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Machine learning of consistent thermodynamic models using automatic differentiation.

David Rosenberger1, Kipton Barros1, Timothy C Germann1

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Summary
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This study introduces a novel data-driven approach using artificial neural networks to generate accurate equations of state (EOS). The method directly learns thermodynamic derivatives, ensuring consistency and preserving key physical relationships.

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Area of Science:

  • Computational physics and chemistry
  • Thermodynamics and statistical mechanics

Background:

  • Equations of state (EOS) are crucial for describing thermodynamic behavior.
  • Traditional methods involve fitting complex analytical expressions to experimental or simulation data.
  • Ensuring thermodynamic consistency, particularly Maxwell relations, is a significant challenge.

Purpose of the Study:

  • To develop a data-driven method for deriving consistent equations of state for arbitrary systems.
  • To leverage artificial intelligence for modeling free energy and its derivatives.

Main Methods:

  • Modeling the system's free energy using an artificial neural network (ANN).
  • Employing automatic differentiation to directly learn the derivatives of the ANN-based free energy.
  • Applying the method to the van der Waals equation of state and Lennard-Jones fluid data.

Main Results:

  • The proposed method accurately describes equations of state from thermophysical data.
  • It demonstrates superior accuracy and exact preservation of Maxwell relations compared to direct learning of thermodynamic properties.
  • The approach implicitly yields the system's free energy without requiring explicit integration.

Conclusions:

  • This data-driven, ANN-based method offers a robust and accurate way to determine consistent equations of state.
  • It provides a powerful alternative to traditional fitting methods, especially for complex systems.
  • The implicit derivation of free energy simplifies thermodynamic calculations.