Related papers: Importance profiles. Visualization of atomic basis…

In recent years, a large amount of model-agnostic methods to improve the transparency, trustability and interpretability of machine learning models have been developed. We introduce local feature importance as a local version of a recent…

The Slater-type orbital basis with non-integer principal quantum numbers is a physically and mathematically motivated choice for molecular electronic structure calculations in both non-relativistic and relativistic theory. The…

This paper is concerned with parameter identification problem for finite impulse response (FIR) systems with binary-valued observations under low computational complexity. Most of the existing algorithms under binary-valued observations…

We aim to develop novel reusable open source infrastructure [Lehtola, J. Chem. Phys. 159, 180901 (2023)] for numerical atomic orbitals (NAOs). Soft confinement potentials are typically used to force the NAO radial basis functions…

In many applications, it is of interest to assess the relative contribution of features (or subsets of features) toward the goal of predicting a response -- in other words, to gauge the variable importance of features. Most recent work on…

Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…

Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing,…

Many signal processing and machine learning applications are built from evaluating a kernel on pairs of signals, e.g. to assess the similarity of an incoming query to a database of known signals. This nonlinear evaluation can be simplified…

This research paper focuses on the implementation of radial Basis Function (RBF) Support Vector Machines (SVM) for classifying asteroid orbits. Asteroids are important astronomical objects, and their orbits play a crucial role in…

Localized basis sets in the projector augmented wave formalism allow for computationally efficient calculations within density functional theory (DFT). However, achieving high numerical accuracy requires an extensive basis set, which also…

Leveraging ab initio data at scale has enabled the development of machine learning models capable of extremely accurate and fast molecular property prediction. A central paradigm of many previous works focuses on generating predictions for…

Density fitting (DF), also known as the resolution of the identity (RI), is a widely used technique in quantum chemical calculations with various types of atomic basis sets - Gaussian-type orbitals, Slater-type orbitals, as well as…

Quantum mechanics owes much of its extraordinary success to a Hilbertian program of mathematical formalization. Yet, the formalism remains poorly aligned with the practical limitations of computations in finite dimensions and under finite…

We study a nonparametric approach to Bayesian computation via feature means, where the expectation of prior features is updated to yield expected kernel posterior features, based on regression from learned neural net or kernel features of…

In the framework of a recently reported linear-scaling method for density-functional-pseudopotential calculations, we investigate the use of localized basis functions for such work. We propose a basis set in which each local orbital is…

In the Projector Augmented Wave (PAW) method, a local potential, basis functions, and projector functions form an All-Electron (AE) basis for valence wave functions in the application of Density Functional Theory (DFT). The construction of…

Predominantly, harmonic oscillator single-particle wave functions are the choice as a basis in ab-initio nuclear many-body calculations. These wave-functions, although very convenient in order to evaluate the matrix elements of the…

The auxiliary functions provide efficient computation of integrals arising at the self-consistent field (SCF) level for molecules using Slater-type bases. This applies both in relativistic and non-relativistic electronic structure theory.…

Most modern calculations of many-electron atoms use basis sets of atomic orbitals. An accurate account for the electronic correlations in heavy atoms is very difficult computational problem and optimization of the basis sets can reduce…

In the era of "big data", it is becoming more of a challenge to not only build state-of-the-art predictive models, but also gain an understanding of what's really going on in the data. For example, it is often of interest to know which, if…