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We propose a physics-constrained machine learning method-based on reservoir computing- to time-accurately predict extreme events and long-term velocity statistics in a model of turbulent shear flow. The method leverages the strengths of two…
The effects of erosion, avalanching and random precipitation are captured in a simple stochastic partial differential equation for modelling the evolution of river networks. Our model leads to a self-organized structured landscape and to…
Accurate rainfall forecasting is critical because it has a great impact on people's social and economic activities. Recent trends on various literatures show that Deep Learning (Neural Network) is a promising methodology to tackle many…
The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
Deep learning has emerged as a promising tool for precipitation downscaling. However, current models rely on likelihood-based loss functions to properly model the precipitation distribution, leading to spatially inconsistent projections…
In this paper, we present a new fractional mathematical model to describe the dynamics and the interaction between plants and water in arid and semi-arid environments with and without slope. By the Caputo fractional operator, the model…
We achieve the multifractal analysis of a class of complex valued statistically self-similar continuous functions. For we use multifractal formalisms associated with pointwise oscillation exponents of all orders. Our study exhibits new…
We consider the distributional equation $\textbf{Z}\stackrel{d}{=}\sum_{k=1}^N\textbf{A}_k\textbf{Z}(k) $, where $N$ is a random variable taking value in $\mathbb N_0=\{0,1,\cdots\}$, $\textbf{A}_1,\textbf{A}_2,\cdots$ are $p\times p$…
The wild bootstrap is a popular resampling method in the context of time-to-event data analyses. Previous works established the large sample properties of it for applications to different estimators and test statistics. It can be used to…
Climate change and increases in drought conditions affect the lives of many and are closely tied to global agricultural output and livestock production. This research presents a novel approach utilizing machine learning frameworks for…
Deep neural networks have made great achievements in rainfall prediction.However, the current forecasting methods have certain limitations, such as with blurry generated images and incorrect spatial positions. To overcome these challenges,…
Relevant comprehension of flood hazards has emerged as a crucial necessity, especially as the severity and the occurrence of flood events intensify with climate changes. Flood simulation and forecast capability have been greatly improved…
We survey some of our recent results on the geometry of spatially independent martingales, in a more concrete setting that allows for shorter, direct proofs, yet is general enough for several applications and contains the well-known fractal…
Robust sensing and perception in adverse weather conditions remain one of the biggest challenges for realizing reliable autonomous vehicle mobility services. Prior work has established that rainfall rate is a useful measure for the…
We derive a new closed-form variance-adaptive confidence sequence (CS) for estimating the average conditional mean of a sequence of bounded random variables. Empirically, it yields the tightest closed-form CS we have found for tracking…
Significant strides have been made in advancing streamflow predictions, notably with the introduction of cutting-edge machine-learning models. Predominantly, Long Short-Term Memories (LSTMs) and Convolution Neural Networks (CNNs) have been…
For a large class of self-similar sets F in R^d analogues of the higher order mean curvatures of differentiable submanifolds are introduced, in particular, the fractal Gauss-type curvature. They are shown to be the densities of associated…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
We construct a modified continuous-state branching process whose Malthusian parameter is replaced by another when passing below a certain level. The construction is obtained via a Lamperti-like transform applied to a refracted L\'evy…