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Operator learning offers a powerful paradigm for solving parametric partial differential equations (PDEs), but scaling probabilistic neural operators such as the recently proposed Gaussian Processes Operators (GPOs) to high-dimensional,…
In this paper, we present a general approach to automatically visual-servo control the position and shape of a deformable object whose deformation parameters are unknown. The servo-control is achieved by online learning a model mapping…
Gaussian random field is a ubiquitous model for spatial phenomena in diverse scientific disciplines. Its approximation is often crucial for computational feasibility in simulation, inference, and uncertainty quantification. The…
The fitting of spectral lines is a common step in the analysis of line observations and simulations. However, the observational noise, the presence of multiple velocity components, and potentially large data sets make it a non-trivial task.…
A framework for performing dynamic mesh adaptation with the discontinuous Galerkin method (DGM) is presented. Adaptations include modifications of the local mesh step size (h-adaptation) and the local degree of the approximating polynomials…
Ordinary differential equations (ODE) have been widely used for modeling dynamical complex systems. For high-dimensional ODE models where the number of differential equations is large, it remains challenging to estimate the ODE parameters…
Spatial modelling often uses Gaussian random fields to capture the stochastic nature of studied phenomena. However, this approach incurs significant computational burdens (O(n3)), primarily due to covariance matrix computations. In this…
We consider the problem of learning Stochastic Differential Equations of the form $dX_t = f(X_t)dt+\sigma(X_t)dW_t $ from one sample trajectory. This problem is more challenging than learning deterministic dynamical systems because one…
Gaussian process (GP) emulators have become essential tools for approximating complex simulators, significantly reducing computational demands in optimization, sensitivity analysis, and model calibration. While traditional GP emulators…
Deep Gaussian Processes (DGPs) compose GP layers to warp inputs, enabling improved emulation of computer models with nonstationary input-output behavior compared with ordinary GPs. In contrast to GPs, the predictive uncertainty for DGP…
This paper proposes an online learning method of Gaussian process state-space model (GP-SSM). GP-SSM is a probabilistic representation learning scheme that represents unknown state transition and/or measurement models as Gaussian processes…
Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…
Previous surface reconstruction methods either suffer from low geometric accuracy or lengthy training times when dealing with real-world complex dynamic scenes involving multi-person activities, and human-object interactions. To tackle the…
Using collisionless N-body simulations of dwarf galaxies orbiting the Milky Way (MW) we construct realistic models of dwarf spheroidal (dSph) galaxies of the Local Group. The dwarfs are initially composed of stellar disks embedded in dark…
Simulation provides a cost-effective and flexible platform for data generation and policy learning to develop robotic systems. However, bridging the gap between simulation and real-world dynamics remains a significant challenge, especially…
Learning dynamical models from data is not only fundamental but also holds great promise for advancing principle discovery, time-series prediction, and controller design. Among various approaches, Gaussian Process State-Space Models…
This paper is concerned with a state-space approach to deep Gaussian process (DGP) regression. We construct the DGP by hierarchically putting transformed Gaussian process (GP) priors on the length scales and magnitudes of the next level of…
Gaussian processes (GPs) have become a common tool in astronomy for analysing time series data, particularly in exoplanet science and stellar astrophysics. However, choosing the appropriate covariance structure for a GP model remains a…
The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…
Recent advancements in 3D Gaussian Splatting (3D-GS) have demonstrated the potential of using 3D Gaussian primitives for high-speed, high-fidelity, and cost-efficient novel view synthesis from continuously calibrated input views. However,…