Climate Modeling with Neural Diffusion Equations
arXiv:2111.06011
Abstract
Owing to the remarkable development of deep learning technology, there have been a series of efforts to build deep learning-based climate models. Whereas most of them utilize recurrent neural networks and/or graph neural networks, we design a novel climate model based on the two concepts, the neural ordinary differential equation (NODE) and the diffusion equation. Many physical processes involving a Brownian motion of particles can be described by the diffusion equation and as a result, it is widely used for modeling climate. On the other hand, neural ordinary differential equations (NODEs) are to learn a latent governing equation of ODE from data. In our presented method, we combine them into a single framework and propose a concept, called neural diffusion equation (NDE). Our NDE, equipped with the diffusion equation and one more additional neural network to model inherent uncertainty, can learn an appropriate latent governing equation that best describes a given climate dataset. In our experiments with two real-world and one synthetic datasets and eleven baselines, our method consistently outperforms existing baselines by non-trivial margins.
Accepted by ICDM 2021
References in corpus (13)
- Simplifying Graph Convolutional Networks
- Neural networks for post-processing ensemble weather forecasts
- Hamiltonian Neural Networks
- Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge
- A test case for application of convolutional neural networks to spatio-temporal climate data: Re-identifying clustered weather patterns
- GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series
- Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning
- Lagrangian Neural Networks
- SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimates
- Differentiable Physics-informed Graph Networks
- Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints
- Dissecting the Diffusion Process in Linear Graph Convolutional Networks
- Neural Networks with Cheap Differential Operators