相关论文: A matrix-free ILU realization based on surrogates

We present new, practical algorithms for the hypersurface implicitization problem: namely, given a parametric description (in terms of polynomials or rational functions) of the hypersurface, find its implicit equation. Two of them are for…

Multiscale mixed methods based on non-overlapping domain decompositions can efficiently handle the solution of significant subsurface flow problems in very heterogeneous formations of interest to the industry, especially when implemented on…

In this paper, we introduce and analyze a new $LU$-factorization technique for square matrices over idempotent semifields. In particular, more emphasis is put on "max-plus" algebra here, but the work is extended to other idempotent…

Optimizing expensive black-box systems with limited data is an extremely challenging problem. As a resolution, we present a new surrogate optimization approach by addressing two gaps in prior research -- unimportant input variables and…

We employ textbook multigrid efficiency (TME), as introduced by Achi Brandt, to construct an asymptotically optimal monolithic multigrid solver for the Stokes system. The geometric multigrid solver builds upon the concept of hierarchical…

In this paper, we introduce MPM Lite, a new hybrid Lagrangian/Eulerian method that eliminates the need for particle-based quadrature at solve time. Standard MPM practices suffer from a performance bottleneck where expensive implicit solves…

This work presents a non-intrusive surrogate modeling scheme based on machine learning technology for predictive modeling of complex systems, described by parametrized time-dependent PDEs. For these problems, typical finite element…

While neural network quantization effectively reduces the cost of matrix multiplications, aggressive quantization can expose non-matrix-multiply operations as significant performance and resource bottlenecks on embedded systems. Addressing…

The capability of discretization of matrix elements in the problem of quadratic functional minimization with linear member built on matrix in N-dimensional configuration space with discrete coordinates is researched. It is shown, that…

In this paper, we revisit model-free policy search on an important robust control benchmark, namely $\mu$-synthesis. In the general output-feedback setting, there do not exist convex formulations for this problem, and hence global…

With the growing maturity of additive manufacturing, the fabrication of architected or lattice-based metamaterials has become a reality for industrial applications. These materials combine lightweight design with tailored mechanical…

Efficient water management in agriculture is important for mitigating the growing freshwater scarcity crisis. Mixed-integer Model Predictive Control (MPC) has emerged as an effective approach for addressing the complex scheduling problems…

We propose a novel preconditioned inexact primal-dual interior point method for constrained convex quadratic programming problems. The algorithm we describe invokes the preconditioned conjugate gradient method on a new reduced Schur…

A reference implementation of a new method in isogeometric analysis (IGA) is presented. It delivers low-cost variable-scale approximations (surrogates) of the matrices which IGA conventionally requires to be computed by element-scale…

Matrix functions such as square root, inverse roots, and orthogonalization play a central role in preconditioned gradient methods for neural network training. This has motivated the development of iterative algorithms that avoid explicit…

With the fast growth of parameter size, it becomes increasingly challenging to deploy large generative models as they typically require large GPU memory consumption and massive computation. Unstructured model pruning has been a common…

With the increasing demand for computing capability given limited resource and power budgets, it is crucial to deploy applications to customized accelerators like FPGAs. However, FPGA programming is non-trivial. Although existing high-level…

Modern computing workloads commonly involve matrix-matrix multiplication (mmul) as a core computing pattern. Coarse-Grained Reconfigurable Arrays (CGRAs) can flexibly and efficiently support it, since they combine operation-level…

Vertex-patch smoothers offer an effective strategy for achieving robust geometric multigrid convergence for the Stokes equations, particularly in the context of high-order finite elements. However, their practical efficiency is often…

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is…