A comparison of single and double generator formalisms for thermodynamics-informed neural networks

Urdeitx, Pau (Universidad de Zaragoza) ; Alfaro, Icíar (Universidad de Zaragoza) ; González, David (Universidad de Zaragoza) ; Chinesta, Francisco ; Cueto, Elías (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1007/s00466-024-02564-3

Año: 2024

Publicado en: COMPUTATIONAL MECHANICS (2024), [17 pp.]
ISSN: 0178-7675

Factor impacto JCR: 3.8 (2024)

Categ. JCR: MATHEMATICS, INTERDISCIPLINARY APPLICATIONS rank: 16 / 136 = 0.118 (2024) - Q1 - T1
Categ. JCR: MECHANICS rank: 36 / 171 = 0.211 (2024) - Q1 - T1

Factor impacto SCIMAGO: 1.256 - Applied Mathematics (Q1) - Computational Mathematics (Q1) - Ocean Engineering (Q1) - Computational Theory and Mathematics (Q1) - Mechanical Engineering (Q1) - Computational Mechanics (Q1)

Financiación: info:eu-repo/grantAgreement/ES/MICINN-AEI/PID2020-113463RB-C31/AEI/10.13039/501100011033
Financiación: info:eu-repo/grantAgreement/ES/MTFP/TSI-100930-2023-1

Tipo y forma: Article (Published version)

Área (Departamento): Área Mec.Med.Cont. y Teor.Est. (Dpto. Ingeniería Mecánica)