A comparison of Single- and Double-generator formalisms for Thermodynamics-Informed Neural Networks
This work addresses the challenge of applying universally valid thermodynamic principles to neural networks for physical modeling, but it is incremental as it compares existing formalisms rather than introducing new methods.
The paper compares single- and double-generator formalisms for incorporating thermodynamic principles into neural networks to improve accuracy and robustness in predicting physical phenomena, finding that these biases increase certainty, reduce error, and allow smaller datasets.
The development of inductive biases has been shown to be a very effective way to increase the accuracy and robustness of neural networks, particularly when they are used to predict physical phenomena. These biases significantly increase the certainty of predictions, decrease the error made and allow considerably smaller datasets to be used. There are a multitude of methods in the literature to develop these biases. One of the most effective ways, when dealing with physical phenomena, is to introduce physical principles of recognised validity into the network architecture. The problem becomes more complex without knowledge of the physical principles governing the phenomena under study. A very interesting possibility then is to turn to the principles of thermodynamics, which are universally valid, regardless of the level of abstraction of the description sought for the phenomenon under study. To ensure compliance with the principles of thermodynamics, there are formulations that have a long tradition in many branches of science. In the field of rheology, for example, two main types of formalisms are used to ensure compliance with these principles: one-generator and two-generator formalisms. In this paper we study the advantages and disadvantages of each, using classical problems with known solutions and synthetic data.