Related papers: Gaussian process regression with additive periodic…
We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression which provides a…
We develop a Gaussian process framework for learning interaction kernels in multi-species interacting particle systems from trajectory data. Such systems provide a canonical setting for multiscale modeling, where simple microscopic…
Gaussian Processes (GPs) provide a general and analytically tractable way of modeling complex time-varying, nonparametric functions. The Automatic Bayesian Covariance Discovery (ABCD) system constructs natural-language description of…
Identifying dynamical system (DS) is a vital task in science and engineering. Traditional methods require numerous calls to the DS solver, rendering likelihood-based or least-squares inference frameworks impractical. For efficient parameter…
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…
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and…
In this paper, we focus on the data-driven discovery of a general second-order particle-based model that contains many state-of-the-art models for modeling the aggregation and collective behavior of interacting agents of similar size and…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…
Additive Gaussian process (GP) models offer flexible tools for modelling complex non-linear relationships and interaction effects among covariates. While most studies have focused on predictive performance, relatively little attention has…
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,…
A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of…
Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…
We discuss the correspondence between Gaussian process regression and Geometric Harmonics, two similar kernel-based methods that are typically used in different contexts. Research communities surrounding the two concepts often pursue…
Employing both Bayesian statistics and the theory of nonlinear dynamics, we present a practically efficient method to extract a phase description of weakly coupled limit-cycle oscillators directly from time series observed in a rhythmic…
Gaussian process regression is a powerful method for predicting states based on given data. It has been successfully applied for probabilistic predictions of structural systems to quantify, for example, the crack growth in mechanical…
Gaussian process regression techniques have been used in fluid mechanics for the reconstruction of flow fields from a reduction-of-dimension perspective. A main ingredient in this setting is the construction of adapted covariance functions,…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
We consider the problem of inferring the interaction kernel of stochastic interacting particle systems from observations of a single particle. We adopt a semi-parametric approach and represent the interaction kernel in terms of a…
Additive-interactive regression has recently been shown to offer attractive minimax error rates over traditional nonparametric multivariate regression in a wide variety of settings, including cases where the predictor count is much larger…