Joint learning equation of state surfaces with uncertainty-aware physically regularized neural networks

Area of Science:

• Materials Science
• Computational Physics
• Machine Learning

Background:

• Understanding material behavior under varying pressure-temperature-volume (P-T-V) conditions is crucial in many scientific fields.
• Traditional equation of state (EOS) models face limitations due to thermodynamic assumptions and expert knowledge requirements.
• Existing machine learning methods, like Gaussian processes, struggle with scalability, extrapolation, and kernel selection sensitivity.

Purpose of the Study:

• To introduce EOSNN, a novel neural network-based, physics-informed deep learning approach for learning multiple EOS surfaces.
• To develop a probabilistic model for quantifying aleatoric and epistemic uncertainties in EOS predictions.
• To demonstrate the superiority of EOSNN over traditional and existing machine learning methods in accuracy and flexibility.

Main Methods:

• EOSNN jointly learns multiple EOS surfaces from diverse data, including static/dynamic compression and ab initio calculations.
• A probabilistic framework is integrated to capture both aleatoric and epistemic uncertainties.
• Physics-informed regularizations (e.g., on heat capacity, Grüneisen parameter, bulk modulus) are employed to enhance physical consistency.

Main Results:

• EOSNN significantly outperforms traditional and Gaussian process methods in accuracy, flexibility, and extensibility.
• On a challenging partially supervised task, EOSNN achieved a R² score of 0.83 and RMSE of 0.52 eV/atom for energy off-Hugoniot predictions.
• Physics-informed regularization further improved accuracy, surpassing traditional fully supervised methods in specific cases.

Conclusions:

• EOSNN offers a robust and accurate method for equation of state modeling, overcoming limitations of existing approaches.
• The integration of physics-informed deep learning and probabilistic uncertainty quantification provides a powerful tool for materials science research.
• EOSNN demonstrates significant potential for various applications requiring precise material behavior prediction under diverse conditions.