DeepPhysiNet: Bridging Deep Learning and Atmospheric Physics for Accurate and Continuous Weather Modeling

TL;DR

DeepPhysiNet proposes a physics-informed neural framework that bridges NWP and DLP by coupling hyper-networks with physics networks. The hyper-networks, Transformer-based, extract spatiotemporal patterns and generate weights for location- and time-dependent physics networks that output weather variables conditioned on coordinates $(x,y,t)$. A PDE-based loss enforces atmospheric physics alongside a regression loss, enabling continuous-resolution outputs and enabling downscaling, bias correction, and forecasting with improved physical consistency. The framework demonstrates strong performance in station-level downscaling, grid-point bias correction, and short- to mid-range forecasting, while also providing interpretable insights into variable contributions and leveraging PDE constraints for robust extrapolation.

Abstract

Accurate weather forecasting holds significant importance to human activities. Currently, there are two paradigms for weather forecasting: Numerical Weather Prediction (NWP) and Deep Learning-based Prediction (DLP). NWP utilizes atmospheric physics for weather modeling but suffers from poor data utilization and high computational costs, while DLP can learn weather patterns from vast amounts of data directly but struggles to incorporate physical laws. Both paradigms possess their respective strengths and weaknesses, and are incompatible, because physical laws adopted in NWP describe the relationship between coordinates and meteorological variables, while DLP directly learns the relationships between meteorological variables without consideration of coordinates. To address these problems, we introduce the DeepPhysiNet framework, incorporating physical laws into deep learning models for accurate and continuous weather system modeling. First, we construct physics networks based on multilayer perceptrons (MLPs) for individual meteorological variable, such as temperature, pressure, and wind speed. Physics networks establish relationships between variables and coordinates by taking coordinates as input and producing variable values as output. The physical laws in the form of Partial Differential Equations (PDEs) can be incorporated as a part of loss function. Next, we construct hyper-networks based on deep learning methods to directly learn weather patterns from a large amount of meteorological data. The output of hyper-networks constitutes a part of the weights for the physics networks. Experimental results demonstrate that, upon successful integration of physical laws, DeepPhysiNet can accomplish multiple tasks simultaneously, not only enhancing forecast accuracy but also obtaining continuous spatiotemporal resolution results, which is unattainable by either the NWP or DLP.

Figures (9)

• Figure 1: a) Overall of the proposed DeepPhysiNet, which incorporates atmospheric physics into deep learning methods for accurate and continuous weather modeling. It combines the advantages of NWP and DLP at the same time. b) Properties of DeepPhysiNet, compared to NWP and DLP. Data Driven. It utilizes deep learning methods to extract spatiotemporal features from large-scale datasets. Physical Laws Incorporation. With the differentiable nature of neural networks, PDEs describing atmospheric physics can be incorporated into deep learning models with the form of loss function. Continuous Resolution. After trained, it can generate forecast results with a continuous resolution with the input of various sample points. c) Once trained, DeepPhysiNet is capable of performing various tasks, such as downscaling, bias correction, and forecasting, using multiple form of input coordinates.
• Figure 2: Details of our proposed framework, DeepPhysiNet. It consists of two main components, hyper-networks and physics networks. The hyper-networks are responsible for extracting high-level spatiotemporal features from a large volume of historical meteorological field data and passing these features to the physics networks. The physics networks serve as neural solvers for partial differential equations describing near-surface meteorological variables.
• Figure 3: Study area with boundary with $72^{\circ} E$ to $136^{\circ} E$ and $18^{\circ} N$ to $54^{\circ} N$. The red circles represent the observational station from Weather2K dataset.
• Figure 4: Station-level downscaling results for wind speed (SPD), temperature (T), and relative humidity (RH) at different forecast periods with 24-hour intervals.
• Figure 5: Continuous downscaling temperature forecasts for sub-regions at resolutions of 1 degree, 0.5 degrees, 0.1 degrees, and 0.01 degrees.