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Deep Gaussian Processes (DGPs) combine the expressiveness of Deep Neural Networks (DNNs) with quantified uncertainty of Gaussian Processes (GPs). Expressive power and intractable inference both result from the non-Gaussian distribution over…

Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…

Effective forces -- derived from experimental or {\it in silico} molecular dynamics time traces -- are critical in developing reduced and computationally efficient descriptions of otherwise complex dynamical problems. Thus, designing…

Wrapping a computation domain with a perfectly matched layer (PML) is one of the most effective methods of imitating/approximating the radiation boundary condition in Maxwell and wave equation solvers. Many PML implementations often use a…

Gaussian processes (GPs) are flexible models that can capture complex structure in large-scale dataset due to their non-parametric nature. However, the usage of GPs in real-world application is limited due to their high computational cost…

Gaussian Processes (GPs) are known to provide accurate predictions and uncertainty estimates even with small amounts of labeled data by capturing similarity between data points through their kernel function. However traditional GP kernels…

Gaussian process regression generally does not scale to beyond a few thousands data points without applying some sort of kernel approximation method. Most approximations focus on the high eigenvalue part of the spectrum of the kernel…

Optimization of very expensive black-box functions requires utilization of maximum information gathered by the process of optimization. Model Guided Sampling Optimization (MGSO) forms a more robust alternative to Jones'…

Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator,…

Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…

This paper presents an analysis of properties of two hybrid discretization methods for Gaussian derivatives, based on convolutions with either the normalized sampled Gaussian kernel or the integrated Gaussian kernel followed by central…

In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty…

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

Sampling from discrete distributions is a ubiquitous task in machine learning, recently revisited by the emergence of discrete diffusion models. While Langevin algorithms constitute the state of the art for continuous spaces, discrete…

Simulations of physical phenomena are essential to the expedient design of precision components in aerospace and other high-tech industries. These phenomena are often described by mathematical models involving partial differential equations…

Coarse-grained (CG) models are simplified representations of soft matter systems that are commonly employed to overcome size and time limitations in computational studies. Many approaches have been developed to construct and parametrise…

A central issue in machine learning is how to train models on sensitive user data. Industry has widely adopted a simple algorithm: Stochastic Gradient Descent with noise (a.k.a. Stochastic Gradient Langevin Dynamics). However, foundational…

Recent neural network models for algorithmic tasks have led to significant improvements in extrapolation to sequences much longer than training, but it remains an outstanding problem that the performance still degrades for very long or…

While reinforcement learning methods such as Group Relative Preference Optimization (GRPO) have significantly enhanced Large Language Models, adapting them to diffusion models remains challenging. In particular, GRPO demands a stochastic…

Sample efficiency is a fundamental challenge in de novo molecular design. Ideally, molecular generative models should learn to satisfy a desired objective under minimal oracle evaluations (computational prediction or wet-lab experiment).…