Journal Club #1: Machine Learning Discovers Novel Magnetocaloric Effects in Holmium-diboride
Published:
Welcome to Journal Club! This is a series of blog posts that will be dedicated to reviewing recent articles in the field of materials informatics. I intend to do one Journal Club per month (time permitting).
In essence, each post will give a brief overview of the research and the findings. I will also take time to consider the implications of the research and other questions that may arise. This will (hopefully) provide a concise overview of the paper that readers find useful.
So without further ado, onto Journal Club #1.
The Research
This month’s paper is:
Castro, P.B.d., Terashima, K., Yamamoto, T.D. et al. "Machine-learning-guided discovery of the gigantic magnetocaloric effect in HoB2 near the hydrogen liquefaction temperature. NPG Asia Mater 12, 35 (2020).
You can find the original article here.
Brief overview
This paper uses a variety of machine learning and data-mining techniques to discover previously unseen magnetocaloric behaviour in the material $HoB_2$. Beginning with a manually curated database of 1,644 materials that exhibit the magnetocaloric effect (see below). Using only composition-based features, the authors train a gradient boosting regression model of the absolute magnetic entropy change. The model shows good generalisability, with an MAE of 1.8 $J/kgK$, over a range of values from 0 to over 40 $J/kgK$.
The predictive model is then screened against an existing database of known ferromagnets to identify if any known magnets should exhibit the magnetocaloric effect. This process identifies $HoB_2$ as a potential candidate, which the authors validate via experiment. This shows that $HoB_2$ is in-fact a gigantic magnetocaloric effect material, with a Curie temperature of 15 K, and magnetic entropy change of 40.1 $J/kgK$. These properties make the material a highly suitable candidate for low-temperature magnetic refrigeration, around the hydrogen liquefaction temperature.
My Thoughts
Overall, this work highlights the efficacy of using data-driven approaches in the materials science domain, and in-particular for magnetic materials. Magnetic materials are vital for a number of applications that involve energy conversion, such as in refrigerators and air conditioners. This is a really important research topic, since it is currently estimated that only around 30% of produced energy actually gets employed in energy services. That is, despite all the attention on primary energy sources, the vast majority of energy is wasted in conversion, regardless of the original source.
For refrigeration, traditional devices utilise ozone-depleting gases to perform the refrigeration cycle. Solid-state refrigerants present an appealing alternative as they are much more efficient. These materials work based on the magnetocaloric effect, which manifests as a remarkable change in their temperature that occurs when they are magnetised.
When searching for a new magnetocaloric material, we are interested in a number of properties. The foremost is the temperature of operation, which is usually characterised by the ferromagnetic Curie temperature. If the material exhibits a ferromagnetic transition around room-temperature, then the material may be ideal for room-temperature refrigeration purposes. Other figures-of-merit include the peak magnetic entropy change that occurs at this temperature. This gives an estimate of the cooling power of the material. Other factors are important, (hysteresis, temperature range, field-dependence etc.) but for now let’s focus on these two.
So the basic idea of this work is this: If we can accurately predict the peak magnetic entropy change of known materials, then applying this model to others should help identify potential candidates that haven’t been previously tested.
This is a nice idea, since the vast majority of previous magnetic materials haven’t been tested for their refrigeration potential. Furthermore, by focussing on screening against known compounds, the authors don’t have to worry about predicting wether or not a material is ferromagnetic in the first place, which is a very difficult problem.
So the first stage is to build a predictive model of the magnetic entropy change. They do this by manually compiling the magnetic entropy change (and associated magnetic field change) of known ferromagnetic materials from pre-tabulated datasets. This yields 1,644 records (more than enough to build a decent regression model).
The features of the regression model are purely composition-based feature vectors. That is, given a composition (such as $A_xB_y$) they create composition-weighted vectors from basic elemental properties of the constituent elements. For instance, they take the ionic radius, electro-negativity, boiling point and others, then take 7 featurisers: weighted average, weighted sum, weighted variance, geometric mean, harmonic mean, max pooling and min pooling.
This is a useful representation since it creates 406 composite features. The biggest limitation is that it takes no account for the materials structure. This would of course be a very complex dataset to create, since it is not trivial to find the structure for all known magnetic materials, and that is before considering problems of polymorphism and disorder.
After data-cleaning, their final model has 408 features, including the magnetic field change of each measurement.
The regression model is trained using gradient boosting regression with a traditional 80:20 train:test split, achieving an out-of-sample MAE of 1.8 $J/kgK$. This is a pretty decent model overall, though from looking at the true-pred plot the model has a slight tendency to under-predict for materials with higher magnetic entropy change values.
The final stage screens this model against known ferromagnets that were sourced from a pre-created database. Funnily enough, the database was one created my myself in this publication, in which I auto-generated a database of ferromagnets from the scientific literature using semi-supervised relationship extraction. I was very happy to see my database being used. It was created for exactly this purpose.
The screening identifies $HoB_2$ as a potential magnetocaloric material, with a predicted magnetic entropy change of 16 $J/kgK$. I noted that this is a lot lower than the actual experimental value (40 $J/kgK$), which seems to line up with my above observation that the model tends to under-estimate.
The experimental validation confirms their prediction that $HoB_2$ is magnetocaloric, which is a massive win.
Overall, I think its a really neat study.
Questions
Feature engineering - Little mention is given to the feature engineering process used in this work. 408 features for a model with 1300 training points is quite a lot (although not into the over-fitting region by any means). I am fairly sure that a lot of the features may be correlated, so perhaps some feature selection routines could have been used.
Model selection - Why use gradient boosting? The SI says it outperformed LASSO, but there are many other model choices: Ridge, Random Forest etc. Often with these models it is unclear why some work better than others. It would be interesting to see the feature importances for the models and see if that can be tied to underlying physical theories.
What else worked? - The authors chose $HoB_2$ for synthesis since it had the highest predicted magnetic entropy change, but it would be interesting to know the 2nd, 3rd, 4th etc. in order to see if these also worked out. Not least because these data points would be valuable for future models!
Avenues for Future Work
This kind of approach can be applied in almost any materials science domain. As such, there is a huge scope for further work.
In the magnetism domain, the natural progression would be to try and predict other important figures-of-merit, such as the adiabatic temperature change or relative cooling power.
Down the line, it may even be possible to predict entirely new materials for magnetic refrigeration purposes.
Conclusions
Im summary, I really like this paper. It emphasises that data-driven approaches to materials discovery don’t need to utilise fancy deep learning models in all cases. By simply aggregating what we already know, its possible to fill in the gaps in our knowledge.