Related papers: Nonstationary multi-output Gaussian processes via …

In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced-order methods are demanded. Combining these…

Solving nonlinear partial differential equations (PDEs) using kernel methods offers a compelling alternative to traditional numerical solvers. However, the performance of these methods strongly depends on the choice of kernel. In this work,…

Multimodal learning aims to discover the relationship between multiple modalities. It has become an important research topic due to extensive multimodal applications such as cross-modal retrieval. This paper attempts to address the modality…

Coarse-graining has become an area of tremendous importance within many different research fields. For molecular simulation, coarse-graining bears the promise of finding simplified models such that long-time simulations of large-scale…

Probabilistic models for sequential data are the basis for a variety of applications concerned with processing timely ordered information. The predominant approach in this domain is given by recurrent neural networks, implementing either an…

Through one decade's development, the kernel-based regularization method (KRM) has become a complement to the classical maximum likelihood/prediction error method and an emerging new system identification paradigm. One recent example is its…

We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…

As one of the most advanced variants in the correntropy family, the multi-kernel correntropy criterion demonstrates superior accuracy in handling non-Gaussian noise, particularly with multimodal distributions. However, current approaches…

Coarse-grained (CG) molecular dynamics simulations extend the length and time scale of atomistic simulations by replacing groups of correlated atoms with CG beads. Machine-learned coarse-graining (MLCG) has recently emerged as a promising…

We provide a survey of nonstationary surrogate models which utilize Gaussian processes (GPs) or variations thereof, including nonstationary kernel adaptations, partition and local GPs, and spatial warpings through deep Gaussian processes.…

A multiple objective simulation optimization algorithm named Multiple Objective Probabilistic Branch and Bound with Single Observation (MOPBnB(so)) is presented for approximating the Pareto optimal set and the associated efficient frontier…

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…

Multitask Gaussian processes (MTGP) are the Gaussian process (GP) framework's solution for multioutput regression problems in which the $T$ elements of the regressors cannot be considered conditionally independent given the observations.…

The state space (SS) representation of Gaussian processes (GP) has recently gained a lot of interest. The main reason is that it allows to compute GPs based inferences in O(n), where $n$ is the number of observations. This implementation…

Additive smooth models, such as Generalized additive models (GAMs) of location, scale, and shape (GAMLSS), are a popular choice for modeling experimental data. However, software available to fit such models is usually not tailored…

In this paper, we apply the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) to first solving a nonlinear poroelasticity problem. The arising system consists of a nonlinear pressure equation and a…

We propose NonStGM, a general nonparametric graphical modeling framework for studying dynamic associations among the components of a nonstationary multivariate time series. It builds on the framework of Gaussian Graphical Models (GGM) and…

Numerous molecular systems, including solutions, proteins, and composite materials, can be modeled using mixed-resolution representations, of which the quantum mechanics/molecular mechanics (QM/MM) approach has become the most widely used.…

We present a model predictive control (MPC) framework to solve the constrained nonlinear output regulation problem. The main feature of the proposed framework is that the application does not require the solution to classical regulator…

Multi-task Gaussian process (MTGP) is a well-known non-parametric Bayesian model for learning correlated tasks effectively by transferring knowledge across tasks. But current MTGPs are usually limited to the multi-task scenario defined in…