Data-efficient and Interpretable Inverse Materials Design using a Disentangled Variational Autoencoder

Inverse materials design has proven successful in accelerating novel material discovery. Many inverse materials design methods use unsupervised learning where a latent space is learned to offer a compact description of materials representations. A latent space learned this way is likely to be entangled, in terms of the target property and other properties of the materials. This makes the inverse design process ambiguous. Here, we present a semi-supervised learning approach based on a disentangled variational autoencoder to learn a probabilistic relationship between features, latent variables and target properties. This approach is data efficient because it combines all labelled and unlabelled data in a coherent manner, and it uses expert-informed prior distributions to improve model robustness even with limited labelled data. It is in essence interpretable, as the learnable target property is disentangled out of the other properties of the materials, and an extra layer of interpretability can be provided by a post-hoc analysis of the classification head of the model. We demonstrate this new approach on an experimental high-entropy alloy dataset with chemical compositions as input and single-phase formation as the single target property. High-entropy alloys were chosen as example materials because of the vast chemical space of their possible combinations of compositions and atomic configurations. While single property is used in this work, the disentangled model can be extended to customize for inverse design of materials with multiple target properties.

💡 Research Summary

The paper introduces a semi‑supervised, disentangled variational autoencoder (DVAE) for inverse materials design, demonstrated on a high‑entropy alloy (HEA) dataset where the target property is binary single‑phase formation. Traditional generative models for materials discovery often learn an entangled latent space, mixing the target property with other latent factors, which hampers direct inverse design. To overcome this, the authors construct a probabilistic model pθ(x, ϕ, z) = pθ(x|ϕ,z) p(ϕ) p(z), where x is the alloy composition vector, ϕ∈{0,1} denotes the phase label, and z∈ℝ^l captures all remaining material factors. A Bernoulli prior is placed on ϕ and a standard normal prior on z; expert knowledge can be injected by biasing these priors.

The recognition (inference) network is factorized under a mean‑field assumption as qψ(ϕ,z|x) = qψϕ(ϕ|f(x)) qψz(z|x,ϕ). The deterministic transformation f(x) computes eight hand‑engineered physicochemical descriptors (atomic size difference, mixing entropy, mixing enthalpy, Pauli electronegativity difference, molar volume, bulk modulus, melting temperature, valence electron concentration). These descriptors are known to be highly predictive of phase stability, and a small neural network ψϕ uses them to predict ϕ. The remaining latent variable z is inferred by a second network ψz conditioned on both the raw composition and the predicted phase, allowing the model to capture any additional information needed for accurate reconstruction.

Training optimizes a combined objective: the standard VAE evidence lower bound (ELBO) on all data (both labelled and unlabelled) plus a supervised cross‑entropy loss on the labelled subset, weighted by a hyperparameter γ. This balances reconstruction quality with phase‑prediction accuracy, enabling the model to learn from abundant unlabelled compositions while still being guided by the scarce experimental labels. Implementation uses Pyro (a probabilistic programming layer on PyTorch), two hidden layers of size 100 for both encoder and decoder, Adam optimizer (initial LR = 1e‑4), batch size = 32, and up to 20 000 epochs with early stopping based on validation performance. Five random seeds are employed to assess robustness; the dataset is split into 864 labelled training, 296 unlabelled training, 75 validation, and 138 test samples.

Performance evaluation shows strong classification results: mean test accuracy = 0.829 ± 0.050 and AUC = 0.890 ± 0.025, with validation AUC exceeding 0.95. Reconstruction experiments on the test set reveal an average mean absolute error of 2.3 % for the composition vector and a maximum of 6 % for binary alloys, indicating that the latent space retains sufficient information for faithful decoding. Moreover, the model can generate new alloy compositions by sampling z from the prior and fixing ϕ to the desired phase, effectively enabling inverse design of single‑phase HEAs.

Interpretability is addressed through post‑hoc SHAP analysis of the classification head. The SHAP values confirm that mixing enthalpy, mixing entropy, atomic size difference, and valence electron concentration are the most influential descriptors for predicting single‑phase formation, aligning with established thermodynamic theories. This dual‑layer interpretability—explicit disentanglement of the target property and model‑agnostic feature importance—provides materials scientists with actionable insights into why a particular composition is predicted to be single‑phase.

In summary, the authors contribute: (1) a data‑efficient semi‑supervised framework that leverages both labelled and unlabelled experimental data; (2) a disentangled latent representation that isolates the target property, facilitating direct inverse design without costly post‑hoc optimization; (3) a principled way to embed domain expertise via engineered features and prior distributions; and (4) a transparent interpretability pipeline combining latent disentanglement with SHAP‑based feature attribution. While the current work focuses on a single binary property, the architecture is readily extensible to multi‑objective scenarios by expanding ϕ to a vector of targets and adapting the prior structure accordingly. Future research directions include scaling to larger compositional spaces, integrating uncertainty quantification for risk‑aware design, and exploring more sophisticated priors that capture known phase diagrams.