Scholarly Works, Computational Science Laboratory
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Linearly Implicit Multistep Methods for Time Integration
(Society for Industrial & Applied Mathematics (SIAM), 2022-12)Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, which significantly ... -
A Fast Time-Stepping Strategy for Dynamical Systems Equipped With a Surrogate Model
(Society for Industrial & Applied Mathematics (SIAM), 2022-01-01)Simulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and other types of surrogate modeling techniques ... -
A stochastic covariance shrinkage approach to particle rejuvenation in the ensemble transform particle filter
(Copernicus, 2022-06-22)Rejuvenation in particle filters is necessary to prevent the collapse of the weights when the number of particles is insufficient to properly sample the high-probability regions of the state space. Rejuvenation is often ... -
Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Theory-Guided Autoencoders
(Frontiers, 2022-06-02)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, and from noisy sparse observations of ... -
Reinforcement Learning for Self-adapting Time Discretizations of Complex Systems
(Virginia Tech, 2021-08-27)The overarching goal of this project is to develop intelligent, self-adapting numerical algorithms for the time discretization of complex real-world problems with Q-Learning methodologies. The specific application is ... -
Combining Data-driven and Theory-guided Models in Ensemble Data Assimilation
(Virginia Tech, 2022-08-23)There once was a dream that data-driven models would replace their theory-guided counterparts. We have awoken from this dream. We now know that data cannot replace theory. Data-driven models still have their advantages, ... -
Linearly Implicit General Linear Methods
(2021-12-01)Linearly implicit Runge–Kutta methods provide a fitting balance of implicit treat- ment of stiff systems and computational cost. In this paper we extend the class of linearly implicit Runge–Kutta methods to include multi-stage ... -
Physics-informed neural networks for PDE-constrained optimization and control
(2022-05-06)A fundamental problem of science is designing optimal control policies that manipulate a given environment into producing the desired outcome. Control PhysicsInformed Neural Networks simultaneously solve a given system ... -
Linearly implicit GARK schemes
(Elsevier, 2021-03-01)Systems driven by multiple physical processes are central to many areas of science and engineering. Time discretization of multiphysics systems is challenging, since different processes have different levels of stiffness ... -
Machine learning based algorithms for uncertainty quantification in numerical weather prediction models
(Elsevier, 2021-03-01)Complex numerical weather prediction models incorporate a variety of physical processes, each described by multiple alternative physical schemes with specific parameters. The selection of the physical schemes and the choice ... -
Partitioned exponential methods for coupled multiphysics systems
(Elsevier, 2021-03-01)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 time integration of multiphysics problems. ... -
Symplectic GARK methods for Hamiltonian systems
(2021-03-06)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 generalizes these GARK schemes to symplectic ... -
Subspace adaptivity in Rosenbrock-Krylov methods for the time integration of initial value problems
(Elsevier, 2021-03-15)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 arising within each stage of the integrator. ... -
Alternating directions implicit integration in a general linear method framework
(Elsevier, 2021-05-15)Alternating Directions Implicit (ADI) integration is an operator splitting approach to solve parabolic and elliptic partial differential equations in multiple dimensions based on solving sequentially a set of related ... -
Multirate implicit Euler schemes for a class of differential-algebraic equations of index-1
(Elsevier, 2021-05-15)Systems of differential equations which consist of subsystems with widely different dynamical behaviour can be integrated by multirate time integration schemes to increase the efficiency. These schemes allow the usage of ... -
Investigation of Nonlinear Model Order Reduction of the Quasigeostrophic Equations through a Physics-Informed Convolutional Autoencoder
(2021-08-27)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 dynamical characteristics with a smaller number ... -
A Stochastic Covariance Shrinkage Approach to Particle Rejuvenation in the Ensemble Transform Particle Filter
(2021-09-20)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 state space. Rejuvenation is often implemented ... -
Adjoint-Matching Neural Network Surrogates for Fast 4D-Var Data Assimilation
(2021-11-16)The data assimilation procedures used in many operational numerical weather forecasting systems are based around variants of the 4D-Var algorithm. The cost of solving the 4D-Var problem is dominated by the cost of forward ... -
An Ensemble Variational Fokker-Planck Method for Data Assimilation
(2021-11-27)Particle flow filters that aim to smoothly transform particles from samples from a prior distribution to samples from a posterior are a major topic of active research. In this work we introduce a generalized framework which ...
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