Knowledge-based Deep Learning for Modeling Chaotic Systems

TL;DR

This paper introduces knowledge-based deep learning (KDL), a novel approach that combines real and simulated data with physical laws to model and forecast chaotic systems and extreme events effectively.

Contribution

The paper proposes KDL, a new deep learning framework that incorporates physical laws and simulated data to improve modeling of chaotic systems with limited real data.

Findings

KDL accurately models chaotic systems like El Nino and dengue.

KDL outperforms traditional models in small data regimes.

KDL ensures physically consistent and generalizable forecasts.

Abstract

Deep Learning has received increased attention due to its unbeatable success in many fields, such as computer vision, natural language processing, recommendation systems, and most recently in simulating multiphysics problems and predicting nonlinear dynamical systems. However, modeling and forecasting the dynamics of chaotic systems remains an open research problem since training deep learning models requires big data, which is not always available in many cases. Such deep learners can be trained from additional information obtained from simulated results and by enforcing the physical laws of the chaotic systems. This paper considers extreme events and their dynamics and proposes elegant models based on deep neural networks, called knowledge-based deep learning (KDL). Our proposed KDL can learn the complex patterns governing chaotic systems by jointly training on real and simulated data directly from the dynamics and their differential equations. This knowledge is transferred to model and forecast real-world chaotic events exhibiting extreme behavior. We validate the efficiency of our model by assessing it on three real-world benchmark datasets: El Nino sea surface temperature, San Juan Dengue viral infection, and Bj{\o}rn{\o}ya daily precipitation, all governed by extreme events' dynamics. Using prior knowledge of extreme events and physics-based loss functions to lead the neural network learning, we ensure physically consistent, generalizable, and accurate forecasting, even in a small data regime.