相关论文: Multi-Fidelity High-Order Gaussian Processes for P…

The sparse pseudo-input Gaussian process (SPGP) is a new approximation method for speeding up GP regression in the case of a large number of data points N. The approximation is controlled by the gradient optimization of a small set of M…

This article proposes an efficient numerical method for solving nonlinear partial differential equations (PDEs) based on sparse Gaussian processes (SGPs). Gaussian processes (GPs) have been extensively studied for solving PDEs by…

Bayesian optimization (BO) is a powerful and data-efficient method for iterative materials discovery and design, particularly valuable when prior knowledge is limited, underlying functional relationships are complex or unknown, and the cost…

This paper presents a novel extension of multi-task Gaussian Cox processes for modeling multiple heterogeneous correlated tasks jointly, e.g., classification and regression, via multi-output Gaussian processes (MOGP). A MOGP prior over the…

Multi-fidelity surrogate modeling aims to learn an accurate surrogate at the highest fidelity level by combining data from multiple sources. Traditional methods relying on Gaussian processes can hardly scale to high-dimensional data. Deep…

Accurate human motion prediction with well-calibrated uncertainty is critical for safe human-robot collaboration (HRC), where robots must anticipate and react to human movements in real time. We propose a structured multitask variational…

Multi-output Gaussian process (MGP) models have attracted significant attention for their flexibility and uncertainty-quantification capabilities, and have been widely adopted in multi-source transfer learning scenarios due to their ability…

Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation involves resolving tails of probability distribution, and Monte Carlo sampling…

We propose the multistep port-Hamiltonian Gaussian process (MS-PHS GP) to learn physically consistent continuous-time dynamics and a posterior over the Hamiltonian from noisy, irregularly-sampled trajectories. By placing a GP prior on the…

We introduce a novel stochastic variational inference method for Gaussian process ($\mathcal{GP}$) regression, by deriving a posterior over a learnable set of coresets: i.e., over pseudo-input/output, weighted pairs. Unlike former free-form…

Multi-fidelity modeling and learning are important in physical simulation-related applications. It can leverage both low-fidelity and high-fidelity examples for training so as to reduce the cost of data generation while still achieving good…

Gaussian Process (GP) models provide a flexible framework for prediction and uncertainty quantification. For most covariance functions, however, exact GP prediction with $n$ points scales as $\mathcal{O}(n^3)$, making it prohibitively…

In biomanufacturing, developing an accurate model to simulate the complex dynamics of bioprocesses is an important yet challenging task. This is partially due to the uncertainty associated with bioprocesses, high data acquisition cost, and…

We introduce a stochastic variational inference procedure for training scalable Gaussian process (GP) models whose per-iteration complexity is independent of both the number of training points, $n$, and the number basis functions used in…

We present a framework for transfer learning based on modular variational Gaussian processes (GP). We develop a module-based method that having a dictionary of well fitted GPs, one could build ensemble GP models without revisiting any data.…

The study of neural operators has paved the way for the development of efficient approaches for solving partial differential equations (PDEs) compared with traditional methods. However, most of the existing neural operators lack the…

Finite element model updating utilizing frequency response functions as inputs is an important procedure in structural analysis, design and control. This paper presents a highly efficient framework that is built upon Gaussian process…

Gaussian processes (GPs) are non-linear probabilistic models popular in many applications. However, na\"ive GP realizations require quadratic memory to store the covariance matrix and cubic computation to perform inference or evaluate the…

Many fields of science and engineering rely on running simulations with complex and computationally expensive models to understand the involved processes in the system of interest. Nevertheless, the high cost involved hamper reliable and…

Mechanistic knowledge about the physical world is virtually always expressed via partial differential equations (PDEs). Recently, there has been a surge of interest in probabilistic PDE solvers -- Bayesian statistical models mostly based on…