108 citations · 525 across the 62 of their papers we have counts for
67 papers
Adversarial Training Using Feedback Loops
Ali Haisam Muhammad Rafid, Adrian Sandu
Deep neural networks (DNN) have found wide applicability in numerous fields due to their ability to accurately learn very complex input-output relations. Despite their accuracy and…
Symplectic multirate generalized additive Runge-Kutta methods for Hamiltonian systems
Kevin Schäfers, Michael Günther, Adrian Sandu
The generalized additive Runge-Kutta (GARK) framework provides a powerful approach for solving additively partitioned ordinary differential equations. This work combines the ideas…
Neural Network Reduction with Guided Regularizers
Ali Haisam Muhammad Rafid, Adrian Sandu
Regularization techniques such as and regularizers are effective in sparsifying neural networks (NNs). However, to remove a certain neuron or channe…
A Two-Level Galerkin Reduced Order Model for the Steady Navier-Stokes Equations
Dylan Park, Changhong Mou, Honghu Liu +2
We propose, analyze, and investigate numerically a novel two-level Galerkin reduced order model (2L-ROM) for the efficient and accurate numerical simulation of the steady Navier-St…
The Model Forest Ensemble Kalman Filter
Andrey A Popov, Adrian Sandu
Traditional data assimilation uses information obtained from the propagation of one physics-driven model and combines it with information derived from real-world observations in or…
A Meta-learning Formulation of the Autoencoder Problem for Non-linear Dimensionality Reduction
Andrey A. Popov, Arash Sarshar, Austin Chennault +1
A rapidly growing area of research is the use of machine learning approaches such as autoencoders for dimensionality reduction of data and models in scientific applications. We sho…
Physics-informed neural networks for PDE-constrained optimization and control
Jostein Barry-Straume, Arash Sarshar, Andrey A. Popov +1
A fundamental problem in science and engineering is designing optimal control policies that steer a given system towards a desired outcome. This work proposes Control Physics-Infor…
Eliminating Order Reduction on Linear, Time-Dependent ODEs with GARK Methods
Steven Roberts, Adrian Sandu
When applied to stiff, linear differential equations with time-dependent forcing, Runge-Kutta methods can exhibit convergence rates lower than predicted by the classical order cond…
Ensemble Variational Fokker-Planck Methods for Data Assimilation
Amit N Subrahmanya, Andrey A Popov, Adrian Sandu
Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space unde…
Adjoint-Matching Neural Network Surrogates for Fast 4D-Var Data Assimilation
Austin Chennault, Andrey A. Popov, Amit N. Subrahmanya +4
Data assimilation is the process of fusing information from imperfect computer simulations with noisy, sparse measurements of reality to obtain improved estimates of the state or p…
A Stochastic Covariance Shrinkage Approach to Particle Rejuvenation in the Ensemble Transform Particle Filter
Andrey A Popov, Amit N Subrahmanya, Adrian Sandu
Rejuvenation in particle filters is necessary to prevent the collapse of the weights when the number of particles is insufficient to sample the high probability regions of the stat…
Investigation of Nonlinear Model Order Reduction of the Quasigeostrophic Equations through a Physics-Informed Convolutional Autoencoder
Rachel Cooper, Andrey A. Popov, Adrian Sandu
Reduced order modeling (ROM) is a field of techniques that approximates complex physics-based models of real-world processes by inexpensive surrogates that capture important dynami…
Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Physics-Informed Autoencoders
Andrey A Popov, Adrian Sandu
Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model,…
Symplectic GARK methods for partitioned Hamiltonian systems
Michael Günther, Adrian Sandu, Kevin Schäfers +1
Generalized Additive Runge-Kutta schemes have shown to be a suitable tool for solving ordinary differential equations with additively partitioned right-hand sides. This work develo…
A unified formulation of splitting-based implicit time integration schemes
Severiano González-Pinto, Domingo Hernández-Abreu, Maria S. Pérez-Rodríguez +3
Splitting-based time integration approaches such as fractional steps, alternating direction implicit, operator splitting, and locally one-dimensional methods partition the system o…
Multirate Linearly-Implicit GARK Schemes
Michael Guenther, Adrian Sandu
Many complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes t…
Linearly Implicit Multistep Methods for Time Integration
Ross Glandon, Mahesh Narayanamurthi, Adrian Sandu
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for t…
A fast time-stepping strategy for dynamical systems equipped with a surrogate model
Steven Roberts, Andrey A Popov, Arash Sarshar +1
Simulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and o…
Linearly implicit GARK schemes
Adrian Sandu, Michael Günther, Steven Roberts
Systems driven by multiple physical processes are central to many areas of science and engineering. Time discretization of multiphysics systems is challenging, since different proc…
A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates
Andrey A Popov, Changhong Mou, Traian Iliescu +1
This work develops a new multifidelity ensemble Kalman filter (MFEnKF) algorithm based on linear control variate framework. The approach allows for rigorous multifidelity extension…
Convergence Results for Implicit--Explicit General Linear Methods
Adrian Sandu
This paper studies fixed-step convergence of implicit-explicit general linear methods. We focus on a subclass of schemes that is internally consistent, has high stage order, and fa…
An Explicit Probabilistic Derivation of Inflation in a Scalar Ensemble Kalman Filter for Finite Step, Finite Ensemble Convergence
Andrey A Popov, Adrian Sandu
This paper uses a probabilistic approach to analyze the converge of an ensemble Kalman filter solution to an exact Kalman filter solution in the simplest possible setting, the scal…
A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering
Andrey A Popov, Adrian Sandu, Elias D. Nino-Ruiz +1
The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent covariance information, and are affected by sampling errors in operational settings where the number o…
Parallel implicit-explicit general linear methods
Steven Roberts, Arash Sarshar, Adrian Sandu
High-order discretizations of partial differential equations (PDEs) necessitate high-order time integration schemes capable of handling both stiff and nonstiff operators in an effi…