Related papers: Physics-Informed CoKriging: A Gaussian-Process-Reg…
Despite the wide implementation of machine learning (ML) techniques in traffic flow modeling recently, those data-driven approaches often fall short of accuracy in the cases with a small or noisy dataset. To address this issue, this study…
We use a Gaussian Process Regression (GPR) strategy that was recently developed [3,16,17] to analyze different types of curves that are commonly encountered in parametric eigenvalue problems. We employ an offline-online decomposition…
Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that…
Gaussian Processes (GPs) are expressive models for capturing signal statistics and expressing prediction uncertainty. As a result, the robotics community has gathered interest in leveraging these methods for inference, planning, and…
Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…
Risk assessment of hurricane-driven storm surge relies on deterministic computer models that produce outputs over a large spatial domain. The surge models can often be run at a range of fidelity levels, with greater precision yielding more…
Simulations of condensed matter systems often focus on the dynamics of a few distinguished components but require integrating the dynamics of the full system. A prime example is a molecular dynamics simulation of a (macro)molecule in…
Pareto Front (PF) modeling is essential in decision making problems across all domains such as economics, medicine or engineering. In Operation Research literature, this task has been addressed based on multi-objective optimization…
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…
In this paper, we apply the practical GADI-HS iteration as a smoother in algebraic multigrid (AMG) method for solving second-order non-selfadjoint elliptic problem. Additionally, we prove the convergence of the derived algorithm and…
We formulate a reduced-order strategy for efficiently forecasting complex high-dimensional dynamical systems entirely based on data streams. The first step of our method involves reconstructing the dynamics in a reduced-order subspace of…
Multi-fidelity modelling arises in many situations in computational science and engineering world. It enables accurate inference even when only a small set of accurate data is available. Those data often come from a high-fidelity model,…
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…
We introduce an RG-inspired coarse-graining for extracting the collective features of data. The key to successful coarse-graining lies in finding appropriate pairs of data sets. We coarse-grain the two closest data in a regular real-space…
Gaussian process (GP) models are effective non-linear models for numerous scientific applications. However, computation of their hyperparameters can be difficult when there is a large number of training observations (n) due to the O(n^3)…
Physics-informed neural networks have emerged as an alternative method for solving partial differential equations. However, for complex problems, the training of such networks can still require high-fidelity data which can be expensive to…
Offline Goal-Conditioned Reinforcement Learning (GCRL) holds great promise for domains such as autonomous navigation and locomotion, where collecting interactive data is costly and unsafe. However, it remains challenging in practice due to…
Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds,…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…