Related papers: Fast Floating-Point Filters for Robust Predicates
Advancements in theoretical and algorithmic approaches, workflow engines, and an ever-increasing computational power have enabled a novel paradigm for materials discovery through first-principles high-throughput simulations. A major…
In the field of High Performance Computing, communications among processes represent a typical bottleneck for massively parallel scientific applications. Object of this research is the development of a network interface card with specific…
We present two novel generative geometric deep learning frameworks, termed Flow Matching PointNet and Diffusion PointNet, for predicting fluid flow variables on irregular geometries by incorporating PointNet into flow matching and diffusion…
Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for…
Applied research in graph algorithms and combinatorial structures needs comprehensive and versatile software libraries. However, the design and the implementation of flexible libraries are challenging activities. Among the other problems…
We extend the Stainless deductive verifier with floating-point support, providing the first automated verification support for floating-point numbers for a subset of Scala that includes polymorphism, recursion and higher-order functions. We…
Achieving high code coverage is essential in testing, which gives us confidence in code quality. Testing floating-point code usually requires painstaking efforts in handling floating-point constraints, e.g., in symbolic execution. This…
Can we assure math computations by automatic verifying floating-point accuracy? We define fast arithmetic (based on Dekker [1971]) over twofold approximations $z\approx z_0+z_1$, such that $z_0$ is standard result and $z_1$ assesses…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
Interval computation is widely used to certify computations that use floating point operations to avoid pitfalls related to rounding error introduced by inaccurate operations. Despite its popularity and practical benefits, support for…
We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…
Early advancements in convolutional neural networks (CNNs) architectures are primarily driven by human expertise and by elaborate design processes. Recently, neural architecture search was proposed with the aim of automating the network…
Matching two images while estimating their relative geometry is a key step in many computer vision applications. For decades, a well-established pipeline, consisting of SIFT, RANSAC, and 8-point algorithm, has been used for this task.…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
An effective strategy for accelerating the calculation of convex hulls for point sets is to filter the input points by discarding interior points. In this paper, we present such a straightforward and efficient preprocessing approach by…
Debugging accumulation of floating-point errors is hard; ideally, computer should track it automatically. Here we consider twofold approximation of an exact real with value + error pair of floating-point numbers. Normally, value + error sum…
With the increasing complexity of machine learning models, managing computational resources like memory and processing power has become a critical concern. Mixed precision techniques, which leverage different numerical precisions during…
Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring…
A Frontal-Delaunay refinement algorithm for mesh generation in piecewise smooth domains is described. Built using a restricted Delaunay framework, this new algorithm combines a number of novel features, including: (i) an unweighted,…
Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the ``shape'' of the set. For that purpose, this paper introduces the formal…