相关论文: The NumericalCertification package in Macaulay2
The paper proposes a control-theoretic framework for verification of numerical software systems, and puts forward software verification as an important application of control and systems theory. The idea is to transfer Lyapunov functions…
Post-hoc attribution methods aim to explain deep learning predictions by highlighting influential input pixels. However, these explanations are highly non-robust: small, imperceptible input perturbations can drastically alter the…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files…
Code verification is a necessary step towards establishing credibility in computational physics simulations. It is used to assess the correctness of the implementation of the numerical methods within the code, and it is a continuous part of…
The possibility of interaction between Maple and numeric compiled languages in performing extensive numeric calculations is exemplified by the Ndynamics package, a tool for studying the (chaotic) behavior of dynamical systems. Programming…
In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point…
We study the problem of {\sl certification}: given queries to a function $f : \{0,1\}^n \to \{0,1\}$ with certificate complexity $\le k$ and an input $x^\star$, output a size-$k$ certificate for $f$'s value on $x^\star$. This abstractly…
Deep learning has emerged as an effective approach for creating modern software systems, with neural networks often surpassing hand-crafted systems. Unfortunately, neural networks are known to suffer from various safety and security issues.…
We develop efficient and accurate numerical methods to solve a class of shallow shell problems of the von Karman type. The governing equations form a fourth-order coupled system of nonlinear biharnomic equations for the transverse…
This document describes our freely distributed Maple library {\sc spectra}, for Semidefinite Programming solved Exactly with Computational Tools of Real Algebra. It solves linear matrix inequalities with symbolic computation in exact…
Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the…
Applying Gr\"obner basis theory to concrete problems in Lean 4 remains difficult since the current formalization of multivariate polynomials is based on a non-computable representation and is therefore not suitable for efficient symbolic…
On the one hand, ordered completion is a fundamental technique in equational theorem proving that is employed by automated tools. On the other hand, their complexity makes such tools inherently error prone. As a remedy to this situation we…
The Novelli-Pak-Stoyanovskii algorithm is a sorting algorithm for Young tableaux of a fixed shape that was originally devised to give a bijective proof of the hook-length formula. We obtain new asymptotic results on the average case and…
We propose a security verification framework for cryptographic protocols using machine learning. In recent years, as cryptographic protocols have become more complex, research on automatic verification techniques has been focused on. The…
We introduce a numerical framework to verify the finite step convergence of first-order methods for parametric convex quadratic optimization. We formulate the verification problem as a mathematical optimization problem where we maximize a…
The paper proposes a control-theoretic framework for verification of numerical software systems, and puts forward software verification as an important application of control and systems theory. The idea is to transfer Lyapunov functions…
We propose an algorithm to construct a certified approximation of a surface by generalizing the Krawczyk test. The Krawczyk test is based on interval arithmetic, and confirms the existence and uniqueness of a solution to a square system of…
The performance of numerical micromagnetic models is limited by the demagnetizing field computation, which typically accounts for the majority of the computation time. For magnetization dynamics simulations explicit evaluation methods are…