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We consider constructing a surface from a given set of point cloud data. We explore two fast algorithms to minimize the weighted minimum surface energy in [Zhao, Osher, Merriman and Kang, Comp.Vision and Image Under., 80(3):295-319, 2000].…
We have repurposed Google Tensor Processing Units (TPUs), application-specific chips developed for machine learning, into large-scale dense linear algebra supercomputers. The TPUs' fast inter-core interconnects (ICI)s, physically…
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…
Large models training is plagued by the intense compute cost and limited hardware memory. A practical solution is low-precision representation but is troubled by loss in numerical accuracy and unstable training rendering the model less…
We apply the Charge Simulation Method (CSM) in order to compute the logarithmic capacity of compact sets consisting of (infinitely) many "small" components. This application allows to use just a single charge point for each component. The…
This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
Thanks to the computational power of modern cluster machines, numerical simulations can provide, with an unprecedented level of details, new insights into fluid mechanics. However, taking full advantage of this hardware remains challenging…
This paper develops and analyzes an efficient numerical method for solving elliptic partial differential equations, where the diffusion coefficients are random perturbations of deterministic diffusion coefficients. The method is based upon…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We present the acceleration of an IMplicit-EXplicit (IMEX) non-hydrostatic atmospheric model on manycore processors such as GPUs and Intel's MIC architecture. IMEX time integration methods sidestep the constraint imposed by the…
Multiple Choice Question Answering (MCQA) is an important problem with numerous real-world applications, such as medicine, law, and education. The high cost of building MCQA datasets makes few-shot learning pivotal in this domain. While…
The evaluation of clustering results is difficult, highly dependent on the evaluated data set and the perspective of the beholder. There are many different clustering quality measures, which try to provide a general measure to validate…
Secure Multi-party Computation (MPC) enables untrusted parties to jointly compute a function without revealing their inputs. Its application to machine learning (ML) has gained significant attention, particularly for secure inference…
We consider the coupled system of equations that describe flow in fractured porous media. To describe such types of problems, multicontinuum and multiscale approaches are used. Because in multicontinuum models, the permeability of each…
In topology optimization, the state of structures is typically obtained by numerically evaluating a discretized PDE-based model. The degrees of freedom of such a model can be partitioned in free and prescribed sets to define the boundary…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
Due to 5G deployment, there is significant interest in LDPC decoding. While much research is devoted on efficient hardwiring of algorithms based on Belief Propagation (BP), it has been shown that LDPC decoding can be formulated as a…
The multi-frontal direct solver is the state-of-the-art algorithm for the direct solution of sparse linear systems. This paper provides computational complexity and memory usage estimates for the application of the multi-frontal direct…
While fast multipole methods (FMMs) are in widespread use for the rapid evaluation of potential fields governed by the Laplace, Helmholtz, Maxwell or Stokes equations, their coupling to high-order quadratures for evaluating layer potentials…