Spatially adaptive sparse grids for high-dimensional data-driven problems. - Dirk Pflüger; Benjamin Peherstorfer; Hans-Joachim Bungartz (J. Complex., 2010)

A Sparse-Grid-Based Out-of-Sample Extension for Dimensionality Reduction and Clustering with Laplacian Eigenmaps. - Benjamin Peherstorfer; Dirk Pflüger; Hans-Joachim Bungartz (Australasian Conference on Artificial Intelligence, 2011)

Fast Insight into High-Dimensional Parametrized Simulation Data. - Daniel Butnaru; Benjamin Peherstorfer; Hans-Joachim Bungartz; Dirk Pflüger (ICMLA (2), 2012)

Sparse grid classifiers as base learners for AdaBoost. - Alexander Heinecke; Benjamin Peherstorfer; Dirk Pflüger; Zhongwen Song (HPCS, 2012)

Clustering Based on Density Estimation with Sparse Grids. - Benjamin Peherstorfer; Dirk Pflüger; Hans-Joachim Bungartz (KI, 2012)

Semi-Coarsening in Space and Time for the Hierarchical Transformation Multigrid Method. - Benjamin Peherstorfer; Hans-Joachim Bungartz (ICCS, 2012)

Image Segmentation with Adaptive Sparse Grids. - Benjamin Peherstorfer; Julius Adorf; Dirk Pflüger; Hans-Joachim Bungartz (Australasian Conference on Artificial Intelligence, 2013)

Analysis of Car Crash Simulation Data with Nonlinear Machine Learning Methods. - Bastian Bohn; Jochen Garcke; Rodrigo Iza-Teran; Alexander Paprotny; Benjamin Peherstorfer; Ulf Schepsmeier; Clemens-August Thole (ICCS, 2013)

Model order reduction of parametrized systems with sparse grid learning techniques. - Benjamin Peherstorfer (2013)

Parametric model order reduction by sparse-grid-based interpolation on matrix manifolds for multidimensional parameter spaces. - Matthias Geuß; Daniel Butnaru; Benjamin Peherstorfer; Hans-Joachim Bungartz; Boris Lohmann (ECC, 2014)

Density Estimation with Adaptive Sparse Grids for Large Data Sets. - Benjamin Peherstorfer; Dirk Pflüger; Hans-Joachim Bungartz (SDM, 2014)

Localized Discrete Empirical Interpolation Method. - Benjamin Peherstorfer; Daniel Butnaru; Karen Willcox; Hans-Joachim Bungartz (SIAM J. Sci. Comput., 2014)

Detecting and Adapting to Parameter Changes for Reduced Models of Dynamic Data-driven Application Systems. - Benjamin Peherstorfer; Karen Willcox (ICCS, 2015)

Reduced models for sparse grid discretizations of the multi-asset Black-Scholes equation. - Benjamin Peherstorfer; Pablo Gómez; Hans-Joachim Bungartz (Adv. Comput. Math., 2015)

Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates. - Benjamin Peherstorfer; Karen Willcox (SIAM J. Sci. Comput., 2015)

A Multigrid Method for Adaptive Sparse Grids. - Benjamin Peherstorfer; Stefan Zimmer 001; Christoph Zenger 001; Hans-Joachim Bungartz (SIAM J. Sci. Comput., 2015)

Dynamic data-driven model reduction: adapting reduced models from incomplete data. - Benjamin Peherstorfer; Karen Willcox (Adv. Model. Simul. Eng. Sci., 2016)

Optimal Model Management for Multifidelity Monte Carlo Estimation. - Benjamin Peherstorfer; Karen Willcox; Max D. Gunzburger (SIAM J. Sci. Comput., 2016)

Combining multiple surrogate models to accelerate failure probability estimation with expensive high-fidelity models. - Benjamin Peherstorfer; Boris Kramer; Karen Willcox (J. Comput. Phys., 2017)

Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models. - Boris Kramer; Benjamin Peherstorfer; Karen Willcox (SIAM J. Appl. Dyn. Syst., 2017)

Data-Driven Reduced Model Construction with Time-Domain Loewner Models. - Benjamin Peherstorfer; Serkan Gugercin; Karen Willcox (SIAM J. Sci. Comput., 2017)

Multifidelity Preconditioning of the Cross-Entropy Method for Rare Event Simulation and Failure Probability Estimation. - Benjamin Peherstorfer; Boris Kramer; Karen Willcox (SIAM/ASA J. Uncertain. Quantification, 2018)

Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices. - Elizabeth Qian; Benjamin Peherstorfer; Daniel O'Malley; Velimir V. Vesselinov; Karen Willcox (SIAM/ASA J. Uncertain. Quantification, 2018)

Convergence analysis of multifidelity Monte Carlo estimation. - Benjamin Peherstorfer; Max D. Gunzburger; Karen Willcox (Numerische Mathematik, 2018)

Geometric Subspace Updates with Applications to Online Adaptive Nonlinear Model Reduction. - Ralf Zimmermann 002; Benjamin Peherstorfer; Karen Willcox (SIAM J. Matrix Anal. Appl., 2018)

Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization. - Benjamin Peherstorfer; Karen Willcox; Max D. Gunzburger (SIAM Rev., 2018)

A transport-based multifidelity preconditioner for Markov chain Monte Carlo. - Benjamin Peherstorfer; Youssef M. Marzouk (Adv. Comput. Math., 2019)

Sampling low-dimensional Markovian dynamics for pre-asymptotically recovering reduced models from data with operator inference. - Benjamin Peherstorfer (CoRR, 2019)

Learning low-dimensional dynamical-system models from noisy frequency-response data with Loewner rational interpolation. - Zlatko Drmac; Benjamin Peherstorfer (CoRR, 2019)

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems. - Elizabeth Qian; Boris Kramer; Benjamin Peherstorfer; Karen Willcox (CoRR, 2019)

Multifidelity probability estimation via fusion of estimators. - Boris Kramer; Alexandre Noll Marques; Benjamin Peherstorfer; Umberto Villa; Karen Willcox (J. Comput. Phys., 2019)

Multifidelity Monte Carlo Estimation with Adaptive Low-Fidelity Models. - Benjamin Peherstorfer (SIAM/ASA J. Uncertain. Quantification, 2019)

Quasi-Optimal Sampling to Learn Basis Updates for Online Adaptive Model Reduction with Adaptive Empirical Interpolation. - Alice Cortinovis; Daniel Kressner; Stefano Massei; Benjamin Peherstorfer (ACC, 2020)

Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms. - Peter Benner; Pawan Goyal 003; Boris Kramer; Benjamin Peherstorfer; Karen Willcox (CoRR, 2020)

Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations. - Wayne Isaac Tan Uy; Benjamin Peherstorfer (CoRR, 2020)

Depth separation for reduced deep networks in nonlinear model reduction: Distilling shock waves in nonlinear hyperbolic problems. - Donsub Rim; Luca Venturi; Joan Bruna; Benjamin Peherstorfer (CoRR, 2020)

Context-aware surrogate modeling for balancing approximation and sampling costs in multi-fidelity importance sampling and Bayesian inverse problems. - Terrence Alsup; Benjamin Peherstorfer (CoRR, 2020)

Model Reduction for Transport-Dominated Problems via Online Adaptive Bases and Adaptive Sampling. - Benjamin Peherstorfer (SIAM J. Sci. Comput., 2020)

Sampling Low-Dimensional Markovian Dynamics for Preasymptotically Recovering Reduced Models from Data with Operator Inference. - Benjamin Peherstorfer (SIAM J. Sci. Comput., 2020)

Stability of Discrete Empirical Interpolation and Gappy Proper Orthogonal Decomposition with Randomized and Deterministic Sampling Points. - Benjamin Peherstorfer; Zlatko Drmac; Serkan Gugercin (SIAM J. Sci. Comput., 2020)

Multilevel Stein variational gradient descent with applications to Bayesian inverse problems. - Terrence Alsup; Luca Venturi; Benjamin Peherstorfer (MSML, 2021)

An Extensible Benchmark Suite for Learning to Simulate Physical Systems. - Karl Otness; Arvi Gjoka; Joan Bruna; Daniele Panozzo; Benjamin Peherstorfer; Teseo Schneider; Denis Zorin (NeurIPS Datasets and Benchmarks, 2021)

Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference. - Nihar Sawant; Boris Kramer; Benjamin Peherstorfer (CoRR, 2021)

Accelerating the estimation of energetic particle confinement statistics in stellarators using multifidelity Monte Carlo. - Frederick Law; Antoine J. Cerfon; Benjamin Peherstorfer (CoRR, 2021)

Operator Inference of Non-Markovian Terms for Learning Reduced Models from Partially Observed State Trajectories. - Wayne Isaac Tan Uy; Benjamin Peherstorfer (J. Sci. Comput., 2021)

Towards context-aware learning for control: Balancing stability and model-learning error. - Nitin Shyamkumar; Serkan Gugercin; Benjamin Peherstorfer (ACC, 2022)

Neural Galerkin Scheme with Active Learning for High-Dimensional Evolution Equations. - Joan Bruna; Benjamin Peherstorfer; Eric Vanden-Eijnden (CoRR, 2022)

Multi-fidelity robust controller design with gradient sampling. - Steffen W. R. Werner; Michael L. Overton; Benjamin Peherstorfer (CoRR, 2022)

Context-aware controller inference for stabilizing dynamical systems from scarce data. - Steffen W. R. Werner; Benjamin Peherstorfer (CoRR, 2022)

Reduced models with nonlinear approximations of latent dynamics for model premixed flame problems. - Wayne Isaac Tan Uy; Christopher R. Wentland; Cheng Huang; Benjamin Peherstorfer (CoRR, 2022)

Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification. - Ionut-Gabriel Farcas; Benjamin Peherstorfer; Tobias Neckel; Frank Jenko; Hans-Joachim Bungartz (CoRR, 2022)

Data-driven low-fidelity models for multi-fidelity Monte Carlo sampling in plasma micro-turbulence analysis. - Julia Konrad; Ionut-Gabriel Farcas; Benjamin Peherstorfer; Alessandro Di Siena; Frank Jenko; Tobias Neckel; Hans-Joachim Bungartz (J. Comput. Phys., 2022)

Multi-Fidelity Covariance Estimation in the Log-Euclidean Geometry. - Aimee Maurais; Terrence Alsup; Benjamin Peherstorfer; Youssef M. Marzouk (ICML, 2023)

Randomized Sparse Neural Galerkin Schemes for Solving Evolution Equations with Deep Networks. - Jules Berman; Benjamin Peherstorfer (NeurIPS, 2023)

Coupling parameter and particle dynamics for adaptive sampling in Neural Galerkin schemes. - Yuxiao Wen; Eric Vanden-Eijnden; Benjamin Peherstorfer (CoRR, 2023)

Lookahead data-gathering strategies for online adaptive model reduction of transport-dominated problems. - Rodrigo Singh; Wayne Isaac Tan Uy; Benjamin Peherstorfer (CoRR, 2023)

Manifold Approximations via Transported Subspaces: Model Reduction for Transport-Dominated Problems. - Donsub Rim; Benjamin Peherstorfer; Kyle T. Mandli (SIAM J. Sci. Comput., 2023)

Context-Aware Surrogate Modeling for Balancing Approximation and Sampling Costs in Multifidelity Importance Sampling and Bayesian Inverse Problems. - Terrence Alsup; Benjamin Peherstorfer (SIAM/ASA J. Uncertain. Quantification, 2023)

Multifidelity Robust Controller Design with Gradient Sampling. - Steffen W. R. Werner; Michael L. Overton; Benjamin Peherstorfer (SIAM J. Sci. Comput., 2023)

Active Operator Inference for Learning Low-Dimensional Dynamical-System Models from Noisy Data. - Wayne Isaac Tan Uy; Yuepeng Wang 006; Yuxiao Wen; Benjamin Peherstorfer (SIAM J. Sci. Comput., 2023)

Operator inference with roll outs for learning reduced models from scarce and low-quality data. - Wayne Isaac Tan Uy; Dirk Hartmann; Benjamin Peherstorfer (Comput. Math. Appl., 2023)

Meta variance reduction for Monte Carlo estimation of energetic particle confinement during stellarator optimization. - Frederick Law; Antoine J. Cerfon; Benjamin Peherstorfer; Florian Wechsung (J. Comput. Phys., 2023)

CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equations. - Jules Berman; Benjamin Peherstorfer (ICML, 2024)

Parametric model reduction of mean-field and stochastic systems via higher-order action matching. - Jules Berman; Tobias Blickhan; Benjamin Peherstorfer (NeurIPS, 2024)

Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction. - Paul Schwerdtner; Benjamin Peherstorfer (CoRR, 2024)

Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial differential equations. - Huan Zhang; Yifan Chen; Eric Vanden-Eijnden; Benjamin Peherstorfer (CoRR, 2024)

System stabilization with policy optimization on unstable latent manifolds. - Steffen W. R. Werner; Benjamin Peherstorfer (CoRR, 2024)

Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction. - Paul Schwerdtner; Prakash Mohan 004; Aleksandra Pachalieva; Julie Bessac; Daniel O'Malley; Benjamin Peherstorfer (CoRR, 2024)

Empirical sparse regression on quadratic manifolds. - Paul Schwerdtner; Serkan Gugercin; Benjamin Peherstorfer (CoRR, 2024)

Rank-Minimizing and Structured Model Inference. - Pawan Goyal 003; Benjamin Peherstorfer; Peter Benner (SIAM J. Sci. Comput., 2024)

Nonlinear Embeddings for Conserving Hamiltonians and Other Quantities with Neural Galerkin Schemes. - Paul Schwerdtner; Philipp Schulze; Jules Berman; Benjamin Peherstorfer (SIAM J. Sci. Comput., 2024)

Neural Galerkin schemes with active learning for high-dimensional evolution equations. - Joan Bruna; Benjamin Peherstorfer; Eric Vanden-Eijnden (J. Comput. Phys., 2024)

On the Sample Complexity of Stabilizing Linear Dynamical Systems from Data. - Steffen W. R. Werner; Benjamin Peherstorfer (Found. Comput. Math., 2024)

Further analysis of multilevel Stein variational gradient descent with an application to the Bayesian inference of glacier ice models. - Terrence Alsup; Tucker Hartland; Benjamin Peherstorfer; Noemi Petra (Adv. Comput. Math., 2024)

Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds. - Philipp Weder; Paul Schwerdtner; Benjamin Peherstorfer (J. Comput. Phys., 2025)

Multifidelity Covariance Estimation via Regression on the Manifold of Symmetric Positive Definite Matrices. - Aimee Maurais; Terrence Alsup; Benjamin Peherstorfer; Youssef M. Marzouk (SIAM J. Math. Data Sci., 2025)

An adaptive data sampling strategy for stabilizing dynamical systems via controller inference. - Steffen W. R. Werner; Benjamin Peherstorfer (CoRR, 2025)

DICE: Discrete inverse continuity equation for learning population dynamics. - Tobias Blickhan; Jules Berman; Andrew Stuart; Benjamin Peherstorfer (CoRR, 2025)

Operator Inference Aware Quadratic Manifolds with Isotropic Reduced Coordinates for Nonintrusive Model Reduction. - Paul Schwerdtner; Prakash Mohan 004; Julie Bessac; Marc T. Henry de Frahan; Benjamin Peherstorfer (CoRR, 2025)