Bridging Theory and Experiment in Materials Discovery: Machine-Learning-Assisted Prediction of Synthesizable Structures

TL;DR

The paper tackles the gap between energy-based crystal structure predictions and experimentally synthesizable materials by introducing a synthesizability-driven CSP framework that combines symmetry-guided structure derivation, Wyckoff-encode-based existence probability filtering, and structure-based screening with ML and ab initio methods. It demonstrates effectiveness by reproducing 13 experimentally synthesized XSe structures, filtering 92,310 synthesizable candidates from 554,054 GNoME predictions, and identifying promising Hf-X-O candidates including near-degenerate HfV2O7 derivatives with viable synthesis routes. This data-driven paradigm bridges theory and experiment and enables targeted discovery of novel materials, while acknowledging limitations in handling disorder and synthesis kinetics and outlining future work to integrate synthesis conditions. Overall, the approach provides a scalable framework to prioritize experimentally realizable candidates and accelerate inorganic materials discovery.

Abstract

Even though thermodynamic energy-based crystal structure prediction (CSP) has revolutionized materials discovery, the energy-driven CSP approaches often struggle to identify experimentally realizable metastable materials synthesized through kinetically controlled pathways, creating a critical gap between theoretical predictions and experimental synthesis. Here, we propose a synthesizability-driven CSP framework that integrates symmetry-guided structure derivation with a Wyckoff encode-based machine-learning model, allowing for the efficient localization of subspaces likely to yield highly synthesizable structures. Within the identified promising subspaces, a structure-based synthesizability evaluation model, fine-tuned using recently synthesized structures to enhance predictive accuracy, is employed in conjunction with ab initio calculations to systematically identify synthesizable candidates. The framework successfully reproduces 13 experimentally known XSe (X = Sc, Ti, Mn, Fe, Ni, Cu, Zn) structures, demonstrating its effectiveness in predicting synthesizable structures. Notably, 92,310 structures are filtered from the 554,054 candidates predicted by GNoME, exhibiting great potential for promising synthesizability. Additionally, eight thermodynamically favorable Hf-X-O (X = Ti, V, and Mn) structures have been identified, among which three HfV$_2$O$_7$ candidates exhibit high synthesizability, presenting viable candidates for experimental realization and potentially associated with experimentally observed temperature-induced phase transitions. This work establishes a data-driven paradigm for machine-learning-assisted inorganic materials synthesis, highlighting its potential to bridge the gap between computational predictions and experimental realization while unlocking new opportunities for the targeted discovery of novel functional materials.

Figures (6)

• Figure 1: The workflow of the synthesizability-driven CSP method. The left-middle panel illustrates the structure derivation process, the middle panel outlines the training of the Wyckoff encode-based existence evaluation model, and the right panel showcases the candidate screening process using universal machine learning potential (UMLP) dunn2020benchmarkingfocassio2024performance, density functional theory (DFT) martin2020electronic, and the structure-based synthesizability evaluation model, fine-tuned on the Positive-Unlabeled Crystal Graph Convolutional Neural Networks (PU-CGCNN) jang2020structure.
• Figure 2: (a) The number of all and inequivalent group-subgroup transformation chains with a subgroup index less than or equal to 10 for the space groups. The height of the dark bar represents the number of all the group-subgroup transformation chains, while the blue bar demonstrates the number of inequivalent ones. (b-k) The schematic representation of the substitutional structure derivation process. (e) depicts a parent structure with $4mm$ symmetry, characterized by eight symmetry operations: $1$, $2$, $4^{+}$, $4^{-}$ and four mirror planes oriented along [01], [-10], [-1-1], and [-11], denoted as $\sigma_{v2}$, $\sigma_{v1}$, $\sigma_{d1}$, and $\sigma_{d2}$, respectively. The circles in (e) represent a Wyckoff orbital with a multiplicity of 8. The uncolored diagrams (b, f, i) illustrate three orbital splitting patterns corresponding to three subgroups with index 2. The original orbital splits into two 4-fold orbitals, depicted by circles with solid and dashed boundaries. Both (b) and (i) exhibit $mm2$ symmetry with different symmetric elements, while (f) retains $4$ symmetry. (c) and (d) illustrate two substitution styles derived from (b), which are equivalent under $\sigma_{v1}$. (g) and (h) depict two substitution styles derived from (f), which are also equivalent under $\sigma_{v1}$. (j) and (k) show two substitution styles derived from (i), which are equivalent under $\sigma_{d1}$.
• Figure 3: (a) The schematic diagram of the Wyckoff encode-based existence probability evaluation model. Each node in the input Wyckoff graph is characterized by the space group number, occupied Wyckoff orbital details, element type, and lattice type. Each row represents an independent Wyckoff encode-based existence probability evaluation model. The initial Wyckoff graph is transformed into a new graph (TG$_i$) through a message-passing network, followed by pooling to generate a latent representation of (R$_i$). A standard classification network is used to assess the existence probability of $P_i$ from R$_i$. The final existence probability score ($P$) for each input graph or Wyckoff encode is evaluated by averaging the probabilities ($P_i$) predicted by all independent models. (b-d) Performance evaluation of the Wyckoff encode-based existence probability model on encodes derived from synthesized and unsynthesized structures in the test set, as well as recently synthesized structures from the Inorganic Crystal Structure Database (ICSD) zagorac2019recentbelsky2002new that are not included in the training dataset.
• Figure 4: (a) Statistics on the elemental distribution of synthesized and synthesizable structures from GNoME materials exploration. $N_{\mathrm{exp}}$ denotes the number of experimentally synthesized structures containing a given element. $N_{\mathrm{GNoME}}$ represents the number of synthesizable structures—defined as those with $P > 0.5$ and CLscore $> 0.5$—from GNoME exploration that contain the element. Structures containing gray-colored highly radioactive elements are excluded from the statistics. (b) Number of structures as a function of the number of constituent elements, considering synthesized structures and synthesizable structures from the GNoME materials exploration.
• Figure 5: The energy and CLscore distribution of candidate structures for the XSe (X = Sc-Zn) compounds, where CLscore $>$ 0.5 indicates high synthesizability. Note that experimentally synthesized structures are marked by purple stars, while predicted structures are represented by cyan squares.