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Performing reliability analysis on complex systems is often computationally expensive. In particular, when dealing with systems having high input dimensionality, reliability estimation becomes a daunting task. A popular approach to overcome…

In engineering design, one often wishes to calculate the probability that the performance of a system is satisfactory under uncertainty. State of the art algorithms exist to solve this problem using active learning with Gaussian process…

Prior beliefs about the latent function to shape inductive biases can be incorporated into a Gaussian Process (GP) via the kernel. However, beyond kernel choices, the decision-making process of GP models remains poorly understood. In this…

This paper addresses distributed learning of a complex object for multiple networked robots based on distributed optimization and kernel-based support vector machine. In order to overcome a fundamental limitation of polynomial kernels…

Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…

Computer experiments are often performed to allow modeling of a response surface of a physical experiment that can be too costly or difficult to run except using a simulator. Running the experiment over a dense grid can be prohibitively…

Quantifying biomechanical properties of the human vasculature could deepen our understanding of cardiovascular diseases. Standard nonlinear regression in constitutive modeling requires considerable high-quality data and an explicit form of…

Coarse graining techniques play an essential role in accelerating molecular simulations of systems with large length and time scales. Theoretically grounded bottom-up models are appealing due to their thermodynamic consistency with the…

Gaussian processes (GP) are widely used as a metamodel for emulating time-consuming computer codes. We focus on problems involving categorical inputs, with a potentially large number L of levels (typically several tens), partitioned in G <<…

Modern computational methods, involving highly sophisticated mathematical formulations, enable several tasks like modeling complex physical phenomenon, predicting key properties and design optimization. The higher fidelity in these computer…

We establish a scalable manifold learning method and theory, motivated by the problem of estimating fMRI activation manifolds in the Human Connectome Project (HCP). Our primary contribution is the development of an efficient estimation…

The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods…

Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes,…

Many machine learning problems can be framed in the context of estimating functions, and often these are time-dependent functions that are estimated in real-time as observations arrive. Gaussian processes (GPs) are an attractive choice for…

Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…

This paper describes a discrete state-space model -- and accompanying methods -- for generative modelling. This model generalises partially observed Markov decision processes to include paths as latent variables, rendering it suitable for…

Gaussian Processes (GPs) are flexible, nonparametric Bayesian models widely used for regression and classification because of their ability to capture complex data patterns and quantify predictive uncertainty. However, the O(n^3)…

The theoretical investigation of gas adsorption, storage, separation, diffusion and related transport processes in porous materials relies on a detailed knowledge of the potential energy surface of molecules in a stationary environment. In…

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…

Simulation techniques such as the finite element method are essential for designing electrical devices, but their computational cost can be prohibitive for repeated or real-time computations. Projection-based model order reduction…