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We propose a new class of physics-informed neural networks, called Physics-Informed Generator-Encoder Adversarial Networks, to effectively address the challenges posed by forward, inverse, and mixed problems in stochastic differential…
Models of spatial transition probabilities, or equivalently, transiogram models have been recently proposed as spatial continuity measures in categorical fields. In this paper, properties of transiogram models are examined analytically, and…
A spatial curve dynamical model framework is adopted for functional prediction of counts in a spatiotemporal log-Gaussian Cox process model. Our spatial functional estimation approach handles both wavelet-based heterogeneity analysis in…
The spatial structure of fluctuations in spatially inhomogeneous processes can be modeled in terms of Gibbs random fields. A local low energy estimator (LLEE) is proposed for the interpolation (prediction) of such processes at points where…
Although spatio-temporal graph neural networks have achieved great empirical success in handling multiple correlated time series, they may be impractical in some real-world scenarios due to a lack of sufficient high-quality training data.…
Paleoclimatology -- the study of past climate -- is relevant beyond climate science itself, such as in archaeology and anthropology for understanding past human dispersal. Information about the Earth's paleoclimate comes from simulations of…
The advent of data science has provided an increasing number of challenges with high data complexity. This paper addresses the challenge of space-time data where the spatial domain is not a planar surface, a sphere, or a linear network, but…
This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…
The efficient simulation of isotropic Gaussian random fields on the unit sphere is a task encountered frequently in numerical applications. A fast algorithm based on Markov properties and fast Fourier Transforms in 1d is presented that…
We develop and analyze a numerical method for stochastic time-fractional diffusion driven by additive fractionally integrated Gaussian noise. The model involves two nonlocal terms in time, i.e., a Caputo fractional derivative of order…
Simulating a depositional (or stratigraphic) sequence conditionally on borehole data is a long-standing problem in hydrogeology and in petroleum geostatistics. This paper presents a new rule-based approach for simulating depositional…
The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…
Complex multivariate time series arise in many fields, ranging from computer vision to robotics or medicine. Often we are interested in the independent underlying factors that give rise to the high-dimensional data we are observing. While…
We consider a fast approximation method for a solution of a certain stochastic non-local pseudodifferential equation. This equation defines a Mat\'ern class random field. The approximation method is based on the spectral compactness of the…
Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…
The terrain survey techniques of photogrammetry, LIDAR, Sonar or seismic studies are subject to limitation of shadow zones. It is not possible to capture the terrain pattern and requires interpolation and extrapolation for conformal mapping…
As the role played by statistical and computational sciences in climate and environmental modelling and prediction becomes more important, Machine Learning researchers are becoming more aware of the relevance of their work to help tackle…
This article introduces novel and practicable Bayesian factor analysis frameworks that are computationally feasible for moderate to large spatiotemporal data. Previous Bayesian analysis of spatiotemporal data has utilized a Bayesian factor…
We study the problem of modeling and inference for spatio-temporal count processes. Our approach uses parsimonious parameterisations of multivariate autoregressive count time series models, including possible regression on covariates. We…
This study proposes a pseudo random number generator of q-Gaussian random variables for a range of q values, -infinity < q < 3, based on deterministic chaotic map dynamics. Our method consists of chaotic maps on the unit circle and map…