Publications (88)
Implicit multirate GARK methods
Steven Roberts, John Loffeld, Arash Sarshar +2
This work considers multirate generalized-structure additively partitioned Runge-Kutta (MrGARK) methods for solving stiff systems of ordinary differential equations (ODEs) with mul…
ODE Test Problems: a MATLAB suite of initial value problems
Steven Roberts, Andrey A. Popov, Adrian Sandu
ODE Test Problems (OTP) is an object-oriented MATLAB package offering a broad range of initial value problems which can be used to test numerical methods such as time integration m…
An Ensemble Kalman Filter Implementation Based on Modified Cholesky Decomposition for Inverse Covariance Matrix Estimation
Elias D. Nino, Adrian Sandu, Xinwei Deng
This paper develops an efficient implementation of the ensemble Kalman filter based on a modified Cholesky decomposition for inverse covariance matrix estimation. This implementati…
Dynamic Response Optimization of Complex Multibody Systems in a Penalty Formulation using Adjoint Sensitivity
Yitao Zhu, Daniel Dopico, Corina Sandu +1
Multibody dynamics simulations are currently widely accepted as valuable means for dynamic performance analysis of mechanical systems. The evolution of theoretical and computationa…
EPIRK-W and EPIRK-K time discretization methods
Mahesh Narayanamurthi, Paul Tranquilli, Adrian Sandu +1
Exponential integrators are special time discretization methods where the traditional linear system solves used by implicit schemes are replaced with computing the action of matrix…
Benchmarking Machine Learning Uncertainty Quantification Methodologies for Predicting Turbine Gas Temperature Degradation
Jostein Barry-Straume, Changmin Son, Adrian Sandu +4
Effective prognostics and health management of modern engines relies on accurate turbine gas temperature predictions and robust uncertainty quantification to ensure reliability and…
Adjoint Sensitivity Analysis of Hybrid Multibody Dynamical Systems
Sebastien Corner, Corina Sandu, Adrian Sandu
Sensitivity analysis of multibody systems computes the derivatives of general cost functions that depend on the system solution with respect to parameters or initial conditions. Th…
Multirate methods for ordinary differential equations
Michael Günther, Adrian Sandu
This survey provides an overview of state-of-the art multirate schemes, which exploit the different time scales in the dynamics of a differential equation model by adapting the com…
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 copula-based rank histogram ensemble filter
Amit N. Subrahmanya, Julie Bessac, Andrey A. Popov +1
Serial ensemble filters implement triangular probability transport maps to reduce high-dimensional inference problems to sequences of state-by-state univariate inference problems.…
Scientific Machine Learning for Engine Health Management and Remaining Useful Life Prediction
Jostein Barry-Straume, Changmin Son, Adrian Sandu +4
Engine Health Management (EHM) depends on reliable forecasting of Remaining Useful Life (RUL) and on tracking thermal indicators such as turbine gas temperature (TGT). In practice,…
Coupled Multirate Infinitesimal GARK Schemes for Stiff Systems with Multiple Time Scales
Steven Roberts, Arash Sarshar, Adrian Sandu
Traditional time discretization methods use a single timestep for the entire system of interest and can perform poorly when the dynamics of the system exhibits a wide range of time…
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-posteriori error estimates for inverse problems
Vishwas Rao, Adrian Sandu
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in…
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…
Partitioned Exponential Methods for Coupled Multiphysics Systems
Mahesh Narayanamurthi, Adrian Sandu
Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the…
Adaptive Krylov-Type Time Integration Methods
Paul Tranquilli, Ross Glandon, Adrian Sandu
The Rosenbrock-Krylov family of time integration schemes is an extension of Rosenbrock-W methods that employs a specific Krylov based approximation of the linear system solutions a…
Multivariate predictions of local reduced-order-model errors and dimensions
Azam Moosavi, Razvan Stefanescu, Adrian Sandu
This paper introduces multivariate input-output models to predict the errors and bases dimensions of local parametric Proper Orthogonal Decomposition reduced-order models. We refer…
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…
Solving stochastic chemical kinetics by Metropolis Hastings sampling
Azam S. Zavar Moosavi, Paul Tranquilli, Adrian Sandu
This study considers using Metropolis-Hastings algorithm for stochastic simulation of chemical reactions. The proposed method uses SSA (Stochastic Simulation Algorithm) distributio…
Feature preserving data assimilation via feature alignment
Amit N. Subrahmanya, Adrian Sandu
Data assimilation combines information from physical observations and numerical simulation results to obtain better estimates of the state and parameters of a physical system. A wi…
Robust data assimilation using and Huber norms
Vishwas Rao, Adrian Sandu, Michael Ng +1
Data assimilation is the process to fuse information from priors, observations of nature, and numerical models, in order to obtain best estimates of the parameters or state of a ph…
High Order Implicit-Explicit General Linear Methods with Optimized Stability Regions
Hong Zhang, Adrian Sandu, Sebastien Blaise
In the numerical solution of partial differential equations using a method-of-lines approach, the availability of high order spatial discretization schemes motivates the developmen…
DATeS: A Highly-Extensible Data Assimilation Testing Suite v1.0
Ahmed Attia, Adrian Sandu
A flexible and highly-extensible data assimilation testing suite, named DATeS, is described in this paper. DATeS aims to offer a unified testing environment that allows researchers…
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…
Biorthogonal Rosenbrock-Krylov time discretization methods
Ross Glandon, Paul Tranquilli, Adrian Sandu
Many scientific applications require the solution of large initial-value problems, such as those produced by the method of lines after semi-discretization in space of partial diffe…
A Hybrid Monte-Carlo Sampling Smoother for Four Dimensional Data Assimilation
Ahmed Attia, Vishwas Rao, Adrian Sandu
This paper constructs an ensemble-based sampling smoother for four-dimensional data assimilation using a Hybrid/Hamiltonian Monte-Carlo approach. The smoother samples efficiently f…
Application of approximate matrix factorization to high order linearly implicit Runge-Kutta methods
Hong Zhang, Adrian Sandu, Paul Tranquilli
Linearly implicit Runge-Kutta methods with approximate matrix factorization can solve efficiently large systems of differential equations that have a stiff linear part, e.g. reacti…
POD/DEIM Reduced-Order Strategies for Efficient Four Dimensional Variational Data Assimilation
RÄzvan ÅtefÄnescu, Adrian Sandu, Ionel Michael Navon
This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is show…
Efficient Construction of Local Parametric Reduced Order Models Using Machine Learning Techniques
Azam Moosavi, Razvan Stefanescu, Adrian Sandu
Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems…
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…
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…
Alternating Directions Implicit Integration in a General Linear Method Framework
Arash Sarshar, Steven Roberts, Adrian Sandu
Alternating Directions Implicit (ADI) integration is an operator splitting approach to solve parabolic and elliptic partial differential equations in multiple dimensions based on s…
Implicit Simulation Methods for Stochastic Chemical Kinetics
Tae-Hyuk Ahn, Adrian Sandu, Xiaoying Han
In biochemical systems some of the chemical species are present with only small numbers of molecules. In this situation discrete and stochastic simulation approaches are more relev…
Improving the Adaptive Moment Estimation (ADAM) stochastic optimizer through an Implicit-Explicit (IMEX) time-stepping approach
Abhinab Bhattacharjee, Andrey A. Popov, Arash Sarshar +1
The Adam optimizer, often used in Machine Learning for neural network training, corresponds to an underlying ordinary differential equation (ODE) in the limit of very small learnin…
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 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…
Goal-oriented a posteriori estimation of numerical errors in the solution of multiphysics systems
Mahesh Narayanamurthi, Ulrich Römer, Adrian Sandu
This paper develops a general methodology for a posteriori error estimation in time-dependent multiphysics numerical simulations. The methodology builds upon the generalized-struct…
A Parallel Implementation of the Ensemble Kalman Filter Based on Modified Cholesky Decomposition
Elias D. Nino, Adrian Sandu, Xinwei Deng
This paper discusses an efficient parallel implementation of the ensemble Kalman filter based on the modified Cholesky decomposition. The proposed implementation starts with decomp…
Design of High-Order Decoupled Multirate GARK Schemes
Arash Sarshar, Steven Roberts, Adrian Sandu
Multirate time integration methods apply different step sizes to resolve different components of the system based on the local activity levels. This local selection of step sizes a…
Ensemble Kalman Filter Implementations Based on Covariance Matrix Estimation
Elias D. Nino-Ruiz, Adrian Sandu
This paper develops efficient ensemble Kalman filter (EnKF) implementations based on shrinkage covariance estimation. The forecast ensemble members at each step are used to estimat…
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…
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…
A Numerical Investigation of Matrix-Free Implicit Time-Stepping Methods for Large CFD Simulations
Arash Sarshar, Paul Tranquilli, Brent Pickering +3
This paper is concerned with the development and testing of advanced time-stepping methods suited for the integration of time-accurate, real-world applications of computational flu…
A Patankar predictor-corrector approach for positivity-preserving time integration
Kamila Nurkhametova, Reid J. Gomillion, Amit N. Subrahmanya +1
Many natural processes, such as chemical reactions and wave dynamics, are modeled as production-destruction (PD) systems that obey positivity and linear conservation laws. Classica…
Extrapolation-based implicit-explicit general linear methods
Angelamaria Cardone, Zdzislaw Jackiewicz, Hong Zhang +1
For many systems of differential equations modeling problems in science and engineering, there are natural splittings of the right hand side into two parts, one non-stiff or mildly…
Ensemble based Closed-Loop Optimal Control using Physics-Informed Neural Networks
Jostein Barry-Straume, Adwait D. Verulkar, Arash Sarshar +2
The objective of designing a control system is to steer a dynamical system with a control signal, guiding it to exhibit the desired behavior. The Hamilton-Jacobi-Bellman (HJB) part…
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…
Efficient implementation of partitioned stiff exponential Runge-Kutta methods
Mahesh Narayanamurthi, Adrian Sandu
Multiphysics systems are driven by multiple processes acting simultaneously, and their simulation leads to partitioned systems of differential equations. This paper studies the sol…
Preserving Nonlinear Constraints in Variational Flow Filtering Data Assimilation
Amit N. Subrahmanya, Andrey A. Popov, Reid J. Gomillion +1
Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by…
A Derivative-Free Trust Region Framework for Variational Data Assimilation
Elias D. Nino, Adrian Sandu
This study develops a hybrid ensemble-variational approach for solving data assimilation problems. The method, called TR-4D-EnKF, is based on a trust region framework and consists…
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…
Simultaneous Optimal System and Controller Design for Multibody Systems with Joint Friction using Direct Sensitivities
Adwait Verulkar, Corina Sandu, Adrian Sandu +1
Real-world multibody systems are often subject to phenomena like friction, joint clearances, and external events. These phenomena can significantly impact the optimal design of the…
Modeling and sensitivity analysis methodology for hybrid dynamical systems
Sebastien Corner, Corina Sandu, Adrian Sandu
This paper provides an analytical methodology to compute the sensitivities with respect to system parameters for any second order hybrid Ordinary Differential Equation (ODE) system…
Approximate Exponential Algorithms to Solve the Chemical Master Equation
Azam S. Zavar Moosavi, Adrian Sandu
This paper discusses new simulation algorithms for stochastic chemical kinetics that exploit the linearity of the chemical master equation and its matrix exponential exact solution…
Comparison of POD reduced order strategies for the nonlinear 2D Shallow Water Equations
RÄzvan ÅtefÄnescu, Adrian Sandu, Ionel M. Navon
This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms.…
LIRK-W: Linearly-implicit Runge-Kutta methods with approximate matrix factorization
Paul Tranquilli, Adrian Sandu, Hong Zhang
This paper develops a new class of linearly implicit time integration schemes called Linearly-Implicit Runge-Kutta-W (LIRK-W) methods. These schemes are based on an implicit-explic…
Efficient methods for computing observation impact in 4D-Var data assimilation
Alexandru Cioaca, Adrian Sandu, Eric de Sturler
This paper presents a practical computational approach to quantify the effect of individual observations in estimating the state of a system. Such an analysis can be used for pruni…
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…
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,…
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…
A class of generalized additive Runge-Kutta methods
Adrian Sandu, Michael Guenther
This work generalizes the additively partitioned Runge-Kutta methods by allowing for different stage values as arguments of different components of the right hand side. An order co…
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…
A Learning Based Approach for Uncertainty Analysis in Numerical Weather Prediction Models
Azam Moosavi, Vishwas Rao, Adrian Sandu
Complex numerical weather prediction models incorporate a variety of physical processes, each described by multiple alternative physical schemes with specific parameters. The selec…
The Reduced-Order Hybrid Monte Carlo Sampling Smoother
Ahmed Attia, Razvan Stefanescu, Adrian Sandu
Hybrid Monte-Carlo (HMC) sampling smoother is a fully non-Gaussian four-dimensional data assimilation algorithm that works by directly sampling the posterior distribution formulate…
Rosenbrock-Krylov Methods for Large Systems of Differential Equations
Paul Tranquilli, Adrian Sandu
This paper develops a new class of Rosenbrock-type integrators based on a Krylov space solution of the linear systems. The new family, called Rosenbrock-Krylov (Rosenbrock-K), is w…
Multirate generalized additive Runge Kutta methods
Michael Guenther, Adrian Sandu
This work constructs a new class of multirate schemes based on the recently developed generalized additive Runge-Kutta (GARK) methods (Sandu and Guenther, 2013). Multirate schemes…
Solving Parameter Estimation Problems with Discrete Adjoint Exponential Integrators
Ulrich Römer, Mahesh Narayanamurthi, Adrian Sandu
The solution of inverse problems in a variational setting finds best estimates of the model parameters by minimizing a cost function that penalizes the mismatch between model outpu…
A unified formulation of splitting-based implicit time integration schemes
Severiano González-Pinto, Domingo Hernández-Abreu, Maria S. Pérez-RodrÃguez +3
Splitting-based time integration approaches such as fractional steps, alternating direction implicit, operator splitting, and locally one-dimensional methods partition the system o…
Optimization of Vehicle Dynamics based on Multibody Models using Adjoint Sensitivity Analysis
Yitao Zhu, Corina Sandu, Daniel Dopico +1
Multibody dynamics simulations have become widely used tools for vehicle systems analysis and design. As this approach evolves, it becomes able to provide additional information fo…
Partitioned and implicit-explicit general linear methods for ordinary differential equations
Hong Zhang, Adrian Sandu
Implicit-explicit (IMEX) time stepping methods can efficiently solve differential equa- tions with both stiff and nonstiff components. IMEX Runge-Kutta methods and IMEX linear mult…
A Time-parallel Approach to Strong-constraint Four-dimensional Variational Data Assimilation
Vishwas Rao, Adrian Sandu
A parallel-in-time algorithm based on an augmented Lagrangian approach is proposed to solve four-dimensional variational (4D-Var) data assimilation problems. The assimilation windo…
A Sampling Filter for Non-Gaussian Data Assimilation
Ahmed Attia, Adrian Sandu
Data assimilation combines information from models, measurements, and priors to estimate the state of a dynamical system such as the atmosphere. The Ensemble Kalman filter (EnKF) i…
A Machine Learning Approach to Adaptive Covariance Localization
Azam Moosavi, Ahmed Attia, Adrian Sandu
Data assimilation plays a key role in large-scale atmospheric weather forecasting, where the state of the physical system is estimated from model outputs and observations, and is t…
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…
Low-rank Approximations for Computing Observation Impact in 4D-Var Data Assimilation
Alexandru Cioaca, Adrian Sandu
We present an efficient computational framework to quantify the impact of individual observations in four dimensional variational data assimilation. The proposed methodology uses f…
An Efficient Implementation of the Ensemble Kalman Filter Based on an Iterative Sherman-Morrison Formula
Elias D. Nino-Ruiz, Adrian Sandu, Jeffrey Anderson
We present a practical implementation of the ensemble Kalman (EnKF) filter based on an iterative Sherman-Morrison formula. The new direct method exploits the special structure of t…
Efficient approximation of sparse Jacobians for time-implicit reduced order models
RÄzvan ÅtefÄnescu, Adrian Sandu
This paper introduces a sparse matrix discrete interpolation method to effectively compute matrix approximations in the reduced order modeling framework. The sparse algorithm devel…
A Class of Multirate Infinitesimal GARK Methods
Adrian Sandu
Differential equations arising in many practical applications are characterized by multiple time scales. Multirate time integration seeks to solve them efficiently by discretizing…
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…
An Optimization Framework to Improve 4D-Var Data Assimilation System Performance
Alexandru Cioaca, Adrian Sandu
This paper develops a computational framework for optimizing the parameters of data assimilation systems in order to improve their performance. The approach formulates a continuous…
Cluster Sampling Filters for Non-Gaussian Data Assimilation
Ahmed Attia, Azam Moosavi, Adrian Sandu
This paper presents a fully non-Gaussian version of the Hamiltonian Monte Carlo (HMC) sampling filter. The Gaussian prior assumption in the original HMC filter is relaxed. Specific…
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…
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…
A Bayesian Approach to Multivariate Adaptive Localization in Ensemble-Based Data Assimilation with Time-Dependent Extensions
Andrey A Popov, Adrian Sandu
Ever since its inception, the Ensemble Kalman Filter has elicited many heuristic methods that sought to correct it. One such method is localization---the thought that `nearby' vari…
Exponential-Krylov methods for ordinary differential equations
Paul Tranquilli, Adrian Sandu
This paper develops a new class of exponential-type integrators where all the matrix exponentiations are performed in a single Krylov space of low dimension. The new family, called…
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…
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…