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This paper introduces the Non-linear Partition of Unity Method, a novel technique integrating Radial Basis Function interpolation and Weighted Essentially Non-Oscillatory algorithms. It addresses challenges in high-accuracy approximations,…
Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…
Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential…
Numerous fields of nonlinear physics, very different in nature, produce signals and images, that share the common feature of being essentially constituted of piecewise homogeneous phases. Analyzing signals and images from corresponding…
We introduce JuliQAOA, a simulation package specifically built for the Quantum Alternating Operator Ansatz (QAOA). JuliQAOA does not require a circuit-level description of QAOA problems, or another package to simulate such circuits, instead…
What do applications like semantic optimization, data exchange and integration, answering queries under dependencies, query reformulation with constraints, and data cleaning have in common? All these applications can be processed by the…
We present Korali, an open-source framework for large-scale Bayesian uncertainty quantification and stochastic optimization. The framework relies on non-intrusive sampling of complex multiphysics models and enables their exploitation for…
Causal analysis plays a foundational role in scientific discovery and reliable decision-making, yet it remains largely inaccessible to domain experts due to its conceptual and algorithmic complexity. This disconnect between causal…
The B5G/6G evolution relies on connect-compute technologies and highly heterogeneous clusters with HW accelerators, which require specialized coding to be efficiently utilized. The current paper proposes a custom tool for generating…
Particle filters for data assimilation in nonlinear problems use "particles" (replicas of the underlying system) to generate a sequence of probability density functions (pdfs) through a Bayesian process. This can be expensive because a…
The realization of novel technological opportunities given by computational and autonomous materials design requires efficient and effective frameworks. For more than two decades, aflow++ (Automatic-Flow Framework for Materials Discovery)…
GomalizingFlow.jl: is a package to generate configurations for quantum field theory on the lattice using the flow based sampling algorithm in Julia programming language. This software serves two main purposes: to accelerate research of…
We present an efficient numerical implementation of the quasi-classical doorway-window approximation, specifically designed for on-the-fly simulations of time-resolved nonlinear spectroscopic signals in the Julia package WaveMixings.jl. The…
The Carreau-Yasuda rheological model is widely employed in both research and industrial applications to describe the shear-thinning behaviour of non-Newtonian inelastic fluids. However, the model parameter traditionally employed to…
AI for Mathematics (AI4Math) is not only intriguing intellectually but also crucial for AI-driven discovery in science, engineering, and beyond. Extensive efforts on AI4Math have mirrored techniques in NLP, in particular, training large…
Tau-leaping is a family of algorithms for the approximate simulation of the discrete state continuous time Markov chains. Motivation for the development of such methods can be found, for instance, in the fields of chemical kinetics and…
Kalman filter is presumably one of the most important and extensively used filtering techniques in modern control systems. Yet, nearly all current variants of Kalman filters are formulated in the Euclidean space $\mathbb{R}^n$, while many…
Program synthesis -- the automatic generation of code given a specification -- is one of the most fundamental tasks in artificial intelligence (AI) and the dream of many programmers. Numerous synthesizers have been developed for program…
Vision-language models have demonstrated impressive capabilities as computer-use agents (CUAs) capable of automating diverse computer tasks. As their commercial potential grows, critical details of the most capable CUA systems remain…
Incorporating natural language input has the potential to improve the capabilities of biomedical data discovery interfaces. However, user interface elements and visualizations are still powerful tools for interacting with data. In our…