Physics-incorporated convolutional recurrent neural networks for source identification and forecasting of dynamical...

Area of Science:

• Computational Physics
• Machine Learning
• Dynamical Systems

Background:

• Physical processes are often governed by partial differential equations (PDEs) but are influenced by unobservable, time-varying external sources.
• Developing purely analytical models for such systems is challenging, necessitating data-driven approaches.

Purpose of the Study:

• To present a hybrid framework integrating physics-based numerical models with deep learning for source identification and forecasting.
• To address spatio-temporal dynamical systems affected by unobservable, time-varying external sources.

Main Methods:

• Developed PhICNet, a hybrid model formulated as a convolutional recurrent neural network (RNN).
• The model is end-to-end trainable for predicting spatio-temporal evolution.
• Learns source behavior as an internal state within the RNN architecture.

Main Results:

• PhICNet demonstrates effective forecasting of spatio-temporal dynamics over extended periods.
• The model successfully identifies unknown external sources driving the system.
• Experimental results validate the hybrid approach's efficacy.

Conclusions:

• The proposed PhICNet framework offers a robust solution for modeling and understanding complex physical systems with hidden external influences.
• This hybrid physics-informed deep learning approach advances the field of data-driven modeling for dynamical systems.