FORGE aims to develop Explainable AI (XAI) guided design and exploration system for Compositionally Complex Alloys (CCAs) and Ceramics (CCCs).

FORGE aims to develop Explainable AI (XAI) guided design and exploration system for Compositionally Complex Alloys (CCAs) and Ceramics (CCCs).

High-entropy alloys (HEAs) or Configurationally Complex Alloys (CCAs) are comprised of multiple elements (5+) with high entropy due to large configurational space 1,2. Typically, CCAs are composed of 5 or more elements with equal or largely varied atomic concentrations. In recent years, CCAs are considered to have the potential to become alloys with better physical properties such as hardness, ductility, corrosion resistance, H2-embrittlement compared to conventional alloys 3,4,4–7. CCAs can have virtually infinite compositional combinations, which opens the door to exploring new physical, chemical, and mechanical properties, just by changing the composition of the constituent elements. The vast composition space also makes it challenging to explore new properties and functionalities of CCAs materials as exploration by sample preparation is expensive and time-consuming.

In recent years, various computational approaches such as Calculation of Phase Diagrams (CALPHAD), molecular dynamics simulation (MD), and density functional theory (DFT) calculations have been utilized to estimate phase and to predict structural and electronic properties. However, these approaches have limitations due to high computational costs and accuracies8.

In the last decade, Machine learning (ML) methods (specifically, Artificial Neural Networks or Deep Learning, DL) have proven to be well suited to handle large data set with large number input parameter space in order to capture underlying features of a problem at hand. DL models have been successfully applied in areas such as image recognition, natural language processing, self-driving car, anomaly detection, predictive modelling, among others. In recent years, ML has been applied in the field of CCAs as a data-driven feature learning approach. Several recent works have shown promising results for estimating physical properties of CCAs. For example, Wen et al.9 proposed a strategy to search for new CCAs with higher hardness values in the AlCoCrCuFeNi alloys by training ML models with measured physical properties of known CCAs. Other works suggested several Deep Learning models to predict phases of CCAs, where the existing empirical phase estimation rules can be modelled by ML/DL models10,11.

On the other hand, High Entropy Ceramics (HECs) or Compositionally complex ceramics (CCCs) are a relatively new class of materials. The CCCs are single-phase ceramics consisting of at least four different equimolar or non-equimolar anions or cations 12,13. In case of CCCs or HECs, only a few phases are investigated yet. Among the investigated materials a distinction has to be made between carbides, borides, and oxides, with oxides being of interest in this project. Consequently, the number of experimental results for compositions with a larger number of cations (four to six) which could be utilized in data-based ML is very limited, close to nil.

Among the technical properties of interest, the coefficient of thermal expansion (CTE) is regarded as the most relevant property as the CTE of the coating, and the substrate must not differ by more than 2 ppm. In general, the CTE of a material depends on the bonding strength and thus on the respective neighbouring atoms/ions (radius, valence, etc.) and their relative position described by the crystal structure. It can vary with direction for anisotropic materials and is temperature-dependent. To date, it is not possible to accurately calculate the CTE of a given material ab initio. However, use of Machine Learning models can help get good estimates. The application of ML to predict material combination with a target CTE would be very beneficial in the development of a suitable coating combination.

There are several key obstacles with ML-guided CCA/CCC property predictions. In most cases, the key issue is the lack of good data. This issue can sometimes be slightly mitigated using regularization; however, having enough training data is essential to obtain a reliable model14. The FORGE project partners will produce a large volume of experimentally measured dataset on CCA properties (Corrosion resistance, H2-embrittlement, Wear /Hardness) and CCC properties (Coefficient of thermal Expansion (CTE), Corrosion Rate) from a selected element pool. This will allow development of ML/DL models that learns general features of the CCA/CCC compositions and their properties.

Another key issue is that DL models are inherently black box models. It is often not clear why a model produces a specific result. When DL model is estimating physical properties, it is important to have an explanation of the estimations of DL models. Explainable AI (XAI) can bring a lot of value in this regard. Explainable AI is a group of methods and approaches to explain results of complex machine learning models from the perspective of input features and output values.

There are various ways, namely statistical analysis, feature visualization, analysis of DL model weights15, counterfactual explanations16,17, to Explain DL models,. It is important that the explanation methods are model agnostic, where the methods work by analysing feature input and output pairs rather than internal details of the DL models.

In short, DL models learn general features of CCA and CCC data and Explainable AI methods explain the underlying relation between CCA/CCC input features and DL estimated properties such as corrosion resistance, H2-embrittlement, Coefficient of thermal expansion.

The one of the major goals of FORGE is to develop Explainable AI based decision support system to help material scientists and engineers discover novel CCAs and CCCs with targeted properties with minimum number of trial and errors.


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