Related papers: Modeling nonstationary spatial processes with norm…

Nonstationary non-Gaussian spatial data are common in many disciplines, including climate science, ecology, epidemiology, and social sciences. Examples include count data on disease incidence and binary satellite data on cloud mask…

Optical flow, inspired by the mechanisms of biological visual systems, calculates spatial motion vectors within visual scenes that are necessary for enabling robotics to excel in complex and dynamic working environments. However, current…

Existing deep learning-based surrogate models facilitate efficient data generation, but fall short in uncertainty quantification, efficient parameter space exploration, and reverse prediction. In our work, we introduce SurroFlow, a novel…

Constructing accurate and computationally efficient surrogate models (or emulators) for predicting dynamical system responses is critical in many engineering domains, yet remains challenging due to the strongly nonlinear and…

Forecasting neural activity in response to naturalistic stimuli remains a key challenge for understanding brain dynamics and enabling downstream neurotechnological applications. Here, we introduce a generative forecasting framework for…

Although Transformer has made breakthrough success in widespread domains especially in Natural Language Processing (NLP), applying it to time series forecasting is still a great challenge. In time series forecasting, the autoregressive…

Obtaining system parameters and reconstructing the full flow state from limited velocity observations using conventional fluid dynamics solvers can be prohibitively expensive. Here we employ machine learning algorithms to overcome the…

Regression on function spaces is typically limited to models with Gaussian process priors. We introduce the notion of universal functional regression, in which we aim to learn a prior distribution over non-Gaussian function spaces that…

Stochastic processes generated by non-stationary distributions are difficult to represent with conventional models such as Gaussian processes. This work presents Recurrent Autoregressive Flows as a method toward general stochastic process…

Gaussian processes (GP) are a popular and powerful tool for spatial modelling of data, especially data that quantify environmental processes. However, in stationary form, whether covariance is isotropic or anisotropic, GPs may lack the…

We report a triangular neural network implementation of neural autoregressive flow (NAF). Unlike many universal autoregressive density models, our design is highly modular, parameter economy, computationally efficient, and applicable to…

In this paper, we focus on isotropic and stationary sphere-cross-time random fields. We first introduce the class of spherical functional autoregressive-moving average processes (SPHARMA), which extend in a natural way the spherical…

A convolutional encoder-decoder-based transformer model is proposed for autoregressively training on spatio-temporal data of turbulent flows. The prediction of future fluid flow fields is based on the previously predicted fluid flow field…

We propose a new approach to the autoregressive spatial functional model, based on the notion of signature, which represents a function as an infinite series of its iterated integrals. It presents the advantage of being applicable to a wide…

This work presents a methodology to predict a near-optimal spacing function, which defines the element sizes, suitable to perform steady RANS turbulent viscous flow simulations. The strategy aims at utilising existing high fidelity…

Partial observations of continuous time-series dynamics at arbitrary time stamps exist in many disciplines. Fitting this type of data using statistical models with continuous dynamics is not only promising at an intuitive level but also has…

The rapid advancement of models based on artificial intelligence demands innovative monitoring techniques which can operate in real time with low computational costs. In machine learning, especially if we consider artificial neural networks…

Statistical shape modeling (SSM) is central to population level analysis of anatomical variability, yet most existing approaches rely on densely annotated segmentations and fixed latent representations. These requirements limit scalability…

Autoregressive models are among the best performing neural density estimators. We describe an approach for increasing the flexibility of an autoregressive model, based on modelling the random numbers that the model uses internally when…

Time warping function provides a mathematical representation to measure phase variability in functional data. Recent studies have developed various approaches to estimate optimal warping between functions and provide non-Euclidean models.…