CROSS-QUALITY FEW-SHOT TRANSFER FOR ALLOY YIELD STRENGTH PREDICTION: A NEW MATERIAL SCIENCE BENCHMARK AND AN INTEGRATED OPTI-MIZATION FRAMEWORK

Abstract

Discovering high-entropy alloys (HEAs) with high yield strength is an important yet challenging task in material science. However, the yield strength can only be accurately measured by very expensive and time-consuming real-world experiments, hence cannot be acquired at scale. Learning-based methods could facilitate the discovery process, but the lack of a comprehensive dataset on HEA yield strength has created barriers. We present X-Yield, a large-scale material science benchmark with 240 experimentally measured ("high-quality") and over 100K simulated (imperfect or "low-quality") HEA yield strength annotations. Due to the scarcity of experimental annotations and the quality gap in imperfectly simulated data, existing transfer learning methods cannot generalize well on our dataset. We address this cross-quality few-shot transfer problem by leveraging model sparsification "twice" -as a noise-robust feature learning regularizer at the pre-training stage, and as a data-efficient learning regularizer at the few-shot transfer stage. While the workflow already performs decently with ad-hoc sparsity patterns tuned independently for either stage, we take a step further by proposing a bi-level optimization framework termed Bi-RPT, that jointly learns optimal masks and automatically allocates sparsity levels for both stages. The optimization problem is solved efficiently using gradient unrolling, which is seamlessly integrated with the training process. The effectiveness of Bi-RPT is validated through extensive experiments on our new challenging X-Yield dataset, alongside other synthesized testbeds. Specifically, we achieve an 8.9 ∼ 19.8% reduction in terms of the test mean squared error and 0.98 ∼ 1.53% in terms of test accuracy, merely using 5-10% of the experimental data. Codes and sample data are in the supplement.

1. INTRODUCTION

Machine learning (ML) methods have recently demonstrated great promise in the important field of material science, and in this paper, we focus on ML-assisted high-entropy alloy (HEA) (Yeh et al., 2004) discovery and property prediction. HEAs own promising properties that traditional alloys do not hold, such as extraordinary mechanical performance at high temperatures, making them wellsuited options for various material applications. One particular property, i.e., the yield strength of HEAs, characterizes the maximum stress a material can endure before starting to deform, which is a critical parameter for customized HEA design. However, in order to accurately measure the yield strength of specific HEAs, expensive scientific experiments need to be conducted for each alloy, often involving hard-to-create experimental conditions, especially at high temperatures (mainly caused by difficulties with oxidation control) as well as extremely long experimental duration. At high temperatures, these measurements are typically taken with the Gleeble system (Gle). From sample preparation to yield strength measurement can take between two to four weeks even for a domain expert team, including melting of the alloy, machining the sample, and preparing and mechanically testing with the Gleeble. Therefore, it is challenging to acquire yield strength measurements from those "high-quality" experiments at scale. Similar to the trends in computer vision fields (Tremblay et al., 2018) , recent efforts attempt to mitigate the scarcity of real-world measurements using ML-based predictors: to directly predict their yield strengths from the alloy inputs (Bhandari et al., 2021a) ; and such ML-based predictors could be trained using simulated data. Indeed, material sciences applications are often blessed by developed simulation models, e.g., Maresca & Curtin (2020) . However, such a blessing is often compromised by the domain gap between the simulated data and the "ground-truth" experimental data, often due to many inevitable simplifications in simulation modeling. For example, the yield strength of a material can vary greatly based on processing and testing conditions as well as grain size and texture (Toda-Carballo et al., 2014; Lin et al., 2014 ); yet simulation models commonly rely on properties intrinsic to the alloy and do not incorporate variations in experimental conditions. The lack of public datasets in this field also renders it difficult to benchmark ML models' progress. In this paper, we start by curating a large-scale benchmark, called X-Yield, that for the first time combines experimental data with simulation data to address the problem of predicting yield strength in HEAs. While using experimental data is always preferred since they are "high-quality" ground truths, it is impractical to generate high quantities of data, especially for capturing yield strength at elevated temperatures. Thus, simulation data can be acquired by massive quantities to fill the gap, despite their relatively "low quality" due to inherent model misspecification or simplification. The low-quality simulation data was selected to represent ternary-septenary systems from an eleven-element palette consisting of mostly refractory elements (Al-Cr-Fe-Hf-Mo-Nb-Ta-Ti-V-W-Zr). While there are existing experimental databases (Borg et al., 2020) and models to predict high-temperature yield strength in HEAs (Maresca & Curtin, 2020) , to our best knowledge, this is the first multi-fidelity dataset in the public domain that combines real experimental measurements and large quantities (over 100K) of simulation data for mechanical property prediction in HEAs. This specialized data set should be able to predict high-temperature yield strength across a broad range of HEAs. The predictions of this model could be used to pinpoint which alloys are the strongest at elevated temperatures, allowing experiments to focus on pre-sorted candidates for future study eliminating the need to spend several weeks testing a candidate without promise.

Sparsity for noise robustness (learning from massive "low-quality" simulation data)

Sparsity for data-efficiency (transferring to fewshot "high-quality" experimental data)

Pretraining

Fine-tuning Figure 1 : Proposed two-stage workflow. The HEA yield strength prediction model is first pretrained on massive "low-quality" simulation data, and is then fine-tuned/transferred on few-shot "high-quality" experimental data to optimize its prediction in this target domain. Note that the tool of sparsity will be leveraged in both pre-training and fine-tuning stages, for the purposes of gaining noise robustness/transferablity and enhancing data efficiency, respectively. The new X-Yield benchmark is set to facilitate ML for HEA yield strength prediction, but learning from such a multi-fidelity dataset is highly non-trivial. To this end, we next conceptualize a cross-quality few-shot transfer workflow: first pre-training the prediction model on the data-rich yet "low-quality" source domain (simulated data), and then fine-tuning the model towards the datascarce yet "high-quality" target domain (experimental data). However, this vanilla workflow is challenged by two issues: a significant quality gap between source and target domains, and an extreme data scarcity of target data. Inspired by the recent success of sparsity regularizers, we propose to

