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While complex simulations of physical systems have been widely used in engineering and scientific computing, lowering their often prohibitive computational requirements has only recently been tackled by deep learning approaches. In this…
In many mechanistic medical, biological, physical and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs) can make simulations impractically slow. Biological models require the…
We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…
As a non-parametric Bayesian model which produces informative predictive distribution, Gaussian process (GP) has been widely used in various fields, like regression, classification and optimization. The cubic complexity of standard GP…
Cooperative online scalar field mapping is an important task for multi-robot systems. Gaussian process regression is widely used to construct a map that represents spatial information with confidence intervals. However, it is difficult to…
High-quality and controllable digital twins of surgical instruments are critical for Real2Sim in robot-assisted surgery, as they enable realistic simulation, synthetic data generation, and perception learning under novel poses. We present…
One of the main challenges in surrogate modeling is the limited availability of data due to resource constraints associated with computationally expensive simulations. Multi-fidelity methods provide a solution by chaining models in a…
Sparse variational Gaussian process (GP) approximations based on inducing points have become the de facto standard for scaling GPs to large datasets, owing to their theoretical elegance, computational efficiency, and ease of implementation.…
In this paper, we explore the application of Gaussian Processes (GPs) for predicting mean-reverting time series with an underlying structure, using relatively unexplored functional and augmented data structures. While many conventional…
Non-conjugate Gaussian processes (NCGPs) define a flexible probabilistic framework to model categorical, ordinal and continuous data, and are widely used in practice. However, exact inference in NCGPs is prohibitively expensive for large…
Gaussian processes (GPs) are an important tool in machine learning and statistics with applications ranging from social and natural science through engineering. They constitute a powerful kernelized non-parametric method with…
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…
The 3D Gaussian splatting methods are getting popular. However, they work directly on the signal, leading to a dense representation of the signal. Even with some techniques such as pruning or distillation, the results are still dense. In…
Transformed Gaussian Processes (TGPs) are stochastic processes specified by transforming samples from the joint distribution from a prior process (typically a GP) using an invertible transformation; increasing the flexibility of the base…
The increasing use of stochastic models for describing complex phenomena warrants surrogate models that capture the reference model characteristics at a fraction of the computational cost, foregoing potentially expensive Monte Carlo…
Gaussian processes (GPs) are powerful tools for nonlinear classification in which latent GPs are combined with link functions. But GPs do not scale well to large training data. This is compounded for classification where the latent GPs…
In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…
Gaussian Processes (GP) have become popular machine-learning methods for kernel-based learning on datasets with complicated covariance structures. In this paper, we present a novel extension to the GP framework using a contaminated normal…
We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity…
This work shows how adaptivity can enhance value realization of digital twins in civil engineering. We focus on adapting the state transition models within digital twins represented through probabilistic graphical models. The bi-directional…