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In this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational…
Linear system solving is a key tool for computational power system studies, e.g., optimal power flow, transmission switching, or unit commitment. CPU-based linear system solver speeds, however, have saturated in recent years. Emerging…
We consider the use of Gaussian process (GP) priors for solving inverse problems in a Bayesian framework. As is well known, the computational complexity of GPs scales cubically in the number of datapoints. We here show that in the context…
In this paper we propose a method for the construction of locally conservative flux fields from Generalized Multiscale Finite Element Method (GMsFEM) pressure solutions. The flux values are obtained from an element-based postprocessing…
Flow-based generative models provide strong unconditional priors for inverse problems, but guiding their dynamics for conditional generation remains challenging. Recent work casts training-free conditional generation in flow models as an…
Autonomous racing control is a challenging research problem as vehicles are pushed to their limits of handling to achieve an optimal lap time; therefore, vehicles exhibit highly nonlinear and complex dynamics. Difficult-to-model effects,…
Multigrid preconditioners and solvers for the indefinite Helmholtz equation suffer from non-stability of the stationary smoothers due to the indefinite spectrum of the operator. In this paper we explore GMRES as a replacement for the…
In [Meurant, Pape\v{z}, Tich\'y; Numerical Algorithms 88, 2021], we presented an adaptive estimate for the energy norm of the error in the conjugate gradient (CG) method. In this paper, we extend the estimate to algorithms for solving…
In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers,…
Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for…
This paper continues to develop a fault tolerant extension of the sparse grid combination technique recently proposed in [B. Harding and M. Hegland, ANZIAM J., 54 (CTAC2012), pp. C394-C411]. The approach is novel for two reasons, first it…
Nowadays, time series forecasting is predominantly approached through the end-to-end training of deep learning architectures using error-based objectives. While this is effective at minimizing average loss, it encourages the encoder to…
Flow-based generative modeling is a powerful tool for solving inverse problems in physical sciences that can be used for sampling and likelihood evaluation with much lower inference times than traditional methods. We propose to refine flows…
Although the performance of commodity computers has improved drastically with the introduction of multicore processors and GPU computing, the standard R distribution is still based on single-threaded model of computation, using only a small…
We consider nonlinear inverse problems arising in the context of parameter identification for parabolic partial differential equations (PDEs). For stable reconstructions, regularization methods such as the iteratively regularized…
This paper presents a goal-oriented a posteriori error estimation framework for linear functionals in the stabilized finite element discretization of the stationary convection-diffusion-reaction (CDR) equation. The theoretical framework for…
Computing the solution of linear systems of equations is invariably the most time consuming task in the numerical solutions of PDEs in many fields of computational science. In this study, we focus on the numerical simulation of…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
Generative Flow Networks (GFlowNets) are a novel class of generative models designed to sample from unnormalized distributions and have found applications in various important tasks, attracting great research interest in their training…
With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems fast and accurately. The solution of least squares (LS) problems $\min_x\|b-Ax\|_2$, where $A…