Related papers: Physics-Informed CoKriging: A Gaussian-Process-Reg…
Koopman operator theory provides a powerful data-driven technique for modeling nonlinear dynamical systems in a linear framework, in comparison to computationally expensive and highly nonlinear physics-based simulations. However, Koopman…
Physics-based models of dynamical systems are often used to study engineering and environmental systems. Despite their extensive use, these models have several well-known limitations due to simplified representations of the physical…
The computational effort for the evaluation of numerical simulations based on e.g. the finite-element method is high. Metamodels can be utilized to create a low-cost alternative. However the number of required samples for the creation of a…
We propose a multi-fidelity Bayesian emulator for the analysis of the Weather Research and Forecasting (WRF) model when the available simulations are not generated based on hierarchically nested experimental design. The proposed procedure,…
We apply Gaussian process (GP) regression, which provides a powerful non-parametric probabilistic method of relating inputs to outputs, to survival data consisting of time-to-event and covariate measurements. In this context, the covariates…
Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…
Computational simulations with different fidelity have been widely used in engineering design. A high-fidelity (HF) model is generally more accurate but also more time-consuming than an low-fidelity (LF) model. To take advantages of both HF…
We propose a general hybrid physics-informed machine learning framework for modeling nonlinear, history-dependent viscoelastic behavior under multiaxial cyclic loading. The approach is built on a generalized internal state variable-based…
How can we efficiently gather information to optimize an unknown function, when presented with multiple, mutually dependent information sources with different costs? For example, when optimizing a robotic system, intelligently trading off…
Knowledge of the force time history of a structure is essential to assess its behaviour, ensure safety and maintain reliability. However, direct measurement of external forces is often challenging due to sensor limitations, unknown force…
We present GP-4DGS, a novel framework that integrates Gaussian Processes (GPs) into 4D Gaussian Splatting (4DGS) for principled probabilistic modeling of dynamic scenes. While existing 4DGS methods focus on deterministic reconstruction,…
Parameter estimation and trajectory reconstruction for data-driven dynamical systems governed by ordinary differential equations (ODEs) are essential tasks in fields such as biology, engineering, and physics. These inverse problems --…
Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture…
The Fokker-Planck (FP) equation is a linear partial differential equation which governs the temporal and spatial evolution of the probability density function (PDF) associated with the response of stochastic dynamical systems. An exact…
Normative modeling has recently been proposed as an alternative for the case-control approach in modeling heterogeneity within clinical cohorts. Normative modeling is based on single-output Gaussian process regression that provides coherent…
We present Blitzkriging, a new approach to fast inference for Gaussian processes, applicable to regression, optimisation and classification. State-of-the-art (stochastic) inference for Gaussian processes on very large datasets scales…
We introduce a physics-informed neural framework for modeling static and time-dependent galactic gravitational potentials. The method combines data-driven learning with embedded physical constraints to capture complex, small-scale features…
We tackle the problem of collaborative filtering (CF) with side information, through the lens of Gaussian Process (GP) regression. Driven by the idea of using the kernel to explicitly model user-item similarities, we formulate the GP in a…
We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…
Gaussian processes (GPs) are powerful and widely used probabilistic regression models, but their effectiveness in practice is often limited by the choice of kernel function. This kernel function is typically handcrafted from a small set of…