Neural network representations of multiphase Equations of State.

Area of Science:

• Thermodynamics
• Computational Physics
• Machine Learning

Background:

• Equations of State (EoS) are crucial for modeling thermodynamic variables across diverse scientific fields.
• Existing analytic models often struggle to simultaneously satisfy thermodynamic laws, incorporate phase transitions, and maintain multiscale accuracy.
• Developing comprehensive EoS models that balance accuracy and efficiency remains a significant challenge.

Purpose of the Study:

• To propose two deep-learning approaches for constructing Equations of State.
• To ensure these models adhere to the Laws of Thermodynamics and accurately represent phase transitions.
• To offer flexible EoS modeling solutions, usable independently or to enhance existing models.

Main Methods:

• Developed a deep-learning method based on learning the thermodynamic potential (generating function).
• Introduced structure-preserving, symplectic neural networks for EoS modeling.
• Both methods are designed to handle phase transition regions effectively.

Main Results:

• The proposed deep-learning methods provably satisfy fundamental thermodynamic laws and model phase transitions.
• Demonstrated the capability of these methods to learn full EoS models from scratch.
• Showcased their utility in refining existing EoS models to better match experimental data.

Conclusions:

• Deep learning offers a powerful framework for developing accurate and versatile Equations of State.
• These novel methods provide a pathway to overcome limitations of traditional analytic EoS models.
• The proposed approaches enhance the reliability and applicability of thermodynamic modeling in science and engineering.