Related papers: A universal preconditioner for simulating condense…

A unified simulator that can model diverse physical phenomena without solver-specific redesign is a long-standing goal across simulation science. We present a learning-based particle simulator built on a single transformer architecture to…

We describe a method for fast approximation of sparse coding. The input space is subdivided by a binary decision tree, and we simultaneously learn a dictionary and assignment of allowed dictionary elements for each leaf of the tree. We…

The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and…

Computing condensed phase spectra from atomistic simulations requires calculating correlation functions from molecular dynamics and can be very expensive. A totally general, data-driven method to reduce cost is to employ an exact rewriting…

We present a novel unified analysis for a broad class of adaptive optimization algorithms with structured (e.g., layerwise, diagonal, and kronecker-factored) preconditioners for both online regret minimization and offline convex…

We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize…

Next generation radio-interferometers, like the Square Kilometre Array, will acquire tremendous amounts of data with the goal of improving the size and sensitivity of the reconstructed images by orders of magnitude. The efficient processing…

Optimization is finding the best solution, which mathematically amounts to locating the global minimum of some cost function. Optimization is traditionally automated with digital or quantum computers, each having their limitations and none…

The compositional model is often used to describe multicomponent multiphase porous media flows in the petroleum industry. The fully implicit method with strong stability and weak constraints on time-step sizes is commonly used in the…

Preconditioning is a technique from numerical linear algebra that can accelerate algorithms to solve systems of equations. In this paper, we demonstrate how preconditioning can circumvent a stringent assumption for sign consistency in…

We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the…

We describe an algorithm that, given any full-rank matrix A having fewer rows than columns, can rapidly compute the orthogonal projection of any vector onto the null space of A, as well as the orthogonal projection onto the row space of A,…

We present a benchmark designed to evaluate the predictive capabilities of universal machine learning interatomic potentials across systems of varying dimensionality. Specifically, our benchmark tests zero- (molecules, atomic clusters,…

In sparse optimization, enforcing hard constraints using the $\ell_0$ pseudo-norm offers advantages like controlled sparsity compared to convex relaxations. However, many real-world applications demand not only sparsity constraints but also…

Compressive sampling has been widely used for sparse polynomial chaos (PC) approximation of stochastic functions. The recovery accuracy of compressive sampling highly depends on the incoherence properties of the measurement matrix. In this…

PDE-constrained optimization problems with control or state constraints are challenging from an analytical as well as numerical perspective. The combination of these constraints with a sparsity-promoting $\rm L^1$ term within the objective…

The convex hull describes the extent or shape of a set of data and is used ubiquitously in computational geometry. Common algorithms to construct the convex hull on a finite set of n points (x,y) range from O(nlogn) time to O(n) time.…

We study first-order methods with preconditioning for solving structured nonlinear convex optimization problems. We propose a new family of preconditioners generated by symmetric polynomials. They provide first-order optimization methods…

The geometric iterative method (GIM) is widely used in data interpolation/fitting, but its slow convergence affects the computational efficiency. Recently, much work was done to guarantee the acceleration of GIM in the literature. In this…

Incomplete LU factorizations of sparse matrices are widely used as preconditioners in Krylov subspace methods to speed up solving linear systems. Unfortunately, computing the preconditioner itself can be time-consuming and sensitive to…