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We propose a probabilistic model for inferring the multivariate function from multiple areal data sets with various granularities. Here, the areal data are observed not at location points but at regions. Existing regression-based models can…

The tuning of fused filament fabrication parameters is notoriously challenging. We propose an autonomous data-driven method to select parameters based on in situ measurements. We use a laser sensor to evaluate the surface roughness of a…

Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial…

Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the…

Computer simulations are becoming an essential tool in many scientific fields from molecular dynamics to aeronautics. In glaciology, future predictions of sea level change require input from ice sheet models. Due to uncertainties in the…

Mesoscale simulations of woven composites using parameterized analytical geometries offer a way to connect constituent material properties and their geometric arrangement to effective composite properties and performance. However, the…

The accelerating pace and expanding scope of materials discovery demand optimization frameworks that efficiently navigate vast, nonlinear design spaces while judiciously allocating limited evaluation resources. We present a cost-aware,…

Multi-fidelity approaches combine different models built on a scarce but accurate data-set (high-fidelity data-set), and a large but approximate one (low-fidelity data-set) in order to improve the prediction accuracy. Gaussian Processes…

Parameter estimation is crucial for modeling, tracking, and control of complex dynamical systems. However, parameter uncertainties can compromise system performance under a controller relying on nominal parameter values. Typically,…

Deep Gaussian Processes (DGPs) were proposed as an expressive Bayesian model capable of a mathematically grounded estimation of uncertainty. The expressivity of DPGs results from not only the compositional character but the distribution…

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

Careful design of semiconductor manufacturing equipment is crucial for ensuring the performance, yield, and reliability of semiconductor devices. Despite this, numerical optimization methods are seldom applied to optimize the design of such…

Despite the advancements in quality and efficiency achieved by 3D Gaussian Splatting (3DGS) in 3D scene rendering, aliasing artifacts remain a persistent challenge. Existing approaches primarily rely on low-pass filtering to mitigate…

We propose a Bayesian nonparametric method for low-pass filtering that can naturally handle unevenly-sampled and noise-corrupted observations. The proposed model is constructed as a latent-factor model for time series, where the latent…

Many methods for machine learning rely on approximate inference from intractable probability distributions. Variational inference approximates such distributions by tractable models that can be subsequently used for approximate inference.…

Local multiscale methods often construct multiscale basis functions in the offline stage without taking into account input parameters, such as source terms, boundary conditions, and so on. These basis functions are then used in the online…

The costs for drilling offshore wells are high and hydrocarbons are often located in complex reservoir formations. To effectively produce from such reservoirs and reduce costs, optimized well placement in real-time (geosteering) is crucial.…

The ability to predict future states is crucial to informed decision-making while interacting with dynamic environments. With cameras providing a prevalent and information-rich sensing modality, the problem of predicting future states from…

In this chapter, we show how to efficiently model high-dimensional extreme peaks-over-threshold events over space in complex non-stationary settings, using extended latent Gaussian Models (LGMs), and how to exploit the fitted model in…

This work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian…