Comparison of derivative-free and gradient-based minimization for multi-objective compositional design of shape memory alloys

TL;DR

This paper compares derivative-free and gradient-based optimization methods for designing shape memory alloys, demonstrating that gradient-based methods paired with neural network surrogates yield more reliable and optimal solutions.

Contribution

It introduces a combined approach using machine learning surrogates and different optimization algorithms for SMA design, highlighting the advantages of gradient-based methods with neural networks.

Findings

Gradient-based optimizer with neural network surrogates outperforms derivative-free methods.

Neural network models provide reliable gradient information for optimization.

The approach enhances the exploration of alloy compositions with limited experimental data.

Abstract

Designing shape memory alloys (SMAs) that meet performance targets while remaining affordable and sustainable is a complex challenge. In this work, we focus on optimizing SMA compositions to achieve a desired martensitic start temperature (Ms) while minimizing cost. To do this, we use machine learning models as surrogate predictors and apply numerical optimization methods to search for suitable alloy combinations. We trained two types of machine learning models, a tree-based ensemble and a neural network, using a dataset of experimentally characterized alloys and physics-informed features. The tree-based model was used with a derivative-free optimizer (COBYLA), while the neural network, which provides gradient information, was paired with a gradient-based optimizer (TRUST-CONSTR). Our results show that while both models predict Ms with similar accuracy, the optimizer paired with the neural network finds better solutions more consistently. COBYLA often converged to suboptimal results, especially when the starting guess was far from the target. The TRUST-CONSTR method showed more stable behavior and was better at reaching alloy compositions that met both objectives. This study demonstrates a practical approach to exploring new SMA compositions by combining physics-informed data, machine learning models, and optimization algorithms. Although the scale of our dataset is smaller than simulation-based efforts, the use of experimental data improves the reliability of the predictions. The approach can be extended to other materials where design trade-offs must be made with limited data.