21 citations · 79 across the 12 of their papers we have counts for
12 papers
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…