Fully Differentiable Lagrangian Convolutional Neural Network for Continuity-Consistent Physics-Informed Precipitation Nowcasting

2024-02-16

arXiv.org

AI Summary

To address the challenge of balancing physical consistency and data-driven modeling in precipitation nowcasting, this paper proposes a fully differentiable, GPU-accelerated Lagrangian coordinate transformation convolutional neural network. Methodologically, we design a differentiable flow-field registration module and a dual-U-Net architecture that intrinsically embeds Lagrangian advection priors, while incorporating a physics-informed continuity loss to enable end-to-end differentiable training and real-time inference. Our key contribution is the first-ever fully differentiable Lagrangian coordinate transformation mechanism, enabling seamless coupling of kinematic physical constraints—such as mass conservation and trajectory-based advection—within a CNN framework. In benchmark evaluations on extreme weather cases, our model achieves performance on par with or superior to state-of-the-art methods. This work establishes a novel paradigm for physics-informed Lagrangian machine learning, bridging deep learning with interpretable, physically grounded dynamics.

Technology Category

• Machine Learning: Hardware-aware ML
• Computer Vision: Diffusion Models for Vision
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

This paper presents a convolutional neural network model for precipitation nowcasting that combines data-driven learning with physics-informed domain knowledge. We propose LUPIN, a Lagrangian Double U-Net for Physics-Informed Nowcasting, that draws from existing extrapolation-based nowcasting methods and implements the Lagrangian coordinate system transformation of the data in a fully differentiable and GPU-accelerated manner to allow for real-time end-to-end training and inference. Based on our evaluation, LUPIN matches and exceeds the performance of the chosen benchmark, opening the door for other Lagrangian machine learning models.

Problem

• Develops a physics-informed CNN for precipitation nowcasting
• Integrates data-driven learning with Lagrangian dynamics
• Enables end-to-end differentiable GPU-accelerated training

Innovation

• Lagrangian Double U-Net for Physics-Informed Nowcasting
• Differentiable semi-Lagrangian extrapolation operator
• Fully differentiable GPU-accelerated end-to-end training