Related papers: Comparing Machine Learning and Interpolation Metho…

Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of non-interacting fermions in 1d, mean absolute errors below 1 kcal/mol on test densities similar to the training set are reached with…

We propose a parallel version of the cross interpolation algorithm and apply it to calculate high-dimensional integrals motivated by Ising model in quantum physics. In contrast to mainstream approaches, such as Monte Carlo and quasi Monte…

We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…

As function approximators, deep neural networks have served as an effective tool to represent various signal types. Recent approaches utilize multi-layer perceptrons (MLPs) to learn a nonlinear mapping from a coordinate to its corresponding…

Artificial intelligence (AI) has revolutionized software development, shifting from task-specific codes (Software 1.0) to neural network-based approaches (Software 2.0). However, applying this transition in engineering software presents…

Interpolation is a fundamental technique in scientific computing and is at the heart of many scientific visualization techniques. There is usually a trade-off between the approximation capabilities of an interpolation scheme and its…

We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…

In this contribution we introduce a mixed interpolation-regression operator for functions defined in some domains of the plane. We focus the attention on the ellipse, an annulus and a polygon. An upper bound for such an operator is…

Implicit Neural Representations (INR) use multilayer perceptrons to represent high-frequency functions in low-dimensional problem domains. Recently these representations achieved state-of-the-art results on tasks related to complex 3D…

The problems of computational data processing involving regression, interpolation, reconstruction and imputation for multidimensional big datasets are becoming more important these days, because of the availability of data and their widely…

The two-loop contributions are now often required by the precision experiments, yet are hard to express analytically while keeping precision. One way to approach this challenging task is via the dispersive approach, allowing to replace…

Computationally expensive Radiative Transfer Models (RTMs) are widely used} to realistically reproduce the light interaction with the Earth surface and atmosphere. Because these models take long processing time, the common practice is to…

This paper addresses the problem of approximating a function of bounded variation from its scattered data. Radial basis function(RBF) interpolation methods are known to approximate only functions in their native spaces, and to date, there…

The use of machine learning algorithms is an attractive way to produce very fast detector simulations for scattering reactions that can otherwise be computationally expensive. Here we develop a factorised approach where we deal with each…

Bootstrapping and rollout are two fundamental principles for value function estimation in reinforcement learning (RL). We introduce a novel class of Bellman operators, called subgraph Bellman operators, that interpolate between…

This paper introduces the concept of hyperpolation: a way of generalising from a limited set of data points that is a peer to the more familiar concepts of interpolation and extrapolation. Hyperpolation is the task of estimating the value…

Imitation learning with visual observations is notoriously inefficient when addressed with end-to-end behavioural cloning methods. In this paper, we explore an alternative paradigm which decomposes reasoning into three phases. First, a…

The interpolation-regression approximation is a powerful tool in numerical analysis for reconstructing functions defined on square or triangular domains from their evaluations at a regular set of nodes. The importance of this technique lies…

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher…

Isosurface visualization is fundamental for exploring and analyzing 3D volumetric data. Marching cubes (MC) algorithms with linear interpolation are commonly used for isosurface extraction and visualization. Although linear interpolation is…