PriMera Scientific Engineering (ISSN: 2834-2550)

Research Article

Volume 4 Issue 4

Thermodynamic Equilibrium State Prediction by Deep Learning Method

Yu Okano*, Takeshi Kaneshita*, Katsuki Okuno, Shimpei Takemoto and Yoshishige Okuno

March 20, 2024

DOI : 10.56831/PSEN-04-120


The method of calculation of phase diagrams (CALPHAD) is a calculation method that searches for a state of providing minimal Gibbs energy as an equilibrium state. To perform a thermodynamic equilibrium calculation for a single material composition and to predict a phase diagram, we can complete the CALPHAD method calculation within a realistic time. However, screening many material compositions associated with predicting the corresponding phase diagrams takes much time. For alloy materials, for example, it would take 161 hours to calculate phase diagrams of all alloy compositions to screen 10,000 sets of explanatory variables, i.e., compositions and manufacturing conditions, since it takes 58 seconds to calculate each set. The present study aims to provide a calculation device, method, and program for quickly predicting the thermodynamic equilibrium state. We developed a deep learning model based on the Transformer architecture to achieve this objective, primarily used for various natural language processing tasks, such as machine translation, text summarization, question answering, and sentiment analysis. The encoder part of our developed model extracts the necessary features for phase diagram prediction from the inputted alloying elements. In contrast, the decoder part predicts a phase diagram for each temperature based on the results from the encoder. We calculated 800,000 species using the CALPHAD method and employed these data to train our developed model. Our trained model can calculate thermodynamic equilibrium states more than 100 times faster than the CALPHAD method and correctly reproduce the phase diagrams of ground truths. Based on the present result, we could invent a calculation device, a calculation method, and a calculation program for predicting the thermodynamic equilibrium state in a short time.

Keywords: Thermodynamic equilibrium state; Transformer; Neural network; Deep learning; CALPHAD


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