About

Benjamin Peherstorfer is an Associate Professor at the Courant Institute of Mathematical Sciences, New York University, where he is engaged in research at the intersection of computational mathematics, machine learning, computational statistics, numerical analysis, and scientific computing. His work focuses on developing advanced methods for scientific modeling, data-driven decision-making, and uncertainty quantification, with a particular emphasis on multifidelity techniques, nonlinear model reduction, and probabilistic scientific machine learning. Peherstorfer has contributed to the advancement of computational models that accelerate energy breakthroughs, improve inverse problem solving, and enhance predictive simulations. He has been actively involved in organizing workshops, serving on editorial boards, and giving invited talks at prominent conferences and institutions worldwide. His research has been recognized through awards such as the NSF CAREER award and the AFRL/AFOSR Young Investigator Program. Peherstorfer's contributions include innovative approaches to learning from scarce data, multi-fidelity gradient sampling, and the development of computational models that support complex scientific and engineering applications. His work aims to bridge scientific computing and machine learning, fostering new methodologies for efficient and accurate scientific simulations.

Research topics

• Computer Science
• Machine Learning
• Artificial Intelligence
• Physics
• Applied mathematics
• Mathematics
• Geometry

Selected publications

• Nonlinear model reduction for transport-dominated problems

  Open MIND · 2026-02-01

  preprint

  This article surveys nonlinear model reduction methods that remain effective in regimes where linear reduced-space approximations are intrinsically inefficient, such as transport-dominated problems with wave-like phenomena and moving coherent structures, which are commonly associated with the Kolmogorov barrier. The article organizes nonlinear model reduction techniques around three key elements -- nonlinear parametrizations, reduced dynamics, and online solvers -- and categorizes existing approaches into transformation-based methods, online adaptive techniques, and formulations that combine generic nonlinear parametrizations with instantaneous residual minimization.

  DOI

• Nonlinear model reduction for transport-dominated problems

  arXiv (Cornell University) · 2026-02-01

  articleOpen access

  This article surveys nonlinear model reduction methods that remain effective in regimes where linear reduced-space approximations are intrinsically inefficient, such as transport-dominated problems with wave-like phenomena and moving coherent structures, which are commonly associated with the Kolmogorov barrier. The article organizes nonlinear model reduction techniques around three key elements -- nonlinear parametrizations, reduced dynamics, and online solvers -- and categorizes existing approaches into transformation-based methods, online adaptive techniques, and formulations that combine generic nonlinear parametrizations with instantaneous residual minimization.

  PublisherOA PDF

• Filtered Neural Galerkin model reduction schemes for efficient propagation of initial condition uncertainties in digital twins

  Journal of Computational Physics · 2026-04-03

  articleSenior authorCorresponding
  PublisherDOI

• A Dirac-Frenkel-Onsager principle: Instantaneous residual minimization with gauge momentum for nonlinear parametrizations of PDE solutions

  arXiv (Cornell University) · 2026-04-30

  preprintOpen accessSenior author

  Dirac-Frenkel instantaneous residual minimization evolves nonlinear parametrizations of PDE solutions in time, but ill-conditioning can render the parameter dynamics non-unique. We interpret this non-uniqueness as a gauge freedom: nullspace directions that leave the time derivative unchanged can be used to select better-conditioned parameter velocities. Building on Onsager's minimum-dissipation principle, we introduce a history variable -- interpretable as momentum -- and inject it only along the nullspace directions. The resulting Dirac-Frenkel-Onsager dynamics preserve instantaneous residual minimization, in contrast to standard regularization that can introduce bias, while promoting temporally smooth parameter evolutions. Examples demonstrate that the approach leads to increased robustness in singular and near-singular regimes.

  PublisherDOI

• A Dirac-Frenkel-Onsager principle: Instantaneous residual minimization with gauge momentum for nonlinear parametrizations of PDE solutions

  arXiv (Cornell University) · 2026-04-30

  articleOpen accessSenior author

  Dirac-Frenkel instantaneous residual minimization evolves nonlinear parametrizations of PDE solutions in time, but ill-conditioning can render the parameter dynamics non-unique. We interpret this non-uniqueness as a gauge freedom: nullspace directions that leave the time derivative unchanged can be used to select better-conditioned parameter velocities. Building on Onsager's minimum-dissipation principle, we introduce a history variable -- interpretable as momentum -- and inject it only along the nullspace directions. The resulting Dirac-Frenkel-Onsager dynamics preserve instantaneous residual minimization, in contrast to standard regularization that can introduce bias, while promoting temporally smooth parameter evolutions. Examples demonstrate that the approach leads to increased robustness in singular and near-singular regimes.

  PublisherOA PDF

• An adaptive data sampling strategy for stabilizing dynamical systems via controller inference

  ArXiv.org · 2025-06-02

  preprintOpen accessSenior author

  Learning stabilizing controllers from data is an important task in engineering applications; however, collecting informative data is challenging because unstable systems often lead to rapidly growing or erratic trajectories. In this work, we propose an adaptive sampling scheme that generates data while simultaneously stabilizing the system to avoid instabilities during the data collection. Under mild assumptions, the approach provably generates data sets that are informative for stabilization and have minimal size. The numerical experiments demonstrate that controller inference with the novel adaptive sampling approach learns controllers with up to one order of magnitude fewer data samples than unguided data generation. The results show that the proposed approach opens the door to stabilizing systems in edge cases and limit states where instabilities often occur and data collection is inherently difficult.

  PublisherOA PDFDOI

• Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction

  Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2025-05-01 · 4 citations

  articleSenior author

  This work introduces an online greedy method for constructing quadratic manifolds from streaming data, designed to enable in situ analysis of numerical simulation data on the Petabyte scale. Unlike traditional batch methods, which require all data to be available upfront and take multiple passes over the data, the proposed online greedy method incrementally updates quadratic manifolds in one pass as data points are received, eliminating the need for expensive disk input/output operations as well as storing and loading data points once they have been processed. A range of numerical examples demonstrate that the online greedy method learns accurate quadratic manifold embeddings while being capable of processing data that far exceed common disk input/output capabilities and volumes as well as main-memory sizes.

  PublisherDOI

• Filtered Neural Galerkin model reduction schemes for efficient propagation of initial condition uncertainties in digital twins

  ArXiv.org · 2025-11-01

  preprintOpen accessSenior author

  Uncertainty quantification in digital twins is critical to enable reliable and credible predictions beyond available data. A key challenge is that ensemble-based approaches can become prohibitively expensive when embedded in control and data assimilation loops in digital twins, even when reduced models are used. We introduce a reduced modeling approach that advances in time the mean and covariance of the reduced solution distribution induced by the initial condition uncertainties, which eliminates the need to maintain and propagate a costly ensemble of reduced solutions. The mean and covariance dynamics are obtained as a moment closure from Neural Galerkin schemes on pre-trained neural networks, which can be interpreted as filtered Neural Galerkin dynamics analogous to Gaussian filtering and the extended Kalman filter. Numerical experiments demonstrate that filtered Neural Galerkin schemes achieve more than one order of magnitude speedup compared to ensemble-based uncertainty propagation.

  PublisherOA PDFDOI

• Randomized time stepping of nonlinearly parametrized solutions of evolution problems

  arXiv (Cornell University) · 2025-12-22

  preprintOpen accessSenior author

  The Dirac-Frenkel variational principle is a widely used building block for using nonlinear parametrizations in the context of model reduction and numerically solving partial differential equations; however, it typically leads to time-dependent least-squares problems that are poorly conditioned. This work introduces a randomized time stepping scheme that solves at each time step a low-dimensional, random projection of the parameter vector via sketching. The sketching has a regularization effect that leads to better conditioned least-squares problems and at the same time reduces the number of unknowns that need to be solved for at each time step. Numerical experiments with benchmark examples demonstrate that randomized time stepping via sketching achieves competitive accuracy and outperforms standard regularization in terms of runtime efficiency.

  PublisherDOI

• Randomized time stepping of nonlinearly parametrized solutions of evolution problems

  ArXiv.org · 2025-12-22

  articleOpen accessSenior author

  The Dirac-Frenkel variational principle is a widely used building block for using nonlinear parametrizations in the context of model reduction and numerically solving partial differential equations; however, it typically leads to time-dependent least-squares problems that are poorly conditioned. This work introduces a randomized time stepping scheme that solves at each time step a low-dimensional, random projection of the parameter vector via sketching. The sketching has a regularization effect that leads to better conditioned least-squares problems and at the same time reduces the number of unknowns that need to be solved for at each time step. Numerical experiments with benchmark examples demonstrate that randomized time stepping via sketching achieves competitive accuracy and outperforms standard regularization in terms of runtime efficiency.

  PublisherOA PDF

Recent grants

• CAREER: Formulations, Theory, and Algorithms for Nonlinear Model Reduction in Transport-Dominated Systems

  NSF · $431k · 2021–2027

• Multifidelity Nonsmooth Optimization and Data-Driven Model Reduction for Robust Stabilization of Large-Scale Linear Dynamical Systems

  NSF · $400k · 2020–2024

Frequent coauthors

• Karen Willcox

  The University of Texas at Austin

  37 shared

• Wayne Isaac Tan Uy

  21 shared

• Hans–Joachim Bungartz

  Technical University of Munich

  20 shared

• Paul Schwerdtner

  Courant Institute of Mathematical Sciences

  17 shared

• Steffen W. R. Werner

  Virginia Tech

  17 shared

• Boris Krämer

  15 shared

• Terrence Alsup

  Courant Institute of Mathematical Sciences

  14 shared

• Frederick Law

  Courant Institute of Mathematical Sciences

  14 shared

Labs

• Benjamin Peherstorfer's Research GroupPI

  Current and past members of Peherstorfer's research group.

Awards & honors

• SIAM Best Student Paper prize
• NSF Graduate Research Fellowship
• Harold Grad Memorial Prize
• Moses A. Greenfield Research Prize
• SIAM Journal on Scientific Computing editorial board