313 citations · 704 across the 32 of their papers we have counts for
33 papers
Feature tracking in physics-informed neural networks via joint optimization of nonlinear deformation manifolds: application to shocks
Akshay Thakur, Matthew Zahr
Physics-informed neural networks (PINNs) often converge to inaccurate solutions for conservation laws with shocks, because uniformly distributed collocation points undersample loca…
Scalable h-adaptive probabilistic solver for time-independent and time-dependent systems
Akshay Thakur, Sawan Kumar, Matthew Zahr +1
Solving partial differential equations (PDEs) within the framework of probabilistic numerics offers a principled approach to quantifying epistemic uncertainty arising from discreti…
An -adaptive method for accurate resolution of shock-dominated viscous flow based on implicit shock tracking
Huijing Dong, Masayuki Yano, Tianci Huang +1
This work introduces an optimization-based -adaptive numerical method to approximate solutions of viscous, shock-dominated flows using implicit shock tracking and a high-order…
Model reduction of convection-dominated viscous conservation laws using implicit feature tracking and landmark image registration
Victor Zucatti, Matthew J. Zahr
Reduced-order models (ROMs) remain generally unreliable for convection-dominated problems, such as those encountered in hypersonic flows, due to the slowly decaying Kolmogorov -…
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
A mesh-based parametrization is a parametrization of a geometric object that is defined solely from a mesh of the object, e.g., without an analytical expression or computer-aided d…
A sharp-interface discontinuous Galerkin method for simulation of two-phase flow of real gases based on implicit shock tracking
Charles Naudet, Brian Taylor, Matthew J. Zahr
We present a high-order, sharp-interface method for simulation of two-phase flow of real gases using implicit shock tracking. The method is based on a phase-field formulation of tw…
Neural network-based Godunov corrections for approximate Riemann solvers using bi-fidelity learning
Akshay Thakur, Matthew J. Zahr
The Riemann problem is fundamental in the computational modeling of hyperbolic partial differential equations, enabling the development of stable and accurate upwind schemes. While…
An augmented Lagrangian trust-region method with inexact gradient evaluations to accelerate constrained optimization problems using model hyperreduction
Tianshu Wen, Matthew J. Zahr
We present an augmented Lagrangian trust-region method to efficiently solve constrained optimization problems governed by large-scale nonlinear systems with application to partial…
Preconditioned iterative solvers for constrained high-order implicit shock tracking methods
Jakob Vandergrift, Matthew J. Zahr
High-order implicit shock tracking (fitting) is a class of high-order numerical methods that use numerical optimization to simultaneously compute a high-order approximation to a co…
Symmetric, Optimization-based, Cross-element Compatible Nodal Distributions for High-order Finite Elements
Julian M. Kaufmann, Matthew J. Zahr
We present a general framework to construct symmetric, well-conditioned, cross-element compatible nodal distributions that can be used for high-order and high-dimensional finite el…
An adaptive model reduction method leveraging locally supported basis functions
Han Gao, Matthew J. Zahr
We propose a new method, the continuous Galerkin method with globally and locally supported basis functions (CG-GL), to address the parametric robustness issues of reduced-order mo…
A space-time high-order implicit shock tracking method for shock-dominated unsteady flows
Charles J. Naudet, Matthew J. Zahr
High-order implicit shock tracking (fitting) is a class of high-order, optimization-based numerical methods to approximate solutions of conservation laws with non-smooth features b…
Accelerated solutions of convection-dominated partial differential equations using implicit feature tracking and empirical quadrature
Marzieh Alireza Mirhoseini, Matthew J. Zahr
This work introduces an empirical quadrature-based hyperreduction procedure and greedy training algorithm to effectively reduce the computational cost of solving convection-dominat…
High-order implicit shock tracking boundary conditions for flows with parametrized shocks
Tianci Huang, Charles Naudet, Matthew J. Zahr
High-order implicit shock tracking (fitting) is a class of high-order, optimization-based numerical methods to approximate solutions of conservation laws with non-smooth features b…
An adaptive, training-free reduced-order model for convection-dominated problems based on hybrid snapshots
Victor Zucatti, Matthew J. Zahr
The vast majority of reduced-order models (ROMs) first obtain a low dimensional representation of the problem from high-dimensional model (HDM) training data which is afterwards us…
A globally convergent method to accelerate large-scale optimization using on-the-fly model hyperreduction: application to shape optimization
Tianshu Wen, Matthew J. Zahr
We present a numerical method to efficiently solve optimization problems governed by large-scale nonlinear systems of equations, including discretized partial differential equation…
Model reduction of convection-dominated partial differential equations via optimization-based implicit feature tracking
Marzieh Alireza Mirhoseini, Matthew J. Zahr
This work introduces a new approach to reduce the computational cost of solving partial differential equations (PDEs) with convection-dominated solutions: model reduction with impl…
Accurate quantification of blood flow wall shear stress using simulation-based imaging: a synthetic, comparative study
Charles J. Naudet, Johannes Toger, Matthew J. Zahr
Simulation-based imaging (SBI) is a blood flow imaging technique that optimally fits a computational fluid dynamics (CFD) simulation to low-resolution, noisy magnetic resonance (MR…
Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems
Han Gao, Matthew J. Zahr, Jian-Xun Wang
Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more c…
A robust, high-order implicit shock tracking method for simulation of complex, high-speed flows
Tianci Huang, Matthew J. Zahr
High-order implicit shock tracking is a new class of numerical methods to approximate solutions of conservation laws with non-smooth features. These methods align elements of the c…
Implicit shock tracking for unsteady flows by the method of lines
Andrew Shi, Per-Olof Persson, Matthew Zahr
A recently developed high-order implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid, steady conservation laws [41, 43] is extended to the un…
Preserving general physical properties in model reduction of dynamical systems via constrained-optimization projection
A. Schein, K. T. Carlberg, M. J. Zahr
Model-reduction techniques aim to reduce the computational complexity of simulating dynamical systems by applying a (Petrov-)Galerkin projection process that enforces the dynamics…
A globally convergent method to accelerate topology optimization using on-the-fly model reduction
Masayuki Yano, Tianci Huang, Matthew J. Zahr
We present a globally convergent method to accelerate density-based topology optimization using projection-based reduced-order models (ROMs) and trust-region methods. To accelerate…
Implicit shock tracking using an optimization-based high-order discontinuous Galerkin method
Matthew J. Zahr, Andrew Shi, Per-Olof Persson
A novel framework for resolving discontinuous solutions of conservation laws, e.g., contact lines, shock waves, and interfaces, using implicit tracking and a high-order discontinuo…