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The ultimate semiclassical wave packet propagation technique is a complex, time-dependent WBK method known as generalized Gaussian wave packet dynamics (GGWPD). It requires overcoming many technical difficulties in order to be carried out…
Circular data arise in many areas of application. Recently, there has been interest in looking at circular data collected separately over time and over space. Here, we extend some of this work to the spatio-temporal setting, introducing…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models.…
Guided wave-based techniques have been used extensively in Structural Health Monitoring (SHM). Models using guided waves can provide information from both time and frequency domains to make themselves accurate and robust. Probabilistic SHM…
Air pollution remains a critical environmental and public health challenge, demanding high-resolution spatial data to better understand its spatial distribution and impacts. This study addresses the challenges of conducting multivariate…
In this study, we introduce a novel analytical Gaussian Process (GP) cosmography methodology, leveraging the differentiable properties of GPs to derive key cosmological quantities analytically. Our approach combines cosmic chronometer (CC)…
Gaussian Processes (GPs) have been widely used in machine learning to model distributions over functions, with applications including multi-modal regression, time-series prediction, and few-shot learning. GPs are particularly useful in the…
Quantifying changes in the probability and magnitude of extreme flooding events is key to mitigating their impacts. While hydrodynamic data are inherently spatially dependent, traditional spatial models such as Gaussian processes are poorly…
Large-scale swarm robotic systems consisting of numerous cooperative agents show considerable promise for performing autonomous tasks across various sectors. Nonetheless, traditional motion planning approaches often face a trade-off between…
Distributed Gaussian process (DGP) is a popular approach to scale GP to big data which divides the training data into some subsets, performs local inference for each partition, and aggregates the results to acquire global prediction. To…
Next-generation gravitational wave (GW) experiments will explore higher frequency ranges, where GW wavelengths approach the size of the detector itself. In this regime, GWs may be detected not just through the well-known mechanical…
Dust storms in the earth's major desert regions significantly influence microphysical weather processes, the CO$_2$-cycle and the global climate in general. Recent increases in the spatio-temporal resolution of remote sensing instruments…
Many datasets are observed on a finite set of equally spaced directions instead of the exact angles, such as the wind direction data. However, in the statistical literature, bivariate models are only available for continuous circular random…
Solving hydrologic inverse problems usually requires repetitive forward simulations. One approach to mitigate the computational cost is to build a surrogate model, i.e., an approximate mapping from model parameters (input) to observable…
We propose a generative model for the spatio-temporal distribution of high dimensional categorical observations. These are commonly produced by robots equipped with an imaging sensor such as a camera, paired with an image classifier,…
An important issue in quadcopter control is that an accurate dynamic model of the system is nonlinear, complex, and costly to obtain. This limits achievable control performance in practice. Gaussian process (GP) based estimation is an…
For autonomous mobile robots, uncertainties in the environment and system model can lead to failure in the motion planning pipeline, resulting in potential collisions. In order to achieve a high level of robust autonomy, these robots should…
Gaussian and discrete non-Gaussian spatial datasets are common across fields like public health, ecology, geosciences, and social sciences. Bayesian spatial generalized linear mixed models (SGLMMs) are a flexible class of models for…
Recent research in multi-robot exploration and mapping has focused on sampling environmental fields, which are typically modeled using the Gaussian process (GP). Existing information-theoretic exploration strategies for learning GP-based…