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Amorphous carbon (a-C) materials have diverse interesting and useful properties, but the understanding of their atomic-scale structures is still incomplete. Here, we report on extensive atomistic simulations of the deposition and growth of…
The composition of multiple Gaussian Processes as a Deep Gaussian Process (DGP) enables a deep probabilistic nonparametric approach to flexibly tackle complex machine learning problems with sound quantification of uncertainty. Existing…
Interatomic potentials are essential for driving molecular dynamics (MD) simulations, directly impacting the reliability of predictions regarding the physical and chemical properties of materials. In recent years, machine-learned potentials…
Molecular dynamics simulations are an invaluable tool in numerous scientific fields. However, the ubiquitous classical force fields cannot describe reactive systems, and quantum molecular dynamics are too computationally demanding to treat…
Gaussian process (GP) predictors are an important component of many Bayesian approaches to machine learning. However, even a straightforward implementation of Gaussian process regression (GPR) requires O(n^2) space and O(n^3) time for a…
Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption…
Machine Learning Interatomic Potentials play a fundamental role in computational chemistry and materials science, enabling applications from molecular dynamics simulations to drug design and materials discovery. While recent approaches can…
Machine learning interatomic potentials (MLIPs) have substantially advanced atomistic simulations in materials science and chemistry by balancing accuracy and computational efficiency. While leading MLIPs rely on representing atomic…
In this paper, we investigate a class of approximate Gaussian processes (GP) obtained by taking a linear combination of compactly supported basis functions with the basis coefficients endowed with a dependent Gaussian prior distribution.…
Machine learning offers an exciting opportunity to improve the calibration of nearly all reconstructed objects in high-energy physics detectors. However, machine learning approaches often depend on the spectra of examples used during…
Machine learning interatomic potentials (MLIPs) enable efficient molecular dynamics (MD) simulations with ab initio accuracy and have been applied across various domains in physical science. However, their performance often relies on…
In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model $y$ with a surrogate model $y_s$ that can be evaluated quickly leads to a significant speedup. The…
We consider the problem of parameter estimation from a generalized linear model with a random design matrix that is orthogonally invariant in law. Such a model allows the design have an arbitrary distribution of singular values and only…
Complex Gaussian basis sets are optimized to accurately represent continuum radial wavefunctions over the whole space. First, attention is put on the technical ability of the optimization method to get more flexible series of Gaussian…
Universal machine learning interatomic potentials (uMLIPs) represent arguably the most successful application of machine learning to materials science, demonstrating remarkable performance across diverse applications. However, critical…
In J. Chem. Phys. 152, 144105 (2020) Lehtola et al introduced the efficient Gaussian-basis representation of Superposition of Atomic Potentials (SAP) which "can be easily implemented in any Gaussian-basis quantum chemistry code in terms of…
In this article, we present a visual introduction to Gaussian Belief Propagation (GBP), an approximate probabilistic inference algorithm that operates by passing messages between the nodes of arbitrarily structured factor graphs. A special…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
Gaussian wave packets (GWPs) are well suited as basis functions to describe the time evolution of arbitrary wave functions in systems with nonsingular smooth potentials. They are less so in atomic systems on account of the singular behavior…
We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…