Theory-Guided Deep Learning Algorithms: An Experimental Evaluation

Abstract

The use of theory-based knowledge in machine learning models has 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.

A General Model for Side Information in Neural Networks

“…In addition, there are different ways of incorporating the knowledge into an ML algorithm, say an NN, for example, by modifying the input, the loss function, and/or the network architecture [9]. Another trend is that of incorporating physical knowledge into deep learning [10], and more specifically encoding differential equations in NNs, leading to physics-informed NNs [11].…”