Theory-guided deep learning algorithms: an experimental evaluation

by Simone Monaco, Daniele Apiletti and Giovanni Malnati

Abstract

The use of theory-based knowledge in machine learning models has had a major impact on many engineering and physics problems. The growth of deep learning algorithms is closely related to an increasing demand for data that is not acceptable or available in many use cases. In this context, the incorporation of physical knowledge or a-priori constraints has proven beneficial in many tasks. On the other hand, this collection of approaches is context-specific, and it is difficult to generalize them to new problems. In this paper, we experimentally compare some of the most commonly used theory injection strategies to perform a systematic analysis of their advantages. Selected state-of-the-art algorithms were reproduced for different use cases to evaluate their effectiveness with smaller training data and to discuss how the underlined strategies can fit into new application contexts.

Reproducing the results

A python script allow to run each of the experiments as follow.

python main.py <exp> [OPTION]

Where exp stays for:

• Lake Temperature, the code is an extension of [1] and [2].
  • With physical loss function: pgnn
  • Without physical loss function: pgnn0
  • With PGA-LSTM: pga
• Convective movements in climate modeling, extended from [3]. The full dataset has been requested to original authors.
  • Basic MLP cbrain1
  • Hard constraints cbrain2
  • Soft constraints cbrain3
• Climate prediction, extended from [4]
  • With physical loss function: dpgn
  • Without physical loss function: dpgn0 Moreover, experiments can have extra arguments as options (run python main.py <exp> --help to see all of them).