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A model hierarchy that is based on the one-dimensional isothermal Euler equations of fluid dynamics is used for the simulation and optimisation of gas flow through a pipeline network. Adaptive refinement strategies have the aim of bringing…
Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of a Hamiltonian matrix with one or more control parameters. It does this by projection onto a subspace of eigenvectors corresponding to…
Traditional fluid flow predictions require large computational resources. Despite recent progress in parallel and GPU computing, the ability to run fluid flow predictions in real-time is often infeasible. Recently developed machine learning…
In this paper, we propose a parallel-in-time algorithm for approximately solving parabolic equations. In particular, we apply the $k$-step backward differentiation formula, and then develop an iterative solver by using the waveform…
The real symmetric tridiagonal eigenproblem is of outstanding importance in numerical computations; it arises frequently as part of eigensolvers for standard and generalized dense Hermitian eigenproblems that are based on a reduction to…
Utility-based shortfall risk (UBSR), a convex risk measure sensitive to tail losses, has gained popularity in recent years. However, research on computational methods for UBSR optimization remains relatively scarce. In this paper, we…
Continuum resonance damping is an important factor in determining the stability of certain global modes in fusion plasmas. A number of analytic and numerical approaches have been developed to compute this damping, particularly in the case…
In one of the most important methods in Density Functional Theory - the Full-Potential Linearized Augmented Plane Wave (FLAPW) method - dense generalized eigenproblems are organized in long sequences. Moreover each eigenproblem is strongly…
This paper presents a novel generative model to synthesize fluid simulations from a set of reduced parameters. A convolutional neural network is trained on a collection of discrete, parameterizable fluid simulation velocity fields. Due to…
The FEAST algorithm is a subspace iteration method that uses a spectral projector as a rational filter in order to efficiently solve interior eigenvalue problems in parallel. Although the solutions from the FEAST algorithm converge rapidly…
In this paper we study the training dynamics for gradient flow on over-parametrized tensor decomposition problems. Empirically, such training process often first fits larger components and then discovers smaller components, which is similar…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
Discrete normalizing flows are promising generative models with advantages such as analytical log-likelihood computation and end-to-end training. However, the architectural constraints to ensure invertibility and tractable Jacobian…
This paper presents a new code for performing multidimensional radiation hydrodynamic (RHD) simulations on parallel computers involving anisotropic radiation fields and nonequilibrium effects. The radiation evolution modules described here…
This study addresses the challenge of simulating realistic particle systems by proposing a novel particle decomposition scheme that improves the parallel performance of surface resolved particle simulations. Realistic particle systems often…
Bilevel optimization has gained significant attention in recent years due to its broad applications in machine learning. This paper focuses on bilevel optimization in decentralized networks and proposes a novel single-loop algorithm for…
We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element…
Parallel stochastic gradient methods are gaining prominence in solving large-scale machine learning problems that involve data distributed across multiple nodes. However, obtaining unbiased stochastic gradients, which have been the focus of…
The characteristic decomposition for GRMHD is not known in a form useful for current numerical simulations. This prevents us from using the most accurate known computational methods, such as full-wave Riemann solvers. In this paper, we…
A high-resolution finite volume method approach to incorporating time-dependent slip across rectangular subfaults when modeling general fault geometry is presented. The fault slip is induced by a modification of the Riemann problem to the…