Related papers: ODE Test Problems: a MATLAB suite of initial value…
We study the use of amortized optimization to predict optimal transport (OT) maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and…
Test time adaptation (TTA) equips deep learning models to handle unseen test data that deviates from the training distribution, even when source data is inaccessible. While traditional TTA methods often rely on entropy as a confidence…
Sequential numerical methods for integrating initial value problems (IVPs) can be prohibitively expensive when high numerical accuracy is required over the entire interval of integration. One remedy is to integrate in a parallel fashion,…
In this paper, we present the first outer approximation algorithm for multi-objective mixed-integer linear programming problems with any number of objectives. The algorithm also works for certain classes of non-linear programming problems.…
We develop spectral methods for ODEs and operator eigenvalue problems that are based on a least-squares formulation of the problem. The key tool is a method for rectangular generalized eigenvalue problems, which we extend to quasimatrices…
Pseudospectral approximation provides a means to approximate the dynamics of delay differential equations (DDE) by ordinary differential equations (ODE). This article develops a computer-aided algorithm to determine the distance between the…
OTTER is a resolution-style theorem-proving program for first-order logic with equality. OTTER includes the inference rules binary resolution, hyperresolution, UR-resolution, and binary paramodulation. Some of its other abilities and…
Autotuning techniques are a promising approach to minimize the otherwise tedious manual effort of optimizing scientific applications for a specific target platform. Ideally, an autotuning approach is capable of reliably identifying the most…
The representation of workflows and processes is essential in materials science engineering, where experimental and computational reproducibility depend on structured and semantically coherent process models. Although numerous ontologies…
We study the learning of numerical algorithms for scientific computing, which combines mathematically driven, handcrafted design of general algorithm structure with a data-driven adaptation to specific classes of tasks. This represents a…
A recent trend in the design of FPT algorithms is exploiting the half-integrality of LP relaxations. In other words, starting with a half-integral optimal solution to an LP relaxation, we assign integral values to variables one-by-one by…
Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of…
The simplicity and the efficiency of a quasi-analytical method for solving nonlinear ordinary differential equations (ODE), is illustrated on the study of anharmonic oscillators (AO) with a potential $V(x) =\beta x^{2}+x^{2m}$ ($m>0$). The…
In this article, we introduce a new technique for precision tuning. This problem consists of finding the least data types for numerical values such that the result of the computation satisfies some accuracy requirement. State of the art…
With the growing adoption of time-series anomaly detection (TAD) technology, numerous studies have employed deep learning-based detectors to analyze time-series data in the fields of Internet services, industrial systems, and sensors. The…
Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…
A new numerical method for solving a scalar ordinary differential equation with a given initial condition is introduced. The method is using a numerical integration procedure for an equivalent integral equation and is called in this paper…
Real-world processes often involve interdependent objects that also carry data values, such as integers, reals, or strings. However, existing process formalisms fall short to combine key modeling features, such as tracking object…
This paper discusses the algorithms and implementations of three Mathematica packages for the study of integrability and the computation of closed-form solutions of nonlinear polynomial PDEs. The first package, PainleveTest.m, symbolically…
SPSMAT (Spectral/Pseudospectral matrix method) is an add-on for Octave, that helps you solve nonfractional-/fractional ordinary/partial differential/integral equations. In this version, as the first version, the well-defined spectral or…