Related papers: The optimal particle-mesh interpolation basis

Simulating water from first principles remains a significant computational challenge due to the slow dynamics of the underlying system. Although machine-learned interatomic potentials (MLPs) can accelerate these simulations, they often fail…

The multiscale patch scheme is built from given small micro-scale simulations of complicated physical processes to empower large macro-scale simulations. By coupling small patches of simulations over unsimulated spatial gaps, large savings…

Mesh refinement in pseudospectral (PS) optimal control is embarrassingly easy --- simply increase the order $N$ of the Lagrange interpolating polynomial and the mathematics of convergence automates the distribution of the grid points.…

Shepard method is a fast algorithm that has been classically used to interpolate scattered data in several dimensions. This is an important and well-known technique in numerical analysis founded in the main idea that data that is far away…

We introduce a comprehensive data-driven framework aimed at enhancing the modeling of physical systems, employing inference techniques and machine learning enhancements. As a demonstrative application, we pursue the modeling of cathodic…

In a previous paper we proposed a Projected Configuration Interaction method that uses sets of axially deformed single particle states to build up the many body basis. We show that the choice of the basis set is essential for the efficiency…

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…

We propose a novel approach for optical flow estimation , targeted at large displacements with significant oc-clusions. It consists of two steps: i) dense matching by edge-preserving interpolation from a sparse set of matches; ii)…

Accurate performance estimation of future many-node machines is challenging because it requires detailed simulation models of both node and network. However, simulating the full system in detail is unfeasible in terms of compute and memory…

We present a fast and accurate method to calculate the electrostatic energy and forces of interacting particles with the boundary conditions appropriate to surfaces, i.e periodic in the two directions parallel to the surface and free in the…

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular…

In recent years important progress has been achieved towards proving the validity of the replica predictions for the (asymptotic) mutual information (or "free energy") in Bayesian inference problems. The proof techniques that have emerged…

Gaussian process regression has recently emerged as a powerful, system-agnostic tool for building global potential energy surfaces (PES) of polyatomic molecules. While the accuracy of GP models of PES increases with the number of potential…

Accurate path integral Monte Carlo or molecular dynamics calculations of isotope effects have until recently been expensive because of the necessity to reduce three types of errors present in such calculations: statistical errors due to…

Controlling electrochemical reactivity requires a detailed understanding of the charging behavior and thermodynamics of the electrochemical interface. Experiments can independently probe the overall charge response of the electrochemical…

Electrostatics is of paramount importance to chemistry, physics, biology, and medicine. The Poisson-Boltzmann (PB) theory is a primary model for electrostatic analysis. However, it is highly challenging to compute accurate PB electrostatic…

In order to generate novel 3D shapes with machine learning, one must allow for interpolation. The typical approach for incorporating this creative process is to interpolate in a learned latent space so as to avoid the problem of generating…

Ewald summation is widely used to calculate electrostatic interactions in computer simulations of condensed-matter systems. We present an analysis of the errors arising from truncating the infinite real- and Fourier-space lattice sums in…

The fundamental purpose of the present work is to constitute an enhanced Euler method with adaptive inverse-quadratic and inverse-multi-quadratic radial basis function (RBF) interpolation technique to solve initial value problems. These…

Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…