Progressive construction of a parametric reduced-order model for PDE-constrained optimization. - Matthew J. Zahr; Charbel Farhat (CoRR, 2014)

Fast local reduced basis updates for the efficient reduction of nonlinear systems with hyper-reduction. - David Amsallem; Matthew J. Zahr; Kyle Washabaugh (Adv. Comput. Math., 2015)

An adjoint method for a high-order discretization of deforming domain conservation laws for optimization of flow problems. - Matthew J. Zahr; Per-Olof Persson (J. Comput. Phys., 2016)

An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions. - Matthew J. Zahr; Per-Olof Persson (J. Comput. Phys., 2018)

Non-intrusive model reduction of large-scale, nonlinear dynamical systems using deep learning. - Han Gao 005; Jian-Xun Wang 001; Matthew J. Zahr (CoRR, 2019)

Implicit shock tracking using an optimization-based, r-adaptive, high-order discontinuous Galerkin method. - Matthew J. Zahr; Andrew Shi; Per-Olof Persson (CoRR, 2019)

An Efficient, Globally Convergent Method for Optimization Under Uncertainty Using Adaptive Model Reduction and Sparse Grids. - Matthew J. Zahr; Kevin T. Carlberg; Drew P. Kouri (SIAM/ASA J. Uncertain. Quantification, 2019)

A globally convergent method to accelerate topology optimization using on-the-fly model reduction. - Masayuki Yano; Tianci Huang; Matthew J. Zahr (CoRR, 2020)

Preserving general physical properties in model reduction of dynamical systems via constrained-optimization projection. - Alexander Schein; Kevin T. Carlberg; Matthew J. Zahr (CoRR, 2020)

High-order partitioned spectral deferred correction solvers for multiphysics problems. - Daniel Zhengyu Huang; Will Pazner; Per-Olof Persson; Matthew J. Zahr (J. Comput. Phys., 2020)

Implicit shock tracking using an optimization-based high-order discontinuous Galerkin method. - Matthew J. Zahr; Andrew Shi; Per-Olof Persson (J. Comput. Phys., 2020)

Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems. - Han Gao 005; Matthew J. Zahr; Jian-Xun Wang 001 (CoRR, 2021)

Accurate quantification of blood flow wall shear stress using simulation-based imaging: a synthetic, comparative study. - Charles J. Naudet; Johannes Töger; Matthew J. Zahr (Eng. Comput., 2022)

A robust, high-order implicit shock tracking method for simulation of complex, high-speed flows. - Tianci Huang; Matthew J. Zahr (J. Comput. Phys., 2022)

Implicit shock tracking for unsteady flows by the method of lines. - Andrew Shi; Per-Olof Persson; Matthew J. Zahr (J. Comput. Phys., 2022)

An adaptive, training-free reduced-order model for convection-dominated problems based on hybrid snapshots. - Victor Zucatti; Matthew J. Zahr (CoRR, 2023)

Accelerated solutions of convection-dominated partial differential equations using implicit feature tracking and empirical quadrature. - Marzieh Alireza Mirhoseini; Matthew J. Zahr (CoRR, 2023)

An adaptive model reduction method leveraging locally supported basis functions. - Han Gao 005; Matthew J. Zahr (CoRR, 2023)

Model reduction of convection-dominated partial differential equations via optimization-based implicit feature tracking. - Marzieh Alireza Mirhoseini; Matthew J. Zahr (J. Comput. Phys., 2023)

A globally convergent method to accelerate large-scale optimization using on-the-fly model hyperreduction: Application to shape optimization. - Tianshu Wen; Matthew J. Zahr (J. Comput. Phys., 2023)

High-order implicit shock tracking boundary conditions for flows with parametrized shocks. - Tianci Huang; Charles J. Naudet; Matthew J. Zahr (J. Comput. Phys., 2023)

Symmetric, Optimization-based, Cross-element Compatible Nodal Distributions for High-order Finite Elements. - Julian M. Kaufmann; Matthew J. Zahr (CoRR, 2024)

An augmented Lagrangian trust-region method with inexact gradient evaluations to accelerate constrained optimization problems using model hyperreduction. - Tianshu Wen; Matthew J. Zahr (CoRR, 2024)

Preconditioned iterative solvers for constrained high-order implicit shock tracking methods. - Jakob Vandergrift; Matthew J. Zahr (J. Comput. Phys., 2024)

A space-time high-order implicit shock tracking method for shock-dominated unsteady flows. - Charles J. Naudet; Matthew J. Zahr (J. Comput. Phys., 2024)

A sharp-interface discontinuous Galerkin method for simulation of two-phase flow of real gases based on implicit shock tracking. - Charles J. Naudet; Brian Taylor; Matthew J. Zahr (CoRR, 2025)

An implicit shock tracking method for simulation of shock-dominated flows over complex domains using mesh-based parametrizations. - Alexander M. Perez Reyes; Matthew J. Zahr (CoRR, 2025)

Neural network-based Godunov corrections for approximate Riemann solvers using bi-fidelity learning. - Akshay Thakur; Matthew J. Zahr (CoRR, 2025)

Model reduction of convection-dominated viscous conservation laws using implicit feature tracking and landmark image registration. - Victor Zucatti; Matthew J. Zahr (CoRR, 2025)

An rp-adaptive method for accurate resolution of shock-dominated viscous flow based on implicit shock tracking. - Huijing Dong; Masayuki Yano; Tianci Huang; Matthew J. Zahr (CoRR, 2025)