A Hierarchical Synergistic Deep Learning Framework Integrating Composition, Structure, and Ionic Transport for Solid-State Electrolyte Discovery

Hongwei Du; Dingyang Lv; Baole Wei; Yongheng Li; Feng Yu; Ziheng Lu; Siqi Shi; Hong Wang

cond-mat.mtrl-sciAug 26, 2026

A Hierarchical Synergistic Deep Learning Framework Integrating Composition, Structure, and Ionic Transport for Solid-State Electrolyte Discovery

Authors: Hongwei Du, Dingyang Lv, Baole Wei, Yongheng Li, Feng Yu, Ziheng Lu, Siqi Shi, Hong Wang

Organizations: Zhongguancun Academy, Beijing, 100094, China. · Zhongguancun Institute of Artificial Intelligence, Beijing, 100094, China. · School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China. · Kairos Materials, Beijing, 100094, China. ·

Abstract

Inorganic solid-state electrolytes must combine high room-temperature ionic conductivity, a wide electrochemical window, excellent electronic insulation, and favorable mechanical compliance. Single models struggle to support reliable multi-objective screening across vast chemical spaces because of training-data distribution mismatch, cross-property dataset heterogeneity, and scarce kinetic transport data. To overcome these limitations, we develop a hierarchical synergistic deep-learning framework that sequentially coordinates efficiency, accuracy, and reliability through four complementary modules. The in-house-developed L-G-DCNN and a multi-fidelity implementation built on DenseGNN serve as compositional and structural experts for thermodynamic coarse screening and multi-property evaluation, respectively; MatterSim and system-specific DeePMD models provide transport pre-assessment and kinetic validation. Systematic benchmarks show that each module outperforms mainstream counterparts in its task, while retrospective validation establishes dual closed-loop verification of module-level accuracy and end-to-end workflow reliability. Applied to 30,364,908 Alex/ICSD-derived candidates, the framework identifies 97 high-performance candidates with room-temperature ionic conductivities of 0.109--59.0 mS/cm, including 94 halides, one borohydride, and two oxides. Consistency with independent experimental data confirms that 76 of the 94 halides fall within reported high-conductivity structural regions. Analysis reveals that Li $^{+}$ jump-network connectivity, rather than the number of geometric Li sites, is the core determinant of room-temperature ionic conductivity. Li-defect engineering effectively enhances oxide transport, whereas the inherent rigidity of the O $^{2-}$ framework suggests a potential upper limit on oxide electrolyte performance.

Figures & tables

Figure 1: Hierarchical synergistic screening framework for materials discovery. The workflow integrates specialized models across sequential screening stages to balance computational efficiency, predictive accuracy, and validation reliability. L-G-DCNN serves as the front-end compositional module for cost-effective coarse filtering of ultra-large candidate spaces. DenseGNN, the structural module, evaluates structure-sensitive static properties via multi-fidelity data fusion. MatterSim assesses Li + mobility through MD-derived diffusion behavior, and DeePMD provides high-precision kinetic validation for top candidates. This staged architecture narrows the candidate pool while progressively increasing physical fidelity from compositional screening to dynamic transport validation.

Figure 2: Quantitative benchmarks of the models used in the hierarchical screening workflow. (a) Composition-based L-G-DCNN benchmarks. The left panel reports the number of Matbench composition-regression tasks for which each model achieves the lowest mean absolute error (MAE). The middle panel shows formation-energy MAE as a function of the number of training formulas on a logarithmic x-axis. The right panel shows five-fold cross-validated MAEs for three composition-only extrapolation tests, with error bars denoting standard deviations. (b) Structure-based DenseGNN benchmarks. The left heatmap summarizes errors for convex-hull energy, band gap, bulk modulus, and shear modulus across multi-scale validation, tail-extrapolation, and experimental-generalization tests. The right heatmap shows normalized Matbench MAE ratios relative to DenseGNN, with DenseGNN set to 1.00. (c) Machine-learning-potential benchmarks for Li-ion diffusion. Bars show mean absolute logarithmic errors of Li + diffusion coefficients relative to DeePMD references for sulfide, oxide, and halide systems at 1100 K and 300 K.

Figure 3: Analysis of Common SSE Families in MP with Relaxed Constraints. (a) Statistics of elemental abundance, 300 K Li + conductivity distribution, space group/crystal system distribution, and violin plots of conductivity grouped by crystal system for 156 SSEs. The horizontal axes represent elements, conductivity ranges, and space groups/crystal systems, respectively, and the vertical axes correspond to counts, frequencies, or Li + conductivities. (b) Correlations between 300 K Li + conductivity and convex hull energy, band gap, reduction potential, and oxidation potential. The horizontal axes represent the corresponding properties, the vertical axis represents Li + conductivity, and colors distinguish sulfides, oxides, halides, and other materials. This figure is used to verify the consistency between the screening workflow and known chemical trends.

Formula	Space group	Energy above hull (eV atom -1 )	Band gap (eV)	Voltage window (V)	Bulk modulus (GPa)	Shear modulus (GPa)	Conductivity (mS cm -1 )
$\text{Li}{\vphantom{\text{X}}}_{\smash[t]{\text{4}}}\text{SiO}{\vphantom{\text{X}}}_{\smash[t]{\text{4}}}$	P1	0.0303	5.2439	3.098	77.437	46.417	0.931
$\text{LiK}{\vphantom{\text{X}}}_{\smash[t]{\text{2}}}\text{NbO}{\vphantom{\text{X}}}_{\smash[t]{\text{4}}}$	P1	0.0371	3.8068	2.726	33.055	19.423	0.891
$\text{Li}{\vphantom{\text{X}}}_{\smash[t]{\text{10}}}\text{Mg}{\vphantom{\text{X}}}_{\smash[t]{\text{7}}}\text{Cl}{\vphantom{\text{X}}}_{\smash[t]{\text{24}}}$	Cm	0.0108	4.5584	3.387	29.427	13.716	0.125
$\text{Li}{\vphantom{\text{X}}}_{\smash[t]{\text{3}}}\text{YBr}{\vphantom{\text{X}}}_{\smash[t]{\text{6}}}$	C2/c	0.0256	4.1363	3.083	16.264	12.767	4.847

Table 1: Four candidate materials retained by the present strategy that are consistent with the DFT reference under the same Materials Project (MP) benchmark protocol.

Figure 4: Multi-stage screening workflow for the Alex/ICSD-derived candidate space. The funnel reports the number of retained structures after each sequential filter, decreasing from 30,364,908 initial candidates to 97 DeePMD-validated room-temperature SSE candidates. The thresholds were arranged from low-cost permissive stability screening to increasingly stringent thermodynamic, electronic, electrochemical, mechanical, and kinetic criteria, so that high-fidelity transport validation was applied only to the most promising late-stage candidates.

Figure 5: Chemical Trends and Candidate Structure Property from Alex/ICSD Screening. (a) 0 K electrochemical window distribution grouped by anions for 2,100 candidates passing the band gap and electrochemical window thresholds. The horizontal axis represents anion elements, and the vertical axis represents window width, comparing the effects of different anions. (b) Changes in elemental counts as the voltage window threshold increases from 1.0 V to 1.5 V and 2.0 V. The horizontal axis represents elements, and the vertical axis represents occurrence counts. (c) Four-dimensional property map of the 124 candidate structures. The horizontal axis represents DeePMD 300 K Li + conductivity, the vertical axis represents electrochemical stability window, the dashed line indicates the 0.1 mS/cm threshold, and point color/size corresponds to convex hull energy and shear modulus, respectively. (d) Correlation between halide structural motifs and conductivity. The horizontal axis represents structural motif categories, and the vertical axis represents log 10 (conductivity).

Figure 6: Quantitative Comparison of the 97 Final Candidates with Halide Experimental Data. (a) Comparison in the cation polarization descriptor space. The horizontal axis represents $\phi_{N}=\frac{\phi_{\mathrm{Li}^{+}}+\phi_{M}}{\phi_{X}}$ , and the vertical axis represents 6 -coordination normalized ${\phi_{Li}}$ . In the Li 2024 dataset, hcp/ccp denote approximate hexagonal close-packed and cubic close-packed halogen anion sublattices, respectively, while T/O/M represent tetrahedral, octahedral, and mixed cation occupancy. Blue circles, green squares, and orange triangles correspond to literature points for hcp-T, hcp-O, and ccp-M phases, respectively. Gray points represent halide candidates from this work, red open circles denote the top 20 candidates by conductivity, blue diamonds indicate candidates overlapping with known halide families, and gold stars mark candidates with identical chemical formulas to those in the Li 2024 literature dataset. (b) Conductivity range comparison with Li-2024 data in nearest-neighbor literature regions. The horizontal axis represents nearest-neighbor literature structure regions, the vertical axis represents Li + conductivity, gray represents Li 2024 experimental data, and colored represents DeePMD-calculated values. (c) Conductivity distribution of candidates overlapping with known families. The horizontal axis represents DeePMD 300 K conductivity, the vertical axis represents candidate chemical formulas and space group, and the gray shaded area represents the experimental dataset range. (d) Statistical hierarchy of experimental consistency evidence. The horizontal axis represents the fraction of the corresponding candidate set, and the vertical axis represents evidence categories.

Figure 7: Comparison of DeePMD Transport Mechanisms for the Three Representative Materials. (a) Comparison of 300 K Li + conductivity, electrochemical window, Ehull, and VASP PBE band gap for Li 6 CaCl 8 , Li 2 B 12 H 12 , and Li 3 BO 3 . (b) 0–1000 ps Li + MSD curves. The horizontal axis represents MD time, the vertical axis represents Li MSD. (c) Jump-active Li site networks. Coordinates are fractional a and b. Gray represents non-jumping sites, and colored nodes and connections represent the actual jump networks from the 1 ns trajectory. (d) Partial radial distribution function (partial RDF)/CN(r) centered on Li. The horizontal axis represents distance r, the left vertical axis represents g(r), and the right vertical axis (dashed line) represents CN(r).

Figure 8: Trade-Offs Between Transport, Window, Band Gap, and Parent-Referenced Ehull for Li 3 BO 3 Derivative Candidates. (a) Global map of conductivity-window-band gap-parent-referenced Ehull for derivative structures. The horizontal axis represents 300 K Li + conductivity, the vertical axis represents Li electrochemical window, point shapes represent Li defect, B-site doping, anion/mixed regulation, and high-entropy strategies, color represents band gap, point size represents parent-referenced Ehull, black circles represent the highest-scoring structure in each category, and the star represents the Li 3 BO 3 parent structure. (b) Comparison of metrics for the best integrated modification structure in each category relative to the Li 3 BO 3 parent structure. The numbers in the cells sequentially represent $\log_{10}\left(\sigma/\sigma_{\mathrm{parent}}\right)$ , window retention rate, band-gap retention rate, and $\Delta E_{\mathrm{hull}}$ . Color indicates relative desirability, with green being more favorable and red indicating higher costs.

Materials Science

Materials science studies how composition, structure, processing, and defects determine material properties and how to design useful materials.

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AQVolt26: High-Temperature r $^2$ SCAN Halide Dataset for Universal ML Potentials and Solid-State Batteries

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The demand for safe, high-energy-density batteries has spotlighted halide solid-state electrolytes, which offer the potential for enhanced ionic mobility, electrochemical stability, and interfacial deformability. Accelerating their discovery requires extensive molecular dynamics, which has been increasingly enabled by universal machine learning interatomic potentials trained on foundational datasets. However, the dynamic softness of halides poses a stringent test of whether general-purpose models can reliably replace first-principles calculations under the highly distorted, elevated-temperature regimes necessary to probe ion transport. Here, we present AQVolt26, a dataset of 322,656 r

^2

SCAN single-point calculations for lithium halides, generated via high-temperature configurational sampling across

\sim

5K structures. We demonstrate that foundational datasets provide a strong baseline for stable halide chemistries and transfer local forces well, however absolute energy predictions degrade in distorted higher-temperature regimes. Co-training with AQVolt26 resolves this blind spot. Furthermore, incorporating Materials Project relaxation data improves near-equilibrium performance but degrades extreme-strain robustness without enhancing high-temperature force accuracy. These results demonstrate that domain-specific configurational sampling is essential for the reliable dynamic screening of halide electrolytes. Furthermore, our findings suggest that while foundational models provide a robust base, they are most effective for dynamically soft solid-state chemistries when augmented with targeted, high-temperature data. Finally, we show that near-equilibrium relaxation data serves as a task-specific complement rather than a universally beneficial addition.

Abstract

Materials Science

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