[Paper Review] DeepPhysiNet: Bridging Deep Learning and Atmospheric Physics for Accurate and Continuous Weather Modeling

Wenyuan Li, Zili Liu+5 more|arXiv (Cornell University)|Jan 4, 2024

Meteorological Phenomena and Simulations7 citations

TL;DR

DeepPhysiNet integrates atmospheric physics with deep learning via physics networks and hyper-networks to deliver continuous-resolution weather modeling, enabling downscaling, bias correction, and forecasting.

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.

Motivation & Objective

• Motivate combining numerical weather prediction (NWP) physics with data-driven deep learning (DLP) to overcome limitations of each paradigm.
• Propose a unified framework that uses physics-informed neural networks to embed PDE-based atmospheric laws into learnable models.
• Enable continuous spatiotemporal forecasting by allowing predictions at arbitrary coordinates and resolutions.
• Demonstrate the framework on downscaling, bias correction, and weather forecasting tasks.
• Provide interpretability analysis to show the role of physical laws and input variables in predictions.

Proposed method

• Introduce physics networks (MLPs) for individual meteorological variables that map coordinates (x, y, t) to variable values.
• Use hyper-networks (Transformer-based) to learn spatiotemporal features from historical data and generate the weights for physics networks.
• Incorporate PDEs as soft constraints in the loss to enforce physical consistency for inner points and use regression losses at grid points.
• Allow continuous resolution by evaluating physics networks at arbitrary input coordinates during inference.
• Train with both ground-truth data and PDE-based losses to enable downscaling, bias correction, and forecasting within a single framework.
• Output six surface variables: u, v, T, p, ρ, q, with inputs comprising field sequences and coordinates.

Experimental results

Research questions

• RQ1 Can physical laws be effectively embedded into a data-driven weather model to achieve continuous-resolution forecasting?
• RQ2 Does a hybrid architecture combining hyper-networks and physics networks outperform traditional NWP and DLP for downscaling and bias correction?
• RQ3 To what extent do PDE-based constraints improve interpretability and physical consistency of forecasts?
• RQ4 Is the model capable of accurate station-level downscaling and grid-point bias correction while preserving physical realism?
• RQ5 How well does the framework extrapolate forecasts beyond the training horizon using PDE supervision alone?

Key findings

• DeepPhysiNet achieves improved station-level downscaling accuracy over NCEP IFS and ECMWF IFS for wind speed, temperature, and relative humidity.
• For station downscaling, DeepPhysiNet yields RMSE and COR of 1.686 and 0.443 for SPD, 3.788 and 0.949 for T, and 16.686 and 0.761 for RH, respectively, outperforming baselines on several metrics.
• In grid-point bias correction, the method shows competitive performance, with strong results for temperature and relative humidity relative to ECMWF and improved bias correction over NCEP for most cases.
• For short-term weather forecasting (0-24h), DeepPhysiNet nearly matches or slightly surpasses NCEP IFS, and demonstrates promising extrapolation capabilities from 24h to 48h under PDE supervision alone.
• The framework provides interpretability insights via input variable contribution analyses, showing substantial influence from pressure and wind variables, and demonstrates PDEs as effective soft constraints to guide physically plausible outputs.