Analytical Gradient-Based Optimization of CALPHAD Model Parameters

TL;DR

This paper introduces an efficient analytic gradient-based optimization framework for CALPHAD models, significantly improving parameter calibration speed and accuracy over traditional gradient-free methods, enabling high-fidelity thermodynamic assessments.

Contribution

It presents a novel semi-analytic gradient evaluation method using the Jansson derivative technique, enabling efficient deterministic optimization of complex CALPHAD models.

Findings

Conjugate gradient optimization outperforms MCMC in efficiency by 10-1000 times.

The method successfully calibrates models for four binary alloy systems.

Gradient-based approach achieves comparable or better results than traditional methods.

Abstract

The calibration of CALPHAD (CALculation of PHAse Diagrams) models involves the solution of a very challenging high-dimensional multiobjective optimization problem. Traditional approaches to parameter fitting predominantly rely on gradient-free methods, which while robust, are computationally inefficient and often scale poorly with model complexity. In this work, we introduce and demonstrate a generalizable framework for analytic gradient-based optimization of the parameters of the CALPHAD model enabled by the recently formalized Jansson derivative technique. This method allows for efficient evaluation of gradients of thermodynamic properties at equilibrium with respect to model parameters, even in the presence of arbitrarily complex internal degrees of freedom. Leveraging these semi-analytic gradients, we employ the conjugate gradient (CG) method to optimize thermodynamic model parameters for four binary alloy systems: Cu-Mg, Fe-Ni, Cr-Ni, and Cr-Fe. Across all systems, CG achieves comparable or superior optimality relative to Bayesian ensemble Markov Chain Monte Carlo (MCMC) with improvements in computational efficiency ranging from one to three orders of magnitude. Our results establish a new paradigm for CALPHAD assessments in which high fidelity data-rich model calibration becomes tractable using deterministic gradient-informed algorithms.