相关论文: Climate Modeling with Neural Diffusion Equations

In the field of weather forecasting, traditional models often grapple with discretization errors and time-dependent source discrepancies, which limit their predictive performance. In this paper, we present WeatherODE, a novel one-stage,…

The forward model in diffuse optical tomography (DOT) describes how light propagates through a turbid medium. It is often approximated by a diffusion equation (DE) that is numerically discretized by the classical finite element method…

Sea Surface Temperature (SST) is crucial for understanding upper-ocean thermal dynamics and ocean-atmosphere interactions, which have profound economic and social impacts. While data-driven models show promise in SST prediction, their…

This book presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward…

Learning multi-agent system dynamics has been extensively studied for various real-world applications, such as molecular dynamics in biology. Most of the existing models are built to learn single system dynamics from observed historical…

Climate-economic modeling under uncertainty presents significant computational challenges that may limit policymakers' ability to address climate change effectively. This paper explores neural network-based approaches for solving…

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…

In this paper, we construct approximated solutions of Differential Equations (DEs) using the Deep Neural Network (DNN). Furthermore, we present an architecture that includes the process of finding model parameters through experimental data,…

Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art…

This study investigates the application of deep-learning diffusion models for the super-resolution of weather data, a novel approach aimed at enhancing the spatial resolution and detail of meteorological variables. Leveraging the…

While diffusion models have shown great success in image generation, their noise-inverting generative process does not explicitly consider the structure of images, such as their inherent multi-scale nature. Inspired by diffusion models and…

Partial differential equation (PDE) models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which…

In this paper, we introduce a novel framework for combining scientific knowledge within physics-based models and recurrent neural networks to advance scientific discovery in many dynamical systems. We will first describe the use of outputs…

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

Flash floods in urban areas occur with increasing frequency. Detecting these floods would greatlyhelp alleviate human and economic losses. However, current flood prediction methods are eithertoo slow or too simplified to capture the flood…

Diffusion models (DMs) have become the dominant paradigm of generative modeling in a variety of domains by learning stochastic processes from noise to data. Recently, diffusion denoising bridge models (DDBMs), a new formulation of…

Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each…

Neural Ordinary Differential Equations (Neural ODEs) construct the continuous dynamics of hidden units using ordinary differential equations specified by a neural network, demonstrating promising results on many tasks. However, Neural ODEs…

This paper addresses imitation learning for motion prediction problem in autonomous driving, especially in multi-agent setting. Different from previous methods based on GAN, we present the conditional latent ordinary differential equation…

A central challenge in climate science and applied mathematics is developing data-driven models of multiscale systems that capture both stationary statistics and responses to external perturbations. Current neural climate emulators aim to…