF), which extends the existing OPINF learning framework to (a) automatically detect translational shifts (advection) in the data and subsequently removes them as a preprocessing step, and (b) learns and simulates ROMs in the advection-free coordinates, where much lower-dimensional models are possible. She tested that framework on three different solar wind models and got nice results that should aid us in uncertainty quantification later on.

November 2, 2022: Congratulations to graduate student Nate Linden for having his first journal paper appear at PLOS Computational Biology (link). The paper proposed a comprehensive framework for Bayesian parameter estimation and complete quantification of the effects of uncertainties in the data and models. We applied these methods to a series of signaling models of increasing mathematical complexity. The results highlighted how focused uncertainty quantification can enrich systems biology modeling and enable additional quantitative analyses for parameter estimation.

October 14, 2022: It was exciting to return to my alma mater Virginia Tech to give a colloqium talk in the Department of Mathematics about Learning of Structured Dynamical Systems from Data.

September 28, 2022: Problems that politics is dealing with can be approached from an engineering perspective! It is common knowledge that the US Electoral College and the Electoral Count Act need reforms. Together with Chris Truax, a member of the Guardrails of Democracy Project we developed a novel way of informing policy makers how to make better decisions, regardless of party affiliation. This non-partisan, quantitiative engineering solution is based on Monte Carlo simulation and essentially computes the probabilities that the Electoral College and the Electoral Count Act produces the correct president. A sneak-peak of our findings is published in the Bulwark under The Electoral Count Act Is Actually an Engineering Problem. This would have not been possible without Jonathan Carreon, a BS/MS student in applied mathematics and aerospace engineering. More details will follow in the coming year.

September 26-30, 2022: The SIAM MDS was in San Diego, so there was a lot of activity from our group. Together with Dr. Christine Allen-Blanchette we are hosting two minisymposia MS14 & MS 31: Learning Dynamical Systems by Preserving Symmetries, Energies, and Variational Principles where Dr. Harsh Sharma is also presenting his work Preserving Lagrangian Structure in Data-Driven Reduced-Order Modeling of Large-Scale Mechanical Systems. Moreover, Nick Galioto is presenting our collaborative work on Learning Partially Observed Stochastic Dynamical Systems. Graduate student Opal Issan presents her work on Predicting Solar Wind Streams from the Inner-Heliosphere to Earth via Shifted Operator Inference. Then, together with Prof. Padmini Rangamani and our co-advised graduate student Nate Linden we are hosting two minisymposia on MS110 & MS126 Parameter Inference and Uncertainty Quantification for Systems Biology and Medicine where Nate presents his work A Framework for Bayesian Parameter Estimation and Uncertainty Quantification in Systems Biology. Lastly, Postdoc Harsh Sharma is organizing MS146: Exploiting Hamiltonian Structure in Learning Dynamical System Models for Prediction and Control where I am also giving a talk on Hamiltonian Operator Inference: Physics-Preserving Learning of Reduced-Order Models for Canonical Hamiltonian Systems.

September 19-23, 2022: I was very honored to be an invited plenary 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.

September 19, 2022: At long last, our first of two papers, Nonlinear Balanced Truncation: Part 1-Computing Energy Functions posted on arxiv. In this two part series, we consider the problem of nonlinear model reduction via the process of balancing certain energy functions (a.k.a., balanced truncation model reduction). Part 1 is dedicated to scalable computation of the energy functions via Taylor-series approximations, and Part 2 will focus on reduced-order modeling on the nonlinear balanced manifolds. This is an exciting area of research and has fascinated me for almost a decade now.

September 19, 2022: Our paper Bayesian Identification of Nonseparable Hamiltonian Systems Using Stochastic Dynamic Models (with Postdoc Harsh Sharma and collaborators Nicholas Galioto and Alex A. Gorodetsky at University of Michigan) posted on arxiv and is accepted for publication at the 61st IEEE Conference on Decision and Control (CDC), December 6-9. In this paper, we propose a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models.

August 18-19, 2022: Postdocs Harsh Sharma and Dongjin Lee attended the USACM Thematic Conference on Uncertainty Quantification for Machine Learning Integrated Physics Modeling (UQ-MLIP) and presented 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 hosted 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.

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