Related papers: Climate Modeling with Neural Diffusion Equations

Across numerous applications, forecasting relies on numerical solvers for partial differential equations (PDEs). Although the use of deep-learning techniques has been proposed, actual applications have been restricted by the fact the…

Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to…

Ensemble weather predictions require statistical post-processing of systematic errors to obtain reliable and accurate probabilistic forecasts. Traditionally, this is accomplished with distributional regression models in which the parameters…

The dynamics of burning plasmas in tokamaks are crucial for advancing controlled thermonuclear fusion. This study applies the NeuralPlasmaODE, a multi-region multi-timescale transport model, to simulate the complex energy transfer processes…

Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…

Because of the impact of extreme heat waves and heat domes on society and biodiversity, their study is a key challenge. We specifically study long-lasting extreme heat waves, which are among the most important for climate impacts. Physics…

Optical satellite sensors cannot see the Earth's surface through clouds. Despite the periodic revisit cycle, image sequences acquired by Earth observation satellites are therefore irregularly sampled in time. State-of-the-art methods for…

Earth System Models (ESMs) are essential tools for understanding the impact of human actions on Earth's climate. One key application of these models is studying extreme weather events, such as heat waves or dry spells, which have…

Climate models play a critical role in understanding and projecting climate change. Due to their complexity, their horizontal resolution of about 40-100 km remains too coarse to resolve processes such as clouds and convection, which need to…

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…

The existing Neural ODE formulation relies on an explicit knowledge of the termination time. We extend Neural ODEs to implicitly defined termination criteria modeled by neural event functions, which can be chained together and…

Neural ordinary differential equations (ODEs) have attracted much attention as continuous-time counterparts of deep residual neural networks (NNs), and numerous extensions for recurrent NNs have been proposed. Since the 1980s, ODEs have…

We present Graph Neural Diffusion (GRAND) that approaches deep learning on graphs as a continuous diffusion process and treats Graph Neural Networks (GNNs) as discretisations of an underlying PDE. In our model, the layer structure and…

We present a novel model Graph Neural Stochastic Differential Equations (Graph Neural SDEs). This technique enhances the Graph Neural Ordinary Differential Equations (Graph Neural ODEs) by embedding randomness into data representation using…

This paper explores the efficacy of diffusion-based generative models as neural operators for partial differential equations (PDEs). Neural operators are neural networks that learn a mapping from the parameter space to the solution space of…

This paper proposes the Nerual Energy Descent (NED) via neural network evolution equations for a wide class of deep learning problems. We show that deep learning can be reformulated as the evolution of network parameters in an evolution…

The fractional advection-dispersion equation (FADE) has attracted increased attention from researchers as it provides an accurate description for challenging phenomenas with long-range time memory and spatial interactions, such as the…

Neural ordinary differential equations (NODEs) treat computation of intermediate feature vectors as trajectories of ordinary differential equation parameterized by a neural network. In this paper, we propose a novel model, delay…

Accurate long-range forecasting of the El \Nino-Southern Oscillation (ENSO) is vital for global climate prediction and disaster risk management. Yet, limited understanding of ENSO's physical mechanisms constrains both numerical and deep…

We present a framework and algorithms to learn controlled dynamics models using neural stochastic differential equations (SDEs) -- SDEs whose drift and diffusion terms are both parametrized by neural networks. We construct the drift term to…