Benjamin Peherstorfer   |   Courant Institute of Mathematical Sciences, New York University
Benjamin Peherstorfer

Benjamin Peherstorfer

Associate Professor
Department of Computer Science | Department of Mathematics (affiliated) | Center for Data Science (affiliated)

Courant Institute of Mathematical Sciences | New York University
251 Mercer Street, New York, NY 10012

Research (Google Scholar)
computational mathematics, machine learning, computational statistics, numerical analysis, and scientific computing

Contact pehersto at cims dot nyu dot edu | 212 998 3297 | Warren Weaver Hall (WWH), Room 421

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News

May 2024
Congratulations to Jules Berman for winning the Harold Grad Memorial Prize.
Jan 2024
Oct 2023
Oct 2023
Looking forward to working as a team of seven PIs on learning fast computational models from data to accelerate energy breakthroughs, as part of a Department of Energy project developing Science Foundations for Energy Earthshots. Press release.
Aug 2023
It is a great honor to be a plenary speaker at the International Conference on Spectral and High Order Methods (ICOSAHOM) 2023.
Aug 2023
Congratulations to Steffen Werner who is starting a new position as a tenure-track assistant professor in the Department of Mathematics at Virginia Tech.
Apr 2023
Excited to have the opportunity to visit the Isaac Newton Institute again and participate in the program on The Mathematical and Statistical Foundation of Future Data-Driven Engineering with a talk about our work on Context-Aware Controller Inference from Scarce Data.
Apr 2023
Looking very much forward to speaking at the Workshop on Scientific Machine Learning at the Oden Institute.
Feb 2023
Dec 2022
Sep 2022
Congratulations to Frederick Law for winning the Moses A. Greenfield Research Prize.
Sep 2022
Sep 2022
Excited to serve on the Scientific Committee of the conference on Model Reduction and Surrogate Modeling (MORE) that will be held in Berlin, Germany in September 2022.
Aug 2022
Looking forward to Mathematical and Scientific Machine Learning (MSML) 2022 and happy to serve on the program committee.
Jul 2022
Co-organizing minisymposium on Model Reduction for Chemically Reacting Flows: Challenges, Advances, and Benchmarks at the SIAM Annual Meeting 2022. Additionally information and benchmarks for model reduction of chemically reacting flows can be found here.
Jun 2022
Looking forward to giving an invited tutorial presentation on multi-fidelity uncertainty quantification at the AIAA Aviation Forum.
Apr 2022
Happy to have the opportunity to highlight the exciting field of nonlinear model reduction, which is emerging at the intersection of scientific computing and machine learning, in the featured article on Breaking the Kolmogorov Barrier with Nonlinear Model Reduction that appeared in the Notices of the American Mathematical Society.
Feb 2022
Invited speaker at the workshop on The Mathematics of Soft Matter, which is held at the Institute for Mathematical and Statistical Innovation (IMSI).
Jan 2022
Looking forward to serving as a panelist in the session on data-driven methods for simulating chemically reacting flows at the upcoming American Institute of Aeronautics and Astronautics (AIAA) SciTech Forum.
Jun 2021
Chairing an Invited Focus Session on "High-Performance Computing for AI" at the ISC High Performance 2021.
Apr 2021
Mar 2021
Feb 2021
I feel very honored to be an NSF CAREER recipient. My proposal Formulations, Theory, and Algorithms for Nonlinear Model Reduction in Transport-Dominated Systems was funded through the Computational Mathematics program in the Division Of Mathematical Sciences.
Nov 2020
Excited to be a 2021 AFRL/AFOSR Young Investigator Program (YIP) award recipient. My proposal is about context-aware learning for intelligent decision-making in science and engineering.
Oct 2020
Looking forward to Mathematical and Scientific Machine Learning (MSML) 2021 and happy to serve on the program committee.
Sep 2020
I am co-organizing the Numerical Analysis and Scientific Computing seminar at Courant Institute starting fall 2020.
Jul 2020
Invited to present our work on multifidelity methods as a keynote lecture in the minisymposium Multifidelity Optimization at the European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS).
Jun 2020
Invited to give a tutorial presentation on multifidelity methods for uncertainty quantification at the workshop Multifidelity Modeling in Support of Design and Uncertainty Quantification that is organized as part of the AIAA Aviation Forum.
May 2020
Co-organizer, with Themistoklis Sapsis (MIT), of minisymposium "Learning Dynamical-System Models for Prediction and Control" at the SIAM Conference on Mathematics of Data Science 2020.
Apr 2020
Congratulations to Elizabeth Qian for winning a 2020 SIAM Student Paper Prize for her work Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices. The paper appeared in SIAM/ASA Journal on Uncertainty Quantification in 2018.
Apr 2020
Congratulations to Frederick Law for winning a DoD NDSEG Fellowship.
Apr 2020
Co-organizer of ICERM workshop on Computational Statistics and Data-Driven Models, which will be held virtually April 20-24, 2020.
Mar 2020
Co-organizer with Youssef Marzouk (MIT) and Yaoliang Yu (U Waterloo) of minisymposium on "Inference and preconditioning via Stein methods, flows, and other transport maps" at the SIAM Conference on Uncertainty Quantification 2020.
Feb 2020
Invited to give a presentation on model reduction for transport-dominated problems at workshop on "Mathematics of Reduced Order Models", which is organized at the Institute for Computational and Experimental Research in Mathematics (ICERM).
Jan 2020
Invited to give a tutorial presentation on learning dynamical-system models from data as part of the program "Model and dimension reduction in uncertain and dynamic systems" at the Institute for Computational and Experimental Research in Mathematics (ICERM).
Aug 2019
Invited to give a presentation in the seminar of the Computational Science Initiative at Brookhaven National Laboratory.
Jun 2019
Invited to give a presentation at the Physics Informed Machine Learning Workshop at University of Washington.
Jun 2019
Invited to give a tutorial presentation for aerospace engineers on our multifidelity uncertainty quantification work at the AIAA Aviation workshop on Multifidelity Modeling In Support Of Design And Uncertainty Quantification.
Mar 2019
There currently are 2 articles that I co-authored under the top-20 downloads of the SIAM/ASA Journal on Uncertainty Quantification (March 30, 2019). The articles are on multifidelity sensitivity analysis (authors Qian, P., O'Malley, Vesselinov, and Willcox) and on multifidelity rare event simulation (authors P., Kramer, and Willcox).
Mar 2019
Invited to give a presentation in the seminar series of the Institute for Computational Engineering and Sciences (ICES) at University of Texas, Austin.
Feb 2019
SIAM selected our minisymposium "Model Reduction for Problems with Strong Convection, Sharp Gradients, and Discontinuities" (co-organized with Maciej Balajewicz and Gerrit Welper) to be a Featured Minisymposium at the SIAM Conference on Computational Science and Engineering 2019.
Nov 2018
Invited to give a presentation in the Applied Mathematics Colloquium at Columbia University.
Oct 2018
Invited to give a presentation in the seminar of the Mathematics in Computational Science and Engineering group at EPFL.
Sep 2018
I will join Courant Institute of Mathematical Sciences at New York University as assistant professor on September 1, 2018.
Sep 2018
I have been selected for a Department of Energy (DoE) Early Career Award in the Applied Mathematics Program (Office of Advanced Scientific Computing Research). My move to Courant Institute (New York University) delayed the process to Fall 2018 and so my grant is not part of the official announcement posted in Summer 2018.
Jul 2018
Apr 2018
Co-organizer of minisymposium on multilevel and multifidelity methods for Bayesian inverse problems at SIAM Uncertainty Quantification 2018; with Tiangang Cui (Monash University).
Apr 2018
Invited speaker at the Model Reduction of Parametrized Systems (MoRePaS) IV conference.
Mar 2018
Sep 2017
Our survey paper on multifidelity methods for outer-loop applications has been accepted by SIAM Review.
Jul 2017
Invited to speak at the workshop Quantification of Uncertainty: Improving Efficiency and Technology that is organized by Marta D'Elia (Sandia), Max Gunzburger (Florida State), and Gianluigi Rozza (SISSA).
Apr 2017
Presentation in the colloquium of the Department of Mathematics at Virginia Tech.
Mar 2017
Invited presentation at the workshop Uncertainty Quantification and Data-Driven Modeling that is organized by James R. Stewart (Sandia) and Krishna Garikipati (UMich).
Oct 2016
Presentation in the Applied and Computational Mathematics Seminar at University of Wisconsin-Madison.
Aug 2016
I started as Assistant Professor at University of Wisconsin-Madison.
Aug 2016
Invited presentation at workshop on Next Generation Mobility Modeling and Simulation, UW-Madison.
Jul 2016
Co-organizer of minisymposium on model reduction at SIAM Annual Meeting 2016.
Nov 2015
Invited talk in the seminar series of the Transregional Collaborative Research Center on Invasive Computing.
Dec 2014
I was awarded the Heinz Schwärtzel prize for my PhD thesis.
Dec 2014
Jan 2014
Started as Postdoctoral Associate in the group of Karen Willcox at MIT..

Selected preprints and submitted articles

[1] Zhang, H., Chen, Y., Vanden-Eijnden, E. & Peherstorfer, B. Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial differential equations.
arXiv, 2404.01145, 2024.
[Abstract] [BibTeX]
[2] Schwerdtner, P. & Peherstorfer, B. Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction.
arXiv, 2403.06732, 2024.
[Abstract] [BibTeX]
[3] Schwerdtner, P., Schulze, P., Berman, J. & Peherstorfer, B. Nonlinear embeddings for conserving Hamiltonians and other quantities with Neural Galerkin schemes.
arXiv, 2310.07485, 2023.
[Abstract] [BibTeX]
[4] Maurais, A., Alsup, T., Peherstorfer, B. & Marzouk, Y. Multifidelity Covariance Estimation via Regression on the Manifold of Symmetric Positive Definite Matrices.
arXiv, 2307.12438, 2023.
[Abstract] [BibTeX]
Full list

Selected publications

[1] Berman, J. & Peherstorfer, B. CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equations.
International Conference on Machine Learning (ICML), 2024.
[Abstract] [BibTeX]
[2] Alsup, T., Hartland, T., Peherstorfer, B. & Petra, N. Further analysis of multilevel Stein variational gradient descent with an application to the Bayesian inference of glacier ice models.
Advances in Computational Mathematics, 2024.
[Abstract] [BibTeX]
[3] Wen, Y., Vanden-Eijnden, E. & Peherstorfer, B. Coupling parameter and particle dynamics for adaptive sampling in Neural Galerkin schemes.
Physica D, 2024.
[Abstract] [BibTeX]
[4] Goyal, P., Peherstorfer, B. & Benner, P. Rank-Minimizing and Structured Model Inference.
SIAM Journal on Scientific Computing, 2024.
[Abstract] [BibTeX]
[5] Bruna, J., Peherstorfer, B. & Vanden-Eijnden, E. Neural Galerkin Scheme with Active Learning for High-Dimensional Evolution Equations.
Journal of Computational Physics, 2023.
[Abstract] [BibTeX]
[6] Kramer, B., Peherstorfer, B. & Willcox, K. Learning Nonlinear Reduced Models from Data with Operator Inference.
Annual Review of Fluid Mechanics, 56, 2024.
[Abstract] [BibTeX]
[7] Berman, J. & Peherstorfer, B. Randomized Sparse Neural Galerkin Schemes for Solving Evolution Equations with Deep Networks.
NeurIPS 2023 (spotlight).
[Abstract] [BibTeX]
[8] Singh, R., Uy, W.I.T. & Peherstorfer, B. Lookahead data-gathering strategies for online adaptive model reduction of transport-dominated problems.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2023. (accepted).
[Abstract] [BibTeX]
[9] Law, F., Cerfon, A., Peherstorfer, B. & Wechsung, F. Meta variance reduction for Monte Carlo estimation of energetic particle confinement during stellarator optimization.
Journal of Computational Physics, 2023.
[Abstract] [BibTeX]
[10] Maurais, A., Alsup, T., Peherstorfer, B. & Marzouk, Y. Multi-fidelity covariance estimation in the log-Euclidean geometry.
International Conference on Machine Learning (ICML), 2023.
[Abstract] [BibTeX]
[11] Uy, W.I.T., Hartmann, D. & Peherstorfer, B. Operator inference with roll outs for learning reduced models from scarce and low-quality data.
Computers & Mathematics with Applications, 145, 2023.
[Abstract] [BibTeX]
[12] Uy, W.I.T., Wang, Y., Wen, Y. & Peherstorfer, B. Active operator inference for learning low-dimensional dynamical-system models from noisy data.
SIAM Journal on Scientific Computing, 2023. (accepted).
[Abstract] [BibTeX]
[13] Werner, S.W.R. & Peherstorfer, B. Context-aware controller inference for stabilizing dynamical systems from scarce data.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2023. (accepted).
[Abstract] [BibTeX]
[14] Farcas, I.G., Peherstorfer, B., Neckel, T., Jenko, F. & Bungartz, H.J. Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification.
Computer Methods in Applied Mechanics and Engineering, 2023. (accepted).
[Abstract] [BibTeX]
[15] Rim, D., Peherstorfer, B. & Mandli, K.T. Manifold approximations via transported subspaces: Model reduction for transport-dominated problems.
SIAM Journal on Scientific Computing, 45, 2023.
[Abstract] [BibTeX]
[16] Werner, S.W.R. & Peherstorfer, B. On the sample complexity of stabilizing linear dynamical systems from data.
Foundations of Computational Mathematics, 2022. (accepted).
[Abstract] [BibTeX]
[17] Sawant, N., Kramer, B. & Peherstorfer, B. Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference.
Computer Methods in Applied Mechanics and Engineering, 2022. (accepted).
[Abstract] [BibTeX]
[18] Werner, S.W.R., Overton, M.L. & Peherstorfer, B. Multi-fidelity robust controller design with gradient sampling.
SIAM Journal on Scientific Computing, 2022. (accepted).
[Abstract] [BibTeX]
[19] Alsup, T. & Peherstorfer, B. Context-aware surrogate modeling for balancing approximation and sampling costs in multi-fidelity importance sampling and Bayesian inverse problems.
SIAM/ASA Journal on Uncertainty Quantification, 2022. (accepted).
[Abstract] [BibTeX]
[20] Peherstorfer, B. Breaking the Kolmogorov Barrier with Nonlinear Model Reduction.
Notices of the American Mathematical Society, 69:725-733, 2022.
[Abstract] [BibTeX]
[21] Law, F., Cerfon, A. & Peherstorfer, B. Accelerating the estimation of collisionless energetic particle confinement statistics in stellarators using multifidelity Monte Carlo.
Nuclear Fusion, 2022. (accepted).
[Abstract] [BibTeX]
[22] Konrad, J., Farcas, I.G., Peherstorfer, B., Siena, A.D., Jenko, F., Neckel, T. & Bungartz, H.J. Data-driven low-fidelity models for multi-fidelity Monte Carlo sampling in plasma micro-turbulence analysis.
Journal of Computational Physics, 2021. (accepted).
[Abstract] [BibTeX]
[23] Alsup, T., Venturi, L. & Peherstorfer, B. Multilevel Stein variational gradient descent with applications to Bayesian inverse problems.
In Mathematical and Scientific Machine Learning (MSML) 2021, 2021.
[Abstract] [BibTeX]
[24] Otness, K., Gjoka, A., Bruna, J., Panozzo, D., Peherstorfer, B., Schneider, T. & Zorin, D. An Extensible Benchmark Suite for Learning to Simulate Physical Systems.
In NeurIPS 2021 Track Datasets and Benchmarks, 2021. (accepted).
[Abstract] [BibTeX]
[25] Uy, W.I.T. & Peherstorfer, B. Operator inference of non-Markovian terms for learning reduced models from partially observed state trajectories.
Journal of Scientific Computing, 2021. (accepted).
[Abstract] [BibTeX]
[26] Uy, W.I.T. & Peherstorfer, B. Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations.
ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 2021. (accepted).
[Abstract] [BibTeX]
[27] Peherstorfer, B. Sampling low-dimensional Markovian dynamics for pre-asymptotically recovering reduced models from data with operator inference.
SIAM Journal on Scientific Computing, 42:A3489-A3515, 2020.
[Abstract] [BibTeX]
[28] Drmac, Z. & Peherstorfer, B. Learning low-dimensional dynamical-system models from noisy frequency-response data with Loewner rational interpolation.
In Realization and Model Reduction of Dynamical Systems: A Festschrift in Honor of the 70th Birthday of Thanos Antoulas, Springer, 2020.
[Abstract] [BibTeX]
[29] Benner, P., Goyal, P., Kramer, B., Peherstorfer, B. & Willcox, K. Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms.
Computer Methods in Applied Mechanics and Engineering, 372, 2020.
[Abstract] [BibTeX]
[30] Peherstorfer, B., Drmac, Z. & Gugercin, S. Stability of discrete empirical interpolation and gappy proper orthogonal decomposition with randomized and deterministic sampling points.
SIAM Journal on Scientific Computing, 42:A2837-A2864, 2020.
[Abstract] [BibTeX]
[31] Peherstorfer, B. Model reduction for transport-dominated problems via online adaptive bases and adaptive sampling.
SIAM Journal on Scientific Computing, 42:A2803-A2836, 2020.
[Abstract] [BibTeX]
[32] Qian, E., Kramer, B., Peherstorfer, B. & Willcox, K. Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems.
Physica D: Nonlinear Phenomena, Volume 406, 2020.
[Abstract] [BibTeX]
[33] Peherstorfer, B. & Marzouk, Y. A transport-based multifidelity preconditioner for Markov chain Monte Carlo.
Advances in Computational Mathematics, 45:2321-2348, 2019.
[Abstract] [BibTeX]
[34] Peherstorfer, B. Multifidelity Monte Carlo estimation with adaptive low-fidelity models.
SIAM/ASA Journal on Uncertainty Quantification, 7:579-603, 2019.
[Abstract] [BibTeX]
[35] Kramer, B., Marques, A., Peherstorfer, B., Villa, U. & Willcox, K. Multifidelity probability estimation via fusion of estimators.
Journal of Computational Physics, 392:385-402, 2019.
[Abstract] [BibTeX]
[36] Swischuk, R., Mainini, L., Peherstorfer, B. & Willcox, K. Projection-based model reduction: Formulations for physics-based machine learning.
Computers & Fluids, 179:704-717, 2019.
[Abstract] [BibTeX]
[37] Peherstorfer, B., Kramer, B. & Willcox, K. Multifidelity preconditioning of the cross-entropy method for rare event simulation and failure probability estimation.
SIAM/ASA Journal on Uncertainty Quantification, 6(2):737-761, 2018.
[Abstract] [BibTeX]
[38] Peherstorfer, B., Gunzburger, M. & Willcox, K. Convergence analysis of multifidelity Monte Carlo estimation.
Numerische Mathematik, 139(3):683-707, 2018.
[Abstract] [BibTeX]
[39] Qian, E., Peherstorfer, B., O'Malley, D., Vesselinov, V.V. & Willcox, K. Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices.
SIAM/ASA Journal on Uncertainty Quantification, 6(2):683-706, 2018.
[Abstract] [BibTeX]
[40] Baptista, R., Marzouk, Y., Willcox, K. & Peherstorfer, B. Optimal Approximations of Coupling in Multidisciplinary Models.
AIAA Journal, 56:2412-2428, 2018.
[Abstract] [BibTeX]
[41] Zimmermann, R., Peherstorfer, B. & Willcox, K. Geometric subspace updates with applications to online adaptive nonlinear model reduction.
SIAM Journal on Matrix Analysis and Applications, 39(1):234-261, 2018.
[Abstract] [BibTeX]
[42] Peherstorfer, B., Willcox, K. & Gunzburger, M. Survey of multifidelity methods in uncertainty propagation, inference, and optimization.
SIAM Review, 60(3):550-591, 2018.
[Abstract] [BibTeX]
[43] Peherstorfer, B., Gugercin, S. & Willcox, K. Data-driven reduced model construction with time-domain Loewner models.
SIAM Journal on Scientific Computing, 39(5):A2152-A2178, 2017.
[Abstract] [BibTeX]
[44] Peherstorfer, B., Kramer, B. & Willcox, K. Combining multiple surrogate models to accelerate failure probability estimation with expensive high-fidelity models.
Journal of Computational Physics, 341:61-75, 2017.
[Abstract] [BibTeX]
[45] Kramer, B., Peherstorfer, B. & Willcox, K. Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models.
SIAM Journal on Applied Dynamical Systems, 16(3):1563-1586, 2017.
[Abstract] [BibTeX]
[46] Peherstorfer, B., Willcox, K. & Gunzburger, M. Optimal model management for multifidelity Monte Carlo estimation.
SIAM Journal on Scientific Computing, 38(5):A3163-A3194, 2016.
[Abstract] [BibTeX]
[47] Peherstorfer, B. & Willcox, K. Data-driven operator inference for nonintrusive projection-based model reduction.
Computer Methods in Applied Mechanics and Engineering, 306:196-215, 2016.
[Abstract] [BibTeX]
[48] Peherstorfer, B. & Willcox, K. Dynamic data-driven model reduction: Adapting reduced models from incomplete data.
Advanced Modeling and Simulation in Engineering Sciences, 3(11), 2016.
[Abstract] [BibTeX]
[49] Peherstorfer, B., Cui, T., Marzouk, Y. & Willcox, K. Multifidelity Importance Sampling.
Computer Methods in Applied Mechanics and Engineering, 300:490-509, 2016.
[Abstract] [BibTeX]
[50] Peherstorfer, B. & Willcox, K. Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates.
SIAM Journal on Scientific Computing, 37(4):A2123-A2150, 2015.
[Abstract] [BibTeX]
[51] Peherstorfer, B., Gómez, P. & Bungartz, H.J. Reduced Models for Sparse Grid Discretizations of the Multi-Asset Black-Scholes Equation.
Advances in Computational Mathematics, 41(5):1365-1389, 2015.
[Abstract] [BibTeX]
[52] Peherstorfer, B. & Willcox, K. Dynamic Data-Driven Reduced-Order Models.
Computer Methods in Applied Mechanics and Engineering, 291:21-41, 2015.
[Abstract] [BibTeX]
[53] Peherstorfer, B., Zimmer, S., Zenger, C. & Bungartz, H.J. A Multigrid Method for Adaptive Sparse Grids.
SIAM Journal on Scientific Computing, 37(5):S51-S70, 2015.
[Abstract] [BibTeX]
[54] Peherstorfer, B., Pflüger, D. & Bungartz, H.J. Density Estimation with Adaptive Sparse Grids for Large Data Sets.
In SIAM Data Mining 2014, SIAM, 2014.
[Abstract] [BibTeX]
[55] Peherstorfer, B., Butnaru, D., Willcox, K. & Bungartz, H.J. Localized Discrete Empirical Interpolation Method.
SIAM Journal on Scientific Computing, 36(1):A168-A192, 2014.
[Abstract] [BibTeX]
[56] Peherstorfer, B., Kowitz, C., Pflüger, D. & Bungartz, H.J. Selected Recent Applications of Sparse Grids.
Numerical Mathematics: Theory, Methods and Applications, 8(1):47-77, 2014.
[Abstract] [BibTeX]
[57] Pflüger, D., Peherstorfer, B. & Bungartz, H.J. Spatially adaptive sparse grids for high-dimensional data-driven problems.
Journal of Complexity, 26(5):508-522, 2010.
[Abstract] [BibTeX]
Full list