AMShortcut: An Inference- and Training-Efficient Inverse Design Model for Amorphous Materials

Yan Lin; Jonas A. Finkler; Tao Du; Jilin Hu; Morten M. Smedskjaer

cs.LGMar 31, 2026

AMShortcut: An Inference- and Training-Efficient Inverse Design Model for Amorphous Materials

Authors: Yan Lin, Jonas A. Finkler, Tao Du, Jilin Hu, Morten M. Smedskjaer

Organizations: Aalborg University · The Hong Kong Polytechnic University · East China Normal University

Abstract

Amorphous materials are solids that lack long-range atomic order but possess complex short- and medium-range order. Unlike crystalline materials that can be described by unit cells containing few up to hundreds of atoms, amorphous materials require larger simulation cells with at least hundreds or often thousands of atoms. Inverse design of amorphous materials with probabilistic generative models aims to generate the atomic positions and elements of amorphous materials given a set of desired properties. It has emerged as a promising approach for facilitating the application of amorphous materials in domains such as energy storage and thermal management. In this paper, we introduce AMShortcut, an inference- and training-efficient probabilistic generative model for amorphous materials. AMShortcut enables accurate inference of diverse short- and medium-range structures in amorphous materials with only a few sampling steps, mitigating the need for an excessive number of sampling steps that hinders inference efficiency. AMShortcut can be trained once with all relevant properties and perform inference conditioned on arbitrary combinations of desired properties, mitigating the need for training one model for each combination. Experiments on three amorphous materials datasets with diverse structures and properties demonstrate that AMShortcut achieves its design goals.

Figures & tables

Figure 1: AMShortcut generates structurally accurate amorphous material samples with one or few sampling steps, enabling high-throughput inverse design of amorphous materials.

$n_{s}$	CDVAE	MatterGen	Graphite	Material ODE	Material SDE	AMShortcut
1	0.69442 / 0.00265 (1.4m)	0.67755 / 0.00286 (1.6m)	0.69555 / 0.00279 (1.2m)	0.69118 / 0.00280 (1.8m)	0.68477 / 0.00282 (1.2m)	0.02513 / 0.00067 (2.2m)
2	0.57868 / 0.00265 (2.3m)	0.60909 / 0.00272 (2.5m)	0.61882 / 0.00264 (1.9m)	0.66442 / 0.00276 (2.2m)	0.60972 / 0.00263 (2.0m)	0.03922 / 0.00044 (2.9m)
3	0.53362 / 0.00251 (3.3m)	0.50540 / 0.00231 (3.5m)	0.51208 / 0.00242 (3.0m)	0.60209 / 0.00259 (2.8m)	0.50904 / 0.00235 (2.9m)	0.04835 / 0.00038 (3.8m)
4	0.43450 / 0.00203 (4.4m)	0.43985 / 0.00221 (5.1m)	0.43101 / 0.00203 (3.8m)	0.49544 / 0.00220 (3.7m)	0.43276 / 0.00210 (3.8m)	0.04653 / 0.00035 (4.7m)
5	0.39258 / 0.00173 (4.4m)	0.38154 / 0.00175 (5.4m)	0.38436 / 0.00198 (4.1m)	0.39007 / 0.00173 (4.6m)	0.37975 / 0.00188 (4.0m)	0.04041 / 0.00034 (5.6m)
10	0.21683 / 0.00137 (8.8m)	0.22949 / 0.00094 (10.0m)	0.22334 / 0.00104 (8.2m)	0.14917 / 0.00073 (9.1m)	0.22054 / 0.00100 (7.9m)	0.02244 / 0.00032 (10.1m)

Table 1: RMSD and generation time comparison across different models and step counts.

Panel of Figure 2 — Figure 2: Distribution comparison of properties in the training samples versus the samples generated by AMShortcut with 100 steps. The target properties extend beyond the training distribution, demonstrating the model’s extrapolation capability.

Shear modulus [GPa]
$n_{s}$	CDVAE (Target)	MatterGen (Target)	Graphite (Target)	Material ODE (All)	Material ODE (Target)	Material SDE (All)	Material SDE (Target)	AMShortcut (All)
1	21.35 / 23.48 / 72.3%	18.92 / 21.45 / 62.8%	17.24 / 19.86 / 52.9 %	25.69 / 27.02 / 88.1%	20.02 / 21.10 / 68.7%	16.55 / 19.73 / 48.5 %	17.75 / 20.32 / 54.8%	15.51 / 19.30 / 53.8%
5	20.12 / 22.05 / 68.2%	18.35 / 20.18 / 62.1%	15.48 / 17.65 / 51.2%	19.93 / 20.75 / 70.6%	14.28 / 14.76 / 52.0%	13.31 / 16.30 / 39.8 %	24.34 / 26.32 / 80.5%	3.10 / 4.10 / 16.0 %
10	22.43 / 24.17 / 74.8%	17.89 / 19.42 / 61.3%	16.75 / 18.23 / 56.8%	12.67 / 13.46 / 45.5%	9.51 / 10.09 / 33.9 %	18.04 / 19.22 / 60.9%	19.17 / 20.31 / 65.8%	2.67 / 3.41 / 13.0 %
25	5.28 / 6.15 / 18.9%	4.52 / 5.38 / 16.4%	3.94 / 4.72 / 15.2%	7.29 / 8.37 / 27.2%	6.14 / 6.96 / 20.1%	4.73 / 5.62 / 17.2%	3.61 / 4.35 / 14.7 %	2.86 / 3.47 / 12.7 %
50	4.73 / 5.62 / 17.1%	4.08 / 4.95 / 15.6%	3.68 / 4.48 / 14.9%	6.38 / 7.54 / 24.1%	5.25 / 6.05 / 17.3%	3.95 / 4.76 / 14.8%	3.37 / 4.12 / 14.7 %	2.91 / 3.51 / 12.7 %

Table 2: Inverse design performance metrics comparison of different models with different numbers of sampling steps on a-

\text{SiO}{\vphantom{\text{X}}}_{\smash[t]{\text{2}}}

dataset.

Young’s modulus [GPa]
$n_{s}$	CDVAE (Target)	MatterGen (Target)	Graphite (Target)	Material ODE (All)	Material ODE (Target)	Material SDE (All)	Material SDE (Target)	AMShortcut (All)
1	52.85 / 63.42 / 68.2%	48.92 / 59.25 / 63.8%	45.18 / 54.92 / 58.5 %	48.52 / 58.15 / 62.2%	51.85 / 62.12 / 66.5%	46.85 / 59.12 / 60.1%	47.18 / 58.32 / 61.5%	38.06 / 45.67 / 48.5 %
5	48.25 / 57.85 / 62.5%	45.62 / 54.75 / 58.8%	43.18 / 51.85 / 55.8%	52.08 / 62.38 / 66.9%	44.12 / 52.85 / 56.7%	41.28 / 49.45 / 53.0 %	42.85 / 51.35 / 55.0%	10.01 / 12.32 / 20.2 %
10	38.52 / 46.25 / 49.5%	36.85 / 44.28 / 47.5%	34.75 / 41.72 / 44.8%	32.82 / 39.38 / 42.2%	31.75 / 38.12 / 40.8 %	34.15 / 40.98 / 43.9%	35.28 / 42.35 / 45.3%	8.20 / 9.83 / 16.2 %
25	14.65 / 17.82 / 29.7%	13.02 / 15.85 / 26.4%	11.38 / 13.88 / 23.1%	14.35 / 17.52 / 29.1%	12.15 / 14.82 / 24.6%	11.25 / 13.72 / 22.8%	10.85 / 13.22 / 22.0 %	8.45 / 10.32 / 17.2 %
50	13.65 / 16.68 / 27.7%	11.95 / 14.58 / 24.2%	10.62 / 12.98 / 21.5%	13.62 / 16.62 / 27.7%	11.52 / 14.05 / 23.4%	10.45 / 12.75 / 21.2%	10.12 / 12.35 / 20.5 %	8.53 / 10.43 / 17.3 %

Table 3: Inverse design performance metrics comparison of different models with different numbers of sampling steps on MEG dataset.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 3 — Figure 3: Structural accuracy evaluation for (a) RDF and (b) ADF of different models on the a-Si dataset with different numbers of sampling steps. ODE, SDE, and Shortcut corresponds to Material ODE, Material SDE, and AMShortcut, respectively.

Panel of Figure 4 — Figure 4: RMSD of (a) RDF and (b) ADF versus generation time per 10,000 a- Si samples across different models and step counts. Labels indicate the number of sampling steps for each run.

Panel of Figure 5 — Figure 5: Property MAPE versus generation time per 2,000 a- $\text{SiO}{\vphantom{\text{X}}}_{\smash[t]{\text{2}}}$ samples across different models and step counts for (a) shear modulus and (b) ring size distribution. Labels indicate the number of sampling steps for each run.

Panel of Figure 6 — Figure 6: Property MAPE versus generation time per 2,000 MEG samples across different models and step counts for (a) Young’s modulus, (b) Lithium molar concentration, and (c) shear modulus. Labels indicate the number of sampling steps for each run.

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AMGenC: Generating Charge Balanced Amorphous Materials

Yan Lin, Jilin Hu, N. M. Anoop Krishnan, Morten M. Smedskjaer

Department of Computer Science, Aalborg University, Denmark · School of Data Science and Engineering, East China Normal University, China · Department of Civil Engineering, Indian Institute of Technology Delhi, India+2

Materials Science Generative Modeling Conditional Generative Modeling Inverse Design

Open paper AskPDF arXiv

Amorphous (disordered) materials are solids that have shown great potential in various domains, including energy storage, thermal management, and advanced materials. Unlike crystalline materials that can be described by unit cells containing a few to hundreds of atoms, amorphous materials require larger simulation cells with at least hundreds to thousands of atoms. To advance the design of amorphous materials with desired properties and facilitate the exploration of their vast design space, generative inverse design has emerged as a promising approach. It aims to directly output materials with properties closely aligned with the desired ones using probabilistic generative models conditioned on desired properties, which can be more resource efficient than the traditional trial-and-error approach. However, due to the inherent stochasticity of probabilistic generative models, when element assignments are unconstrained, a large portion of generated materials may be charge unbalanced, and no existing methods can effectively mitigate this limitation. In this work, we propose AMGenC, a new generative inverse design method for amorphous materials that can guarantee the generation of charge balanced samples, with minimal additional computational overhead and without sacrificing inverse design accuracy. AMGenC achieves this through an element noise that gives the generation process a starting point centered around charge balance, and the combination of a per-step soft projection and a final discrete projection for steering the elements toward exact charge balance throughout the generation. We perform extensive experiments on two amorphous materials datasets. Experimental results provide evidence that AMGenC achieves its design goal.

Abstract

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