A comparison of Single- and Double-generator formalisms for
  Thermodynamics-Informed Neural Networks
Pau Urdeitx Icíar Alfaro David González Francisco Chinesta Elías Cueto
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.