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PYROBOCOP is a lightweight Python-based package for control and optimization of robotic systems described by nonlinear Differential Algebraic Equations (DAEs). In particular, the package can handle systems with contacts that are described…

We present a scalable strategy for development of mesh-free hybrid neuro-symbolic partial differential equation solvers based on existing mesh-based numerical discretization methods. Particularly, this strategy can be used to efficiently…

We show how to efficiently compute the derivative (when it exists) of the solution map of log-log convex programs (LLCPs). These are nonconvex, nonsmooth optimization problems with positive variables that become convex when the variables,…

Optimally hybrid numerical solvers were constructed for massively parallel generalized eigenvalue problem (GEP).The strong scaling benchmark was carried out on the K computer and other supercomputers for electronic structure calculation…

In this paper, we explore a specific optimization problem that involves the combination of a differentiable nonconvex function and a nondifferentiable function. The differentiable component lacks a global Lipschitz continuous gradient,…

In [McDonald, Pestana and Wathen, \textit{SIAM J. Sci. Comput.}, 40 (2018), pp. A1012--A1033], a block circulant preconditioner is proposed for all-at-once linear systems arising from evolutionary partial differential equations, in which…

We propose a multiscale method for mixed-dimensional elliptic problems with highly heterogeneous coefficients arising, for example, in the modeling of fractured porous media. The method is based on the Localized Orthogonal Decomposition…

Linear solvers for large and sparse systems are a key element of scientific applications, and their efficient implementation is necessary to harness the computational power of current computers. Algebraic MultiGrid (AMG) preconditioners are…

In this paper, we consider a class of nonsmooth nonconvex optimization problems whose objective is the sum of a block relative smooth function and a proper and lower semicontinuous block separable function. Although the analysis of block…

In this paper, we present new stochastic methods for solving two important classes of nonconvex optimization problems. We first introduce a randomized accelerated proximal gradient (RapGrad) method for solving a class of nonconvex…

In this paper, we are concerned with the weighted plane wave least-squares (PWLS) method for three-dimensional Helmholtz equations, and develop the multi-level adaptive BDDC algorithms for solving the resulting discrete system. In order to…

In this study, we propose the lopsided HSS (LHSS) iteration method for solving a class of complex symmetric indefinite systems of linear equations. This method employs an alternating iterative scheme, where each iteration entails solving…

Many problems of substantial current interest in machine learning, statistics, and data science can be formulated as sparse and low-rank optimization problems. In this paper, we present the nonconvex exterior-point optimization solver NExOS…

A novel and scalable geometric multi-level algorithm is presented for the numerical solution of elliptic partial differential equations, specially designed to run with high occupancy of streaming processors inside Graphics Processing…

We present a framework to solve non-linear eigenvalue problems suitable for a Finite Element discretization. The implementation is based on the open-source finite element software GetDP and the open-source library SLEPc. As template…

Loop transformations are semantics-preserving optimization techniques, widely used to maximize objectives such as parallelism. Despite decades of research, applying the optimal composition of loop transformations remains challenging due to…

We present LBsoft, an open-source software developed mainly to simulate the hydro-dynamics of colloidal systems based on the concurrent coupling between lattice Boltzmann methods for the fluid and discrete particle dynamics for the…

Long-context training of large language models (LLMs) is commonly distributed with Context Parallelism (CP) and Head Parallelism (HP), but existing training systems largely assume homogeneous GPU meshes. This paper extends CP and HP to…

Many combinatorial optimization problems can be approximated within $(1 \pm \epsilon)$ factors in $\text{poly}(\log n, 1/\epsilon)$ rounds in the LOCAL model via network decompositions [Ghaffari, Kuhn, and Maus, STOC 2018]. These approaches…

In order to realize the significant potential of optical materials such as metal halides, computational techniques which give accurate optical properties are needed, which can work hand-in-hand with experiments to generate high efficiency…