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Electric Vehicles (EVs) are becoming increasingly prevalent nowadays, with studies highlighting their potential as mobile energy storage systems to provide grid support. Realising this potential requires effective charging coordination,…
Transport properties of strongly correlated quantum systems are of central interest in condensed matter, ultracold atoms and in dense plasmas. There, the proper treatment of strong correlations poses a great challenge to theory. Here, we…
A step by step procedure to derive analytically the exact dynamical evolution equations of the probability density functions (PDF) of well known kinetic wealth exchange economic models is shown. This technique gives a dynamical insight into…
We present a generalized linear response theory for mixed jump-diffusion models -- combining Gaussian and L\'evy noise interacting with nonlinear dynamics -- by deriving comprehensive response formulas accounting for perturbations to both…
In this article, we are interested in the strong well-posedness together with the numerical approximation of some one-dimensional stochastic differential equations with a non-linear drift, in the sense of McKean-Vlasov, driven by a…
We construct a deterministic, Lagrangian many-particle approximation to a class of nonlocal transport PDEs with nonlinear mobility arising in many contexts in biology and social sciences. The approximating particle system is a nonlocal…
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
Reliable uncertainty quantification in deep neural networks is very crucial in safety-critical applications such as automated driving for trustworthy and informed decision-making. Assessing the quality of uncertainty estimates is…
We study the sample complexity of entropic optimal transport in high dimensions using computationally efficient plug-in estimators. We significantly advance the state of the art by establishing dimension-free, parametric rates for…
Heavy goods vehicles are vital backbones of the supply chain delivery system but also contribute significantly to carbon emissions with only 60% loading efficiency in the United Kingdom. Collaborative vehicle routing has been proposed as a…
Recent works on the application of Physics-Informed Neural Networks to traffic density estimation have shown to be promising for future developments due to their robustness to model errors and noisy data. In this paper, we introduce a…
Learning priors on trajectory distributions can help accelerate robot motion planning optimization. Given previously successful plans, learning trajectory generative models as priors for a new planning problem is highly desirable. Prior…
Diffusion models are promising for joint trajectory prediction and controllable generation in autonomous driving, but they face challenges of inefficient inference steps and high computational demands. To tackle these challenges, we…
Connected vehicles disseminate detailed data, including their position and speed, at a very high frequency. Such data can be used for accurate real-time analysis, prediction and control of transportation systems. The outstanding challenge…
A cascade model is described based on multiplier distributions determined from 3D direct numerical simulations (DNS) of turbulent particle laden flows, which include two-way coupling between the phases at global mass loadings equal to…
This paper proposes a probabilistic model for uncontrolled charging of electric vehicles (EVs). EV charging will add significant load to power systems in the coming years and, due to the convenience of charging at home, this is likely to…
Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…
This paper concerns the numerical approximation for the invariant distribution of Markovian switching L\'evy-driven stochastic differential equations. By combining the tamed-adaptive Euler-Maruyama scheme with the Multi-level Monte Carlo…
In this study, two initial boundary value problems for one dimensional advection-dispersion equation are solved by differential quadrature method based on sine cardinal functions. Pure advection problem modeling transport of conservative…
Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities over time. These tracking data motivate the use of mathematical models to characterise the motion…