Harsh Sharma

I am a Postdoctoral Scholar working with Boris Krämer in the Department of Mechanical and Aerospace Engineering at UC San Diego. I am broadly interested in using ideas from mechanics and dynamical systems to develop computational analysis tools that can improve our understanding and prediction of complex dynamical systems. In my postdoctoral research, I am working on combining the perspectives of structure-preserving model reduction and machine learning to build physics-informed surrogate models of large-scale dynamical systems.

In 2020, I completed my PhD in Aerospace Engineering at Virginia Tech, where I was jointly supervised by Mayuresh Patil and Craig Woolsey. My thesis developed a variety of structure-preserving algorithms for mechanical systems with external forcing and systems that evolve on non-Euclidean manifolds, and demonstrated these methods on a variety of engineering applications which include limit cycle oscillations of an aeroelastic system, dynamics of a neutrally buoyant underwater vehicle, and optimization for spherical shape correlation and matching. I also obtained my MS in Mathematics at Virginia Tech where I worked under the guidance of Jeff Borggaard

As a graduate student, I was a two-time recipient of the John L. Pratt Fellowship. During my graduate school, I spent two summers as a visiting research scholar at George Washington University working with Taeyoung Lee on developing structure-preserving methods on Lie groups. I obtained my B.Tech and M.Tech degrees in Mechanical Engineering from IIT-Bombay in 2015.

Upcoming Events

June 26-28, 2024: I will be attending a three-day workshop on Mathematical and Statistical Foundations of Digital Twins in Chicago at the Institute for Mathematical and Statistical Innovation. Looking forward to the talks and discussions on addressing foundational mathematical, statistical, and computational challenges to support complex applications of digital twins to scientific, engineering, medical, and societal problems.

July 21-26, 2024: I will be attending the 16th World Congress on Computational Mechanics in Vancouver where I will present our work on Symplectic Model Reduction of Hamiltonian Systems using Data-driven Quadratic Manifolds. Feel free to reach out if you are planning to attend the conference and want to chat.

September 09-13, 2024:  I am excited to attend the Model Reduction and Surrogate Modeling (MORE) Conference which will be held at the Scripps Seaside Forum on the campus of the University of California San Diego. This 5-day conference will bring together the international community of computational scientists, engineers, mathematicians, and domain experts from industry, national laboratories, and academia to address the topic of model reduction and surrogate modeling for high-dimensional complex systems. 

Recent News

March 14, 2024: Our paper Preserving Lagrangian structure in data-driven reduced-order modeling of large-scale dynamical systems (with Boris Kramer) is posted online at Physica D: Nonlinear Phenomena. This work presents a nonintrusive physics-preserving method to learn reduced-order models of Lagrangian mechanical systems and nonlinear wave equations. The numerical results demonstrate Lagrangian operator inference on an Euler-Bernoulli beam model, the sine-Gordon (nonlinear) wave equation, and a soft-robotic fishtail model with 779,232 degrees of freedom.

February 20, 2024: Our paper Lagrangian operator inference enhanced with structure-preserving machine learning for nonintrusive model reduction of mechanical systems has been accepted for publication in Computer Methods in Applied Mechanics and Engineering. This work presents an ML-enhanced model reduction method that learns structure-preserving ROMs of nonlinear mechanical systems from data in a nonintrusive manner. The proposed framework is well-suited for engineering applications where the data are generated from complicated high-fidelity computational models or experimental measurements. This work was done in collaboration with David Najera and Michael Todd from the Structural Engineering department at UCSD.

January 23, 2024: Our paper Bayesian identification of nonseparable Hamiltonians with multiplicative noise using deep learning and reduced-order modeling is up on arXiv.  This work presents a structure-preserving Bayesian framework for learning deep neural network parametrizations of complex mechanical systems from noisy data. For high-dimensional systems, we also add a model reduction step so that the Bayesian learning algorithms can operate on low-dimensional data. This paper is based on our collaboration with Nick Galioto and Alex Gorodetsky from the University of Michigan.

September 25- December 16, 2023:  I had a great time teaching the graduate-level course on Numerical Methods for Linear Algebra and ODE Simulation (MAE 290A) during the Fall of 2023 at UC San Diego. 

October 18, 2023: I gave a talk at the Optimization, Control, and Learning Seminar in the Electrical and Computer Engineering department at UCSD on the topic of "Structure-preserving Learning of Reduced-order Models for Large-scale Dynamical Systems". 

September 14-15, 2023: I attended the Southern California Robotics Symposium 2023 at UC Irvine where Iman Adibnazari presented our work on Full-Body Optimal Control of a Swimming Soft Robot Enabled by Data-Driven Model Reduction. This work is based on our collaboration with Michael Tolley's group where we are using my work in data-driven structure-preserving model reduction for model predictive control of a soft anguilliform robot.

September 8, 2023: Our paper Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifolds has been accepted for publication in Computer Methods in Applied Mechanics and Engineering. This work combines the expressiveness of quadratic approximation manifolds with projection-based model reduction that enforces symplecticity. The proposed approaches constitute a first step towards the model reduction of dynamical systems on nonlinear manifolds using interpretable manifold constructions that ensure that the approximate solution satisfies key physical properties of the high-dimensional problem.

August 13, 2023: I successfully completed the summer course on An Introduction to Evidence-Based STEM Undergraduate Teaching offered by the Center for the Integration of Research, Teaching, and Learning. This eight-week course focused on the implementation of evidence-based teaching strategies in university classrooms as well as effective methods for assessing teaching and learning. It was a great learning experience and I am looking forward to making use of the strategies and techniques covered in my teaching.

May 22- May 26, 2023: I presented our work on Lagrangian operator inference at Workshop and Conference: Nonlinear Model Reduction for Control at Virginia Tech.  It was a great experience to go back to my alma mater and interact with researchers working on model reduction for control. 

April 22, 2023: I presented our work on Physics-preserving Learning of Reduced-order Models for Large-scale Dynamical Systems at the Southern California Applied Mathematics Symposium 2023.

March 17, 2023: I presented our work (in collaboration with Nick Galioto and Alex Gorodetsky from the University of Michigan) on Bayesian System Identification at the Scientific Machine Learning Symposium 2023.

February 26- March 3, 2023:  I presented our work on Lagrangian operator inference at SIAM Conference on Computational Science and Engineering (CSE23). I also co-organized a two-part minisymposium with Silke Glas and Boris Kramer on Structure-Preserving Model Reduction for Lagrangian and Hamiltonian Systems.

December 6-9, 2022: I presented our work (in collaboration with Nick Galioto and Alex Gorodetsky from the University of Michigan) on Bayesian Identification of Nonseparable Hamiltonian Systems Using Stochastic Dynamic Models at the 61st IEEE Conference on Decision and Control (CDC)

September 26-30, 2022: I presented our work on Lagrangian operator inference at SIAM Conference on Mathematics of Data Science (MDS22). I also co-organized a minisymposium with Molei Tao (from Georgia Tech) on Exploiting Hamiltonian Structure in Learning Dynamical System Models for Prediction and Control

September 2022: Our paper Bayesian Identification of Nonseparable Hamiltonian Systems Using Stochastic Dynamic Models (with Nick Galioto, Alex Gorodetsky, and Boris Kramer) has been accepted for publication at the 61st IEEE Conference on Decision and Control (CDC). In this paper, we propose a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. 

August 1- September 6, 2022:  I taught an upper-division course on Computational Methods in Engineering (MAE 107) during Summer Session 2 at UC San Diego. I had a great time teaching this course and interacting with undergraduate students. In my Course and Professor Evaluations (CAPE), I received an instructor rating of 96.7% (the departmental average instructor rating for this course is 75.38%).

August 18-19, 2022:  I presented our work on Bayesian identification of nonseparable Hamiltonian systems using stochastic dynamic models at the USACM Thematic Conference on Uncertainty Quantification for Machine Learning Integrated Physics Modeling (UQ-MLIP)

June 2022: Our paper Performance Assessment of Energy-preserving, Adaptive Time-Step Variational Integrators (with Jeff Borggaard, Mayuresh Patil, and Craig Woolsey) has been accepted for publication in Communications in Nonlinear Science and Numerical Simulation. This work presents a numerical and theoretical assessment of energy-preserving, adaptive time-step variational integrators.

May 2022: I presented our recent work on Data-driven reduced-order modeling of large-scale mechanical systems at Southern California Applied Mathematics Symposium at Harvey Mudd College

April 2022: Our group along with the Triton Rocket Club at UCSD participated in the Barrio Logan Science & Art Expo on Saturday, April 16. We had a great time representing UCSD MAE and talking to students about our research. The UCSD School of Engineering Blog has written a nice article about our outreach event. 

April 2022: I presented our recent work on Preserving Lagrangian structure in data-driven reduced-order modeling of large-scale mechanical systems at the 39th Southern California Control Workshop at UC Irvine

January 2022: Our paper Hermite-based, One-step, Variational and Galerkin Time Integrators for Mechanical Systems (with Mayuresh Patil and Craig Woolsey) is up on arXiv. This work presents Hermite polynomial based one-step variational and Galerkin methods for mechanical systems with external forcing.

December 2021: Our paper Hamiltonian Operator Inference: Physics-preserving Learning of Reduced-order Models for Canonical Hamiltonian Systems (with Zhu Wang and Boris Kramer) is 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.

September 2021: I am speaking at MMLDT-CSET 2021 on Hamiltonian Operator Inference: Physics-preserving Learning of Low-dimensional Models for Hamiltonian Systems. This is joint work with Zhu Wang and Boris Kramer.

August 2021: I was invited to give a Computational Mathematics Seminar at the University of Pittsburgh on August 31.


Google Scholar: Papers and citations



ORCiD: Persistant digital identifier



ResearchGate: Published research and discussions

Contact

Harsh Sharma

Postdoctoral Scholar

Department of Mechanical and Aerospace Engineering 

University of California San Diego 

Jacobs Hall (EBU1) | Room 4205

9500 Gilman Drive | La Jolla | CA 92093-0411

Email: hasharma at ucsd dot edu