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Signal Temporal Logic (STL) offers a concise yet expressive framework for specifying and reasoning about spatio-temporal behaviors of robotic systems. Attractively, STL admits the notion of robustness, the degree to which an input signal…
We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…
This methodology paper addresses high-performance high-productivity programming on spatial architectures. Spatial architectures are efficient for executing dataflow algorithms, yet for high-performance programming, the productivity is low…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
In this work, we consider alternative discretizations for PDEs which use expansions involving integral operators to approximate spatial derivatives. These constructions use explicit information within the integral terms, but treat boundary…
Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank…
We present the design, implementation, and evaluation of optimized matrix-free stencil kernels for multigrid smoothing in the incompressible Stokes equations with variable viscosity, motivated by geophysical flow problems. We investigate…
Matrix computations are a fundamental building-block of edge computing systems, with a major recent uptick in demand due to their use in AI/ML training and inference procedures. Existing approaches for distributing matrix computations…
We introduce SpDISTAL, a compiler for sparse tensor algebra that targets distributed systems. SpDISTAL combines separate descriptions of tensor algebra expressions, sparse data structures, data distribution, and computation distribution.…
Speculative Decoding (SD) is a widely used approach to accelerate the inference of large language models (LLMs) without reducing generation quality. It operates by first using a compact model to draft multiple tokens efficiently, followed…
Approximating partial differential equations for extensive industrial and scientific applications requires leveraging the power of modern high-performance computing. In large-scale parallel computations, the geometrical discretisation…
We describe an efficient parallel implementation of the selected inversion algorithm for distributed memory computer systems, which we call \texttt{PSelInv}. The \texttt{PSelInv} method computes selected elements of a general sparse matrix…
Partial differential equations (PDEs) underpin the modeling of many natural and engineered systems. It can be convenient to express such models as neural PDEs rather than using traditional numerical PDE solvers by replacing part or all of…
Deploying DNNs on System-on-Chips (SoC) with multiple heterogeneous acceleration engines is challenging, and the majority of deployment frameworks cannot fully exploit heterogeneity. We present MATCHA, a unified DNN deployment framework…
Multiphysics problems such as multicomponent diffusion, phase transformations in multiphase systems and alloy solidification involve numerical solution of a coupled system of nonlinear partial differential equations (PDEs). Numerical…
We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than…
Field programmable gate arrays (FPGAs) can accelerate image processing by exploiting fine-grained parallelism opportunities in image operations. FPGA language designs are often subsets or extensions of existing languages, though these…
We present a set of programming tools (classes and functions written in C++ and based on Message Passing Interface) for fast development of generic parallel (and non-parallel) lattice simulations. They are collectively called MDP 1.2. These…
Modern general-purpose accelerators integrate a large number of programmable area- and energy-efficient processing elements (PEs), to deliver high performance while meeting stringent power delivery and thermal dissipation constraints. In…
The efficient solution of discretisations of coupled systems of partial differential equations (PDEs) is at the core of much of numerical simulation. Significant effort has been expended on scalable algorithms to precondition Krylov…