Related papers: An Optimizing Symbolic Algebra Approach for Genera…
We provide algorithms for symbolic integration of hyperlogarithms multiplied by rational functions, which also include multiple polylogarithms when their arguments are rational functions. These algorithms are implemented in Maple and we…
In the last decade major steps towards an algorithmic treatment of orthogonal polynomials and special functions (OP & SF) have been made, notably Zeilberger's brilliant extension of Gosper's algorithm on algorithmic definite hypergeometric…
We introduce harmonization, an ensembling method that combines several "noisy" decoders to generate highly accurate decoding predictions. Harmonized ensembles of MWPM-based decoders achieve lower logical error rates than their individual…
Large language models (LLMs) excel at solving complex tasks by executing agentic workflows composed of detailed instructions and structured operations. Yet, building general-purpose agents by manually embedding foundation models into…
We consider fast kernel summations in high dimensions: given a large set of points in $d$ dimensions (with $d \gg 3$) and a pair-potential function (the {\em kernel} function), we compute a weighted sum of all pairwise kernel interactions…
Fast multipole methods (FMM) were originally developed for accelerating $N$-body problems for particle-based methods. FMM is more than an $N$-body solver, however. Recent efforts to view the FMM as an elliptic Partial Differential Equation…
The scientific code generation package lbmpy supports the automated design and the efficient implementation of lattice Boltzmann methods (LBMs) through metaprogramming. It is based on a new, concise calculus for describing multiple…
Coalgebraic bisimilarity minimization generalizes classical automaton minimization to a large class of automata whose transition structure is specified by a functor, subsuming strong, weighted, and probabilistic bisimilarity. This offers…
Symbolic regression is the process of identifying mathematical expressions that fit observed output from a black-box process. It is a discrete optimization problem generally believed to be NP-hard. Prior approaches to solving the problem…
When treating Markov decision processes (MDPs) with large state spaces, using explicit representations quickly becomes unfeasible. Lately, Wimmer et al. have proposed a so-called symblicit algorithm for the synthesis of optimal strategies…
When treating Markov decision processes (MDPs) with large state spaces, using explicit representations quickly becomes unfeasible. Lately, Wimmer et al. have proposed a so-called symblicit algorithm for the synthesis of optimal strategies…
Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often do not perform well except for very large matrix sizes, due…
A computation scheme for solving elliptic boundary value problems with axially symmetric confining potentials using different sets of one-parameter basis functions is presented. The efficiency of the proposed symbolic-numerical algorithms…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this…
We present a versatile open-source framework designed to facilitate efficient, numerically-tailored Matrix-Matrix Multiplications (MMMs). The framework offers two primary contributions: first, a fine-tuned, automated pipeline for arithmetic…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
Explicit topology optimization methods have received ever-increasing interest in recent years. In particular, a 188-line Matlab code of the two-dimensional (2D) Moving Morphable Component (MMC)-based topology optimization method was…
Efficient Matlab codes in 2D and 3D have been proposed recently to assemble finite element matrices. In this paper we present simple, compact and efficient vectorized algorithms, which are variants of these codes, in arbitrary dimension,…
The implementation of discontinuous Galerkin finite element methods (DGFEMs) represents a very challenging computational task, particularly for systems of coupled nonlinear PDEs, including multiphysics problems, whose parameters may consist…