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Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…
Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
Paradoxically, while the assumptions of second-order stationarity and isotropy appear outdated in light of modern spatial data, they remain remarkably robust in practice, as nonstationary methods often provide marginal improvements in…
The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…
Incorporating atomistic and molecular information into models of cellular behaviour is challenging because of a vast separation of spatial and temporal scales between processes happening at the atomic and cellular levels. Multiscale or…
Neural Ordinary Differential Equations (ODE) are a promising approach to learn dynamic models from time-series data in science and engineering applications. This work aims at learning Neural ODE for stiff systems, which are usually raised…
For many applications with multivariate data, random field models capturing departures from Gaussianity within realisations are appropriate. For this reason, we formulate a new class of multivariate non-Gaussian models based on systems of…
The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which…
We introduce the spatial disorder-generalized Langevin equation (SD-GLE), a data-driven method for constructing coarse-grained (CG) dynamics in heterogeneous systems. Unlike conventional CG approaches that rely on a mean-field potential,…
Standard geostatistical models assume stationarity and rely on a variogram model to account for the spatial dependence in the observed data. In some instances, this assumption that the spatial dependence structure is constant throughout the…
Many econometric analyses involve spatio--temporal data. A considerable amount of literature has addressed spatio--temporal models, with Spatial Dynamic Panel Data (SDPD) being widely investigated and applied. In real data applications,…
In several application fields like daily pluviometry data modelling, or motion analysis from image sequences, observations contain two components of different nature. A first part is made with discrete values accounting for some symbolic…
Stochastic differential equations (SDEs) are used to describe a wide variety of complex stochastic dynamical systems. Learning the hidden physics within SDEs is crucial for unraveling fundamental understanding of these systems' stochastic…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
The analysis of area-level aggregated summary data is common in many disciplines including epidemiology and the social sciences. Typically, Markov random field spatial models have been employed to acknowledge spatial dependence and allow…
Inverse problems with spatiotemporal observations are ubiquitous in scientific studies and engineering applications. In these spatiotemporal inverse problems, observed multivariate time series are used to infer parameters of physical or…
We present a data-driven machine-learning approach for modeling space-time socioeconomic dynamics. Through coarse-graining fine-scale observations, our modeling framework simplifies these complex systems to a set of tractable mechanistic…
In this work we demonstrate that SVD-based model reduction techniques known for ordinary differential equations, such as the proper orthogonal decomposition, can be extended to stochastic differential equations in order to reduce the…
Stochastic differential equations (SDEs) are increasingly used in longitudinal data analysis, compartmental models, growth modelling, and other applications in a number of disciplines. Parameter estimation, however, currently requires…