Related papers: A scalable weakly-synchronous algorithm for solvin…
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in…
Time-parallel methods can reduce the wall clock time required for the accurate numerical solution of differential equations by parallelizing across the time-dimension. In this paper, we present and test the convergence behavior of a…
Solving partial differential equations (PDEs) with machine learning typically requires training a new neural network for every new equation. This optimization is slow. We introduce MetaColloc. It is an optimization-free and data-free…
Asynchronous distributed algorithms are a popular way to reduce synchronization costs in large-scale optimization, and in particular for neural network training. However, for nonsmooth and nonconvex objectives, few convergence guarantees…
In the era of big data, optimizing large scale machine learning problems becomes a challenging task and draws significant attention. Asynchronous optimization algorithms come out as a promising solution. Recently, decoupled asynchronous…
We present a number of novel algorithms, based on mathematical optimization formulations, in order to solve a homogeneous multiprocessor scheduling problem, while minimizing the total energy consumption. In particular, for a system with a…
Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it…
We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…
Machine learned partial differential equation (PDE) solvers trade the reliability of standard numerical methods for potential gains in accuracy and/or speed. The only way for a solver to guarantee that it outputs the exact solution is to…
A new parallel algorithm utilizing partitioned global address space (PGAS) programming model to achieve high scalability is reported for particle tracking in direct numerical simulations of turbulent flow. The work is motivated by the…
In this paper, a parallel symmetric eigensolver with very small matrices in massively parallel processing is considered. We define very small matrices that fit the sizes of caches per node in a supercomputer. We assume that the sizes also…
We present a novel, practical, and provable approach for solving diagonally constrained semi-definite programming (SDP) problems at scale using accelerated non-convex programming. Our algorithm non-trivially combines acceleration motions…
We consider a large-scale parallel-server system, where each server independently adjusts its processing speed in a decentralized manner. The objective is to minimize the overall cost, which comprises the average cost of maintaining the…
The problem of time synchronization in dense wireless networks is considered. Well established synchronization techniques suffer from an inherent scalability problem in that synchronization errors grow with an increasing number of hops…
This paper develops two orthogonal contributions to scalable sparse regression for competing risks time-to-event data. First, we study and accelerate the broken adaptive ridge method (BAR), an $\ell_0$-based iteratively reweighted…
In this work we show that randomized (block) coordinate descent methods can be accelerated by parallelization when applied to the problem of minimizing the sum of a partially separable smooth convex function and a simple separable convex…
Asynchronous stochastic gradient descent (ASGD) is a popular parallel optimization algorithm in machine learning. Most theoretical analysis on ASGD take a discrete view and prove upper bounds for their convergence rates. However, the…
Parallel architectures are continually increasing in performance and scale, while underlying algorithmic infrastructure often fail to take full advantage of available compute power. Within the context of MPI, irregular communication…
The operation of large-scale infrastructure networks requires scalable optimization schemes. To guarantee safe system operation, a high degree of feasibility in a small number of iterations is important. Decomposition schemes can help to…
Tremendous efforts have been paid for realization of fault-tolerant quantum computation so far. However, preexisting fault-tolerant schemes assume that a lot of qubits live together in a single quantum system, which is incompatible with…