Related papers: Efficient non-parametric fitting of potential ener…

We present GP-4DGS, a novel framework that integrates Gaussian Processes (GPs) into 4D Gaussian Splatting (4DGS) for principled probabilistic modeling of dynamic scenes. While existing 4DGS methods focus on deterministic reconstruction,…

We propose a novel training objective for GPs constructed using lower-dimensional linear projections of the data, referred to as \emph{projected likelihood} (PL). We provide a closed-form expression for the information loss related to the…

The Gaussian process (GP) is a Bayesian nonparametric paradigm that is widely adopted for uncertainty quantification (UQ) in a number of safety-critical applications, including robotics, healthcare, as well as surveillance. The consistency…

Parametric partial differential equations (PDEs) serve as fundamental mathematical tools for modeling complex physical phenomena, yet repeated high-fidelity numerical simulations across parameter spaces remain computationally prohibitive.…

We present a new strategy for learning the functional relation between a pair of variables, while addressing inhomogeneities in the correlation structure of the available data, by modelling the sought function as a sample function of a…

Artificial neural network (ANN) potentials enable highly accurate atomistic simulations of complex materials at unprecedented scales. Despite their promise, training ANN potentials to represent intricate potential energy surfaces (PES) with…

Gaussian processes (GPs) are Bayesian non-parametric models useful in a myriad of applications. Despite their popularity, the cost of GP predictions (quadratic storage and cubic complexity with respect to the number of training points)…

``$\Delta$-machine learning" refers to a machine learning approach to bring a property such as a potential energy surface (PES) based on low-level (LL) density functional theory (DFT) energies and gradients to close to a coupled cluster…

New manufacturing techniques such as 3D printing have recently enabled the creation of previously infeasible chemical reactor designs. Optimizing the geometry of the next generation of chemical reactors is important to understand the…

The numerical approximation of partial differential equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and…

The predictive simulation of molecular liquids requires models that are not only accurate, but computationally efficient enough to handle the large systems and long time scales required for reliable prediction of macroscopic properties. We…

In this paper, the process of forecasting household energy consumption is studied within the framework of the nonparametric Gaussian Process (GP), using multiple short time series data. As we begin to use smart meter data to paint a clearer…

We present an optimized implementation of the recently proposed symmetric gradient domain machine learning (sGDML) model. The sGDML model is able to faithfully reproduce global potential energy surfaces (PES) for molecules with a few dozen…

Accurate phase diagram calculation from molecular dynamics requires systematic treatment and convergence of statistical averages. In this work we propose a Gaussian process regression based framework for reconstructing the free energy…

Gaussian processes are typically used for smoothing and interpolation on small datasets. We introduce a new Bayesian nonparametric framework -- GPatt -- enabling automatic pattern extrapolation with Gaussian processes on large…

Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…

High-dimensional optimization is a critical challenge for operating large-scale scientific facilities. We apply a physics-informed Gaussian process (GP) optimizer to tune a complex system by conducting efficient global search. Typical GP…

Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…

We show that the Gaussian Approximation Potential machine learning framework can describe complex magnetic potential energy surfaces, taking ferromagnetic iron as a paradigmatic challenging case. The training database includes total…

We present a novel computational approach for extracting weak signals, whose exact location and width may be unknown, from complex background distributions with an arbitrary functional form. We focus on datasets that can be naturally…