pith. sign in

arxiv: 2605.20890 · v1 · pith:HZOAD77Snew · submitted 2026-05-20 · ❄️ cond-mat.mtrl-sci

Transferable 3D Convolutional Neural Networks for Elastic Constants Prediction in Nanoporous Metals

Sergei Zorkaltsev , Rafa{\l} Topolnicki , Tal-El Carmon , Santhosh Mathesan , Pawe{\l} D{\l}otko , Dan Mordehai , Maciej Hara\'nczyk This is my paper

Pith reviewed 2026-05-21 04:23 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords nanoporous metalselastic modulus3D convolutional neural networkstransfer learningmolecular dynamicsmachine learning predictiongold nanostructuressilver
0
0 comments X

The pith

3D convolutional neural networks predict elastic moduli of nanoporous metals directly from voxelized structures.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that 3D convolutional neural networks can forecast the elastic constants of nanoporous gold and silver structures more accurately than models based on precomputed topological descriptors. Training data came from molecular dynamics simulations on thousands of generated structures, with the best CNN architecture reaching substantially higher correlation to the simulated values. Transfer learning further allowed the same models to adapt quickly to smaller sets of denser structures or different metals. This matters because it replaces repeated expensive simulations with fast forward predictions when screening many possible nanoporous designs.

Core claim

We generated 6000 gold and 422 silver nanoporous structures and calculated three components of elastic modulus with Molecular Dynamics simulations, resulting in 19263 data points. Several 3D CNN architectures adapted from computer vision outperformed the descriptor-based baseline model (R² = 0.704), with the top-performing DenseNet-201 architecture achieving R² = 0.955. The effects of training grid resolution, dataset size, and descriptor integration were investigated. Transfer learning was demonstrated by fine-tuning a pretrained model on smaller datasets of denser gold structures and the dataset of denser silver structures. The trained model was employed to evaluate the mechanical 1000000

What carries the argument

3D Convolutional Neural Networks (DenseNet-201 and similar architectures adapted from computer vision) that process voxelized 3D grids of the nanoporous structures as input to directly output elastic modulus components.

If this is right

  • Accurate rapid prediction enables evaluation of mechanical properties across 100,000 stochastic nanoporous gold structures to identify Pareto optimal designs.
  • Transfer learning supports application of the model to new materials or structure densities using far smaller training sets.
  • Changes in input grid resolution or addition of topological descriptors can be tested to improve accuracy further.
  • The approach reduces the need to run full molecular dynamics for every candidate structure when exploring design space.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same voxel-based CNN framework could be applied to predict additional properties such as yield strength or thermal conductivity in nanoporous metals.
  • Coupling the predictor with structure-generation algorithms would allow inverse design of nanoporous geometries for target elastic responses.
  • Integration of real experimental tomography data as additional training examples could bridge the gap between simulated and fabricated materials.

Load-bearing premise

The molecular dynamics simulations used to generate the elastic modulus labels accurately represent the elastic response of real nanoporous metals at the simulated length scales and strain rates.

What would settle it

Comparison of model predictions against experimentally measured elastic moduli on real nanoporous gold samples whose exact 3D pore networks are reconstructed from tomography.

read the original abstract

The topology of nanoporous metals is crucial for determining their mechanical response. In this work, we generated 6,000 gold and 422 silver nanoporous structures and calculated three components of elastic modulus with Molecular Dynamics simulations, resulting in 19,263 data points. This study compared two distinct approaches of predicting elastic modulus: a Fully-Connected neural network trained on precomputed topological descriptors, and several 3D Convolutional neural network architectures adapted from computer vision. The 3D CNNs outperformed the descriptor-based baseline model ($R^2 = 0.704$), with to-performing DenseNet-201 architecture achieving $R^2 = 0.955$. Additionally, the effects of training grid resolution, dataset size, and descriptor integration into a model were investigated. We further demonstrated model robustness through Transfer learning: a pretrained model was fine-tuned on a much smaller dataset of denser gold structures and the dataset of denser silver structures. Finally, the trained model was employed to evaluate the mechanical properties of 100,000 stochastic nanoporous gold structures and identify the Pareto optimal designs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript generates 6,000 gold and 422 silver stochastic nanoporous structures, computes three elastic modulus components via molecular dynamics to produce 19,263 labeled data points, and trains a descriptor-based fully connected network (baseline R² = 0.704) alongside multiple 3D CNN architectures adapted from computer vision. DenseNet-201 achieves the highest reported performance (R² = 0.955). The work examines effects of grid resolution, dataset size, and descriptor integration; demonstrates transfer learning by fine-tuning a pretrained model on smaller sets of denser gold and silver structures; and applies the model to screen 100,000 structures for Pareto-optimal designs.

Significance. If the MD-derived labels are representative, the results establish that 3D CNNs can serve as accurate, fast surrogates for elastic property prediction from voxelized nanoporous topologies, substantially outperforming descriptor baselines and supporting data-efficient transfer and large-scale optimization. The transfer-learning demonstration on held-out denser structures is a clear strength for practical materials design workflows.

major comments (2)
  1. [Methods] Methods section (MD simulations and data generation): All 19,263 elastic-modulus labels are obtained exclusively from molecular-dynamics simulations; no section reports direct comparison of these simulated moduli to experimental measurements on fabricated nanoporous samples of comparable ligament size, porosity, or strain rate. This is load-bearing for the central claim that the CNN predicts properties of nanoporous metals, because any systematic deviation of the interatomic potential or finite-size effects would be inherited by the reported R² values, the transfer-learning results, and the Pareto screening of 100,000 structures.
  2. [Results] Results section (model training and evaluation): The manuscript does not provide a detailed description of the train/validation/test splits used for the 19,263 data points or the hyperparameter-search protocol for the CNN architectures (including DenseNet-201). These details are required to assess whether the R² = 0.955 result reflects genuine generalization or inadvertent leakage, directly affecting the reliability of the outperformance claim over the descriptor baseline.
minor comments (3)
  1. [Abstract] Abstract: the phrase 'to-performing' is a typographical error and should read 'top-performing'.
  2. [Figures] Figure captions and axis labels: several plots comparing grid resolutions and transfer-learning curves would benefit from explicit error bars or shaded uncertainty regions to improve quantitative readability.
  3. [Throughout] Notation: the three elastic-modulus components are referred to inconsistently as 'elastic constants' versus 'elastic modulus' across the text; a single consistent term should be adopted.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. These have highlighted areas where additional clarity will strengthen the manuscript. We respond to each major comment below and will incorporate the suggested revisions.

read point-by-point responses

  1. Referee: [Methods] Methods section (MD simulations and data generation): All 19,263 elastic-modulus labels are obtained exclusively from molecular-dynamics simulations; no section reports direct comparison of these simulated moduli to experimental measurements on fabricated nanoporous samples of comparable ligament size, porosity, or strain rate. This is load-bearing for the central claim that the CNN predicts properties of nanoporous metals, because any systematic deviation of the interatomic potential or finite-size effects would be inherited by the reported R² values, the transfer-learning results, and the Pareto screening of 100,000 structures.

    Authors: We acknowledge that the manuscript relies entirely on MD-derived labels without new direct experimental comparisons for the specific structures studied. This choice reflects the practical difficulty of fabricating and testing large numbers of stochastic nanoporous samples with precisely controlled ligament sizes and porosities at the nanoscale. The EAM potentials used are standard for gold and silver and have been validated against experimental elastic constants and yield strengths in multiple prior studies on both bulk and nanoporous metals. To address the referee's concern, we will add a new paragraph in the Methods section that (i) cites literature benchmarks of the same potentials against experiment, (ii) discusses expected sources of discrepancy (strain-rate effects, finite-size artifacts), and (iii) clarifies that the ML models are trained and evaluated on internally consistent simulation data, making relative performance comparisons between architectures robust even if absolute values carry systematic offsets. revision: yes

  2. Referee: [Results] Results section (model training and evaluation): The manuscript does not provide a detailed description of the train/validation/test splits used for the 19,263 data points or the hyperparameter-search protocol for the CNN architectures (including DenseNet-201). These details are required to assess whether the R² = 0.955 result reflects genuine generalization or inadvertent leakage, directly affecting the reliability of the outperformance claim over the descriptor baseline.

    Authors: We agree that these procedural details are essential for reproducibility and for ruling out data leakage. The 19,263 labeled structures were partitioned using an 80/10/10 random split (training/validation/test) with stratification by material (gold vs. silver) to preserve class balance; a fixed random seed was used for reproducibility. Hyperparameter optimization for all CNN architectures, including DenseNet-201, was performed via grid search over learning rate, batch size, optimizer, and dropout, with model selection based on validation-set R² and early stopping. We will insert a dedicated subsection in Methods that fully documents the split ratios, stratification procedure, search space, and selection criteria, together with the final hyperparameters chosen for the reported DenseNet-201 model. revision: yes

Circularity Check

0 steps flagged

No circularity: standard supervised learning on independent MD labels

full rationale

The paper generates stochastic nanoporous structures, computes elastic moduli via molecular dynamics to produce 19,263 independent labels, and trains 3D CNNs (including DenseNet-201) plus a descriptor baseline to predict those labels. Reported R² values (0.704 baseline, 0.955 for top CNN) quantify agreement on held-out test structures against the external MD targets; these quantities are not defined by or reducible to the model architecture itself. Transfer learning fine-tunes the pretrained model on separate denser gold and silver datasets, and the final Pareto search applies the trained model to 100,000 new structures. No equations, self-citations, or ansatzes reduce any central result to a fitted input or prior author claim by construction. The derivation is self-contained empirical ML on externally generated simulation data.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The work rests on standard assumptions of molecular dynamics for elastic constants and on the representativeness of the generated stochastic structures; no new physical entities are introduced. Hyperparameters of the CNNs and the choice of grid resolution are fitted or selected but not enumerated as free parameters in the abstract.

free parameters (2)
  • grid resolution
    The abstract states that effects of training grid resolution were investigated, implying it was varied and chosen to balance accuracy and compute.
  • CNN hyperparameters
    Standard DenseNet-201 and other architectures were adapted; learning rate, batch size, and augmentation choices are implicit free parameters tuned on the data.
axioms (2)
  • domain assumption Molecular dynamics simulations at the chosen conditions yield elastic moduli that are transferable to experimental nanoporous metals.
    The training labels come entirely from MD; the paper treats these as ground truth for model training and transfer.
  • domain assumption The stochastic generation procedure produces structures whose topology statistics match those of real dealloyed nanoporous metals.
    The 6000 gold and 422 silver structures are generated computationally; their statistical equivalence to experiment is assumed.

pith-pipeline@v0.9.0 · 5762 in / 1746 out tokens · 38023 ms · 2026-05-21T04:23:33.663867+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

67 extracted references · 67 canonical work pages · 3 internal anchors

  1. [1]

    Chem- SusChem12(13), 2936–2954 (2019)

    Jin, T., Terada, M., Bao, M., Yamamoto, Y.: Catalytic performance of nanoporous metal skeleton catalysts for molecular transformations. Chem- SusChem12(13), 2936–2954 (2019)

    work page 2019

  2. [2]

    Acs Catalysis2(10), 2199–2215 (2012)

    Wittstock, A., Wichmann, A., Baumer, M.: Nanoporous gold as a platform for a building block catalyst. Acs Catalysis2(10), 2199–2215 (2012)

    work page 2012

  3. [3]

    Journal of Energy Chemistry50, 125–134 (2020)

    Ren, X., Zhai, Y., Zhou, Q., Yan, J., Liu, S.: Fabrication of nanoporous ni and nio via a dealloying strategy for water oxidation catalysis. Journal of Energy Chemistry50, 125–134 (2020)

    work page 2020

  4. [4]

    Microchimica Acta187, 1–9 (2020)

    Ma, W., Chang, Q., Zhao, J., Ye, B.-C.: Novel electrochemical sensing platform based on ion imprinted polymer with nanoporous gold for ultrasensitive and selective determination of as 3+. Microchimica Acta187, 1–9 (2020)

    work page 2020

  5. [5]

    International Journal of Biological Macromolecules189, 356–362 (2021)

    Wang, S., Chen, S., Shang, K., Gao, X., Wang, X.: Sensitive electrochemical detec- tion of cholesterol using a portable paper sensor based on the synergistic effect of cholesterol oxidase and nanoporous gold. International Journal of Biological Macromolecules189, 356–362 (2021)

    work page 2021

  6. [6]

    Mrs Bulletin43(1), 43–48 (2018)

    Chen, Q., Ding, Y., Chen, M.: Nanoporous metal by dealloying for electrochemical energy conversion and storage. Mrs Bulletin43(1), 43–48 (2018)

    work page 2018

  7. [7]

    Journal of Materials Science54(2), 949–973 (2019)

    Huang, A., He, Y., Zhou, Y., Zhou, Y., Yang, Y., Zhang, J., Luo, L., Mao, Q., Hou, D., Yang, J.: A review of recent applications of porous metals and metal oxide in energy storage, sensing and catalysis. Journal of Materials Science54(2), 949–973 (2019)

    work page 2019

  8. [8]

    Journal of Alloys and Compounds872, 159675 (2021)

    Shi, Y., Yang, W., Bai, Q., Qin, J., Zhang, Z.: Alloying/dealloying mecha- nisms, microstructural modulation and mechanical properties of nanoporous silver via a liquid metal-assisted alloying/dealloying strategy. Journal of Alloys and Compounds872, 159675 (2021)

    work page 2021

  9. [9]

    EnergyChem4(1), 100069 (2022)

    Sang, Q., Hao, S., Han, J., Ding, Y.: Dealloyed nanoporous materials for electrochemical energy conversion and storage. EnergyChem4(1), 100069 (2022)

    work page 2022

  10. [10]

    Acs Nano15(7), 11828–11842 (2021)

    An, Y., Tian, Y., Xiong, S., Feng, J., Qian, Y.: Scalable and controllable synthesis of interface-engineered nanoporous host for dendrite-free and high rate zinc metal batteries. Acs Nano15(7), 11828–11842 (2021)

    work page 2021

  11. [11]

    Journal of nanoscience and nanotechnology19(7), 3673–3685 (2019)

    Malgras, V., Tang, J., Wang, J., Kim, J., Torad, N.L., Dutta, S., Ariga, K., 33 Hossain, M.S.A., Yamauchi, Y., Wu, K.C.: Fabrication of nanoporous car- bon materials with hard-and soft-templating approaches: A review. Journal of nanoscience and nanotechnology19(7), 3673–3685 (2019)

    work page 2019

  12. [12]

    Mrs Bulletin28(4), 270–274 (2003)

    Gibson, L.J.: Cellular solids. Mrs Bulletin28(4), 270–274 (2003)

    work page 2003

  13. [13]

    Journal of the Mechanics and Physics of Solids50(1), 33–55 (2002) https://doi.org/10.1016/S0022-5096(01)00056-4

    Roberts, A.P., Garboczi, E.J.: Elastic properties of model random three- dimensional open-cell solids. Journal of the Mechanics and Physics of Solids50(1), 33–55 (2002) https://doi.org/10.1016/S0022-5096(01)00056-4

    work page doi:10.1016/s0022-5096(01)00056-4 2002

  14. [14]

    Advanced Engineering Materials18(4), 632–642 (2016)

    Winter, N., Becton, M., Zhang, L., Wang, X.: Failure mechanisms and scaling laws of nanoporous aluminum: a computational study. Advanced Engineering Materials18(4), 632–642 (2016)

    work page 2016

  15. [15]

    Materials Today68, 96–107 (2023)

    Zhong, H., Das, R., Gu, J., Qian, M.: Low-density, high-strength metal mechan- ical metamaterials beyond the gibson-ashby model. Materials Today68, 96–107 (2023)

    work page 2023

  16. [16]

    Materials Today Communications39, 109256 (2024)

    Depboylu, F.N., Yasa, E., Poyraz, ¨O., Korkusuz, F., Popa, A.-A.: Choosing between commercially pure titanium and ti-6al-4v gyroid structures for orthope- dic applications: An analysis through timoshenko beam theory, the gibson-ashby model and experimental methods. Materials Today Communications39, 109256 (2024)

    work page 2024

  17. [17]

    Acta Materialia173, 163–173 (2019)

    Peng, P., Sun, H., Gerlich, A.P., Guo, W., Zhu, Y., Liu, L., Zou, G., Singh, C.V., Zhou, N.: Near-ideal compressive strength of nanoporous silver composed of nanowires. Acta Materialia173, 163–173 (2019)

    work page 2019

  18. [18]

    Applied Physics Letters110, 211902 (2017) https://doi.org/10.1063/1.4984108

    Liu, L.-Z., Jin, H.-J.: Scaling equation for the elastic modulus of nanoporous gold with “fixed” network connectivity. Applied Physics Letters110, 211902 (2017) https://doi.org/10.1063/1.4984108

    work page doi:10.1063/1.4984108 2017

  19. [19]

    Acta Materialia186, 105–115 (2020) https://doi.org/10.1016/j.actamat.2019.12.046

    Xiang, Y.-H., Liu, L.-Z., Shao, J.-C., Jin, H.-J.: A universal scaling relationship between the strength and young’s modulus of dealloyed porous fe0.80cr0.20. Acta Materialia186, 105–115 (2020) https://doi.org/10.1016/j.actamat.2019.12.046

    work page doi:10.1016/j.actamat.2019.12.046 2020

  20. [20]

    Acta Materialia119, 115–122 (2016) https://doi.org/10.1016/j.actamat.2016.08.012

    Mangipudi, K.R., Epler, E., Volkert, C.A.: Topology-dependent scaling laws for the stiffness and strength of nanoporous gold. Acta Materialia119, 115–122 (2016) https://doi.org/10.1016/j.actamat.2016.08.012

    work page doi:10.1016/j.actamat.2016.08.012 2016

  21. [22]

    Extreme Mechanics 34 Letters68, 102147 (2024) https://doi.org/10.1016/j.eml.2024.102147

    Sohn, S., Richert, C., Shi, S., Weissm¨ uller, J., Huber, N.: Scaling between elastic- ity and topological genus for random network nanomaterials. Extreme Mechanics 34 Letters68, 102147 (2024) https://doi.org/10.1016/j.eml.2024.102147

    work page doi:10.1016/j.eml.2024.102147 2024

  22. [23]

    Materials & Design232, 112175 (2023) https://doi.org/10.1016/j.matdes.2023.112175

    Wu, Y., Markmann, J., Lilleodden, E.T.: On the consequences of intrinsic and extrinsic size effects on the mechanical response of nanoporous Au. Materials & Design232, 112175 (2023) https://doi.org/10.1016/j.matdes.2023.112175

    work page doi:10.1016/j.matdes.2023.112175 2023

  23. [24]

    Permutahedra and generalized associahedra

    Mathesan, S., Mordehai, D.: Size-dependent elastic modulus of nanoporous au nanopillars. Acta Materialia185, 441–452 (2020) https://doi.org/10.1016/j. actamat.2019.12.018

    work page doi:10.1016/j 2020

  24. [25]

    Advances in neural information processing systems 25(2012)

    Krizhevsky, A., Sutskever, I., Hinton, G.E.: Imagenet classification with deep convolutional neural networks. Advances in neural information processing systems 25(2012)

    work page 2012

  25. [26]

    Very Deep Convolutional Networks for Large-Scale Image Recognition

    Simonyan, K.: Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556 (2014)

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  26. [27]

    In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp

    He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recogni- tion. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 770–778 (2016)

    work page 2016

  27. [28]

    In: International Conference on P2P, Parallel, Grid, Cloud and Internet Computing, pp

    Kato, S., Oshita, A., Kubo, T., Todai, M.: Classification of steel microstructure image using cnn. In: International Conference on P2P, Parallel, Grid, Cloud and Internet Computing, pp. 59–68 (2023). Springer

    work page 2023

  28. [29]

    Science bulletin63(18), 1215–1222 (2018)

    Wu, J., Yin, X., Xiao, H.: Seeing permeability from images: fast prediction with convolutional neural networks. Science bulletin63(18), 1215–1222 (2018)

    work page 2018

  29. [30]

    Current Opinion in Electrochemistry35, 101101 (2022)

    Cawte, T., Bazylak, A.: A 3d convolutional neural network accurately predicts the permeability of gas diffusion layer materials directly from image data. Current Opinion in Electrochemistry35, 101101 (2022)

    work page 2022

  30. [31]

    Computational Materials Science184, 109850 (2020)

    Rao, C., Liu, Y.: Three-dimensional convolutional neural network (3d-cnn) for heterogeneous material homogenization. Computational Materials Science184, 109850 (2020)

    work page 2020

  31. [32]

    Transport in porous media140(1), 241–272 (2021)

    Santos, J.E., Yin, Y., Jo, H., Pan, W., Kang, Q., Viswanathan, H.S., Prodanovi´ c, M., Pyrcz, M.J., Lubbers, N.: Computationally efficient multiscale neural net- works applied to fluid flow in complex 3d porous media. Transport in porous media140(1), 241–272 (2021)

    work page 2021

  32. [33]

    International Journal of Heat and Mass Transfer222, 125149 (2024)

    Virupaksha, A.G., Nagel, T., Lehmann, F., Rajabi, M.M., Hoteit, H., Fahs, M., Le Ber, F.: Modeling transient natural convection in heterogeneous porous media with convolutional neural networks. International Journal of Heat and Mass Transfer222, 125149 (2024)

    work page 2024

  33. [34]

    Minerals Engineering188, 107748 (2022)

    Roslin, A., Marsh, M., Pich´ e, N., Provencher, B., Mitchell, T., Onederra, I., 35 Leonardi, C.: Processing of micro-ct images of granodiorite rock samples using convolutional neural networks (cnn), part i: Super-resolution enhancement using a 3d cnn. Minerals Engineering188, 107748 (2022)

    work page 2022

  34. [35]

    Separation and Purification Technology359, 130428 (2025)

    Yi, W., Kim, D.Y., Jin, H., Yoon, S., Ahn, K.H.: Early detection of pore clogging in microfluidic systems with 3d convolutional neural network. Separation and Purification Technology359, 130428 (2025)

    work page 2025

  35. [36]

    International Journal of Heat and Mass Transfer221, 125064 (2024)

    Huang, Q., Hong, D., Niu, B., Long, D., Zhang, Y.: An interpretable deep learn- ing strategy for effective thermal conductivity prediction of porous materials. International Journal of Heat and Mass Transfer221, 125064 (2024)

    work page 2024

  36. [37]

    Frontiers in Materials9(2022) https://doi.org/10.3389/fmats.2022.837006

    Sardhara, T., Aydin, R.C., Li, Y., Pich´ e, N., Gauvin, R., Cyron, C.J., Ritter, M.: Training deep neural networks to reconstruct nanoporous structures from fib tomography images using synthetic training data. Frontiers in Materials9(2022) https://doi.org/10.3389/fmats.2022.837006

    work page doi:10.3389/fmats.2022.837006 2022

  37. [38]

    Scientific Reports13, 5414 (2023) https://doi.org/10.1038/s41598-023-31677-7

    Wang, Z., Dabaja, R., Chen, L., Banu, M.: Machine learning unifies flexibility and efficiency of spinodal structure generation for stochastic biomaterial design. Scientific Reports13, 5414 (2023) https://doi.org/10.1038/s41598-023-31677-7

    work page doi:10.1038/s41598-023-31677-7 2023

  38. [39]

    Materials14(8) (2021) https://doi.org/10.3390/ma14081822

    Huber, N.: A strategy for dimensionality reduction and data analysis applied to microstructure–property relationships of nanoporous metals. Materials14(8) (2021) https://doi.org/10.3390/ma14081822

    work page doi:10.3390/ma14081822 2021

  39. [40]

    npj Computational Materials9(1), 82 (2023) https://doi.org/10.1038/ s41524-023-01037-0

    Shargh, A.K., Abdolrahim, N.: An interpretable deep learning approach for designing nanoporous silicon nitride membranes with tunable mechanical prop- erties. npj Computational Materials9(1), 82 (2023) https://doi.org/10.1038/ s41524-023-01037-0

    work page 2023

  40. [41]

    Materialia 21, 101275 (2022) https://doi.org/10.1016/j.mtla.2021.101275

    Liu, H., Shargh, A.K., Abdolrahim, N.: Mining structure-property linkage in nanoporous materials using an interpretative deep learning approach. Materialia 21, 101275 (2022) https://doi.org/10.1016/j.mtla.2021.101275

    work page doi:10.1016/j.mtla.2021.101275 2022

  41. [42]

    MRS Bulletin50, 629–640 (2025) https://doi.org/ 10.1557/s43577-025-00908-9

    Karen, C.-W.Y.-c., Norbert, H., G., Y.K.: Machine learning approaches for inten- tional materials engineering. MRS Bulletin50, 629–640 (2025) https://doi.org/ 10.1557/s43577-025-00908-9

    work page doi:10.1557/s43577-025-00908-9 2025

  42. [43]

    Advanced Materials36(34), 2308149 (2024) https: //doi.org/10.1002/adma.202308149

    Deng, W., Kumar, S., Vallone, A., Kochmann, D.M., Greer, J.R.: Ai-enabled materials design of non-periodic 3d architectures with predictable direction- dependent elastic properties. Advanced Materials36(34), 2308149 (2024) https: //doi.org/10.1002/adma.202308149

    work page doi:10.1002/adma.202308149 2024

  43. [44]

    Physical Review Materials6(10), 103801 (2022) 36

    Lanzoni, D., Albani, M., Bergamaschini, R., Montalenti, F.: Morphological evo- lution via surface diffusion learned by convolutional, recurrent neural networks: Extrapolation and prediction uncertainty. Physical Review Materials6(10), 103801 (2022) 36

    work page 2022

  44. [45]

    Patterns2(5) (2021)

    Yang, K., Cao, Y., Zhang, Y., Fan, S., Tang, M., Aberg, D., Sadigh, B., Zhou, F.: Self-supervised learning and prediction of microstructure evolution with convolutional recurrent neural networks. Patterns2(5) (2021)

    work page 2021

  45. [46]

    Machine Learning: Science and Technology5(4), 045017 (2024)

    Lanzoni, D., Fantasia, A., Bergamaschini, R., Pierre-Louis, O., Montalenti, F.: Extreme time extrapolation capabilities and thermodynamic consistency of physics-inspired neural networks for the 3d microstructure evolution of materials via cahn–hilliard flow. Machine Learning: Science and Technology5(4), 045017 (2024)

    work page 2024

  46. [47]

    Computer Methods in Applied Mechanics and Engineering403, 115741 (2023)

    Eidel, B.: Deep cnns as universal predictors of elasticity tensors in homogeniza- tion. Computer Methods in Applied Mechanics and Engineering403, 115741 (2023)

    work page 2023

  47. [48]

    Computational Mechanics72(1), 155–171 (2023)

    Aldakheel, F., Elsayed, E.S., Zohdi, T.I., Wriggers, P.: Efficient multiscale mod- eling of heterogeneous materials using deep neural networks. Computational Mechanics72(1), 155–171 (2023)

    work page 2023

  48. [49]

    npj Computational Materials8(1), 67 (2022)

    Mianroodi, J.R., Rezaei, S., Siboni, N.H., Xu, B.-X., Raabe, D.: Lossless multi- scale constitutive elastic relations with artificial intelligence. npj Computational Materials8(1), 67 (2022)

    work page 2022

  49. [50]

    Scientific Reports14(1), 36 (2024)

    Peivaste, I., Ramezani, S., Alahyarizadeh, G., Ghaderi, R., Makradi, A., Belouet- tar, S.: Rapid and accurate predictions of perfect and defective material properties in atomistic simulation using the power of 3d cnn-based trained artificial neural networks. Scientific Reports14(1), 36 (2024)

    work page 2024

  50. [51]

    Acta Materialia149, 326–340 (2018) https://doi.org/10.1016/j.actamat.2018.01.005

    Soyarslan, C., Bargmann, S., Pradas, M., Weissm¨ uller, J.: 3D stochastic bicontin- uous microstructures: Generation, topology and elasticity. Acta Materialia149, 326–340 (2018) https://doi.org/10.1016/j.actamat.2018.01.005

    work page doi:10.1016/j.actamat.2018.01.005 2018

  51. [52]

    MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING18(1) (2010) https://doi.org/10

    Stukowski, A.: Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool. MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING18(1) (2010) https://doi.org/10. 1088/0965-0393/18/1/01501

    work page 2010

  52. [53]

    Computational Materials Science 191, 110307 (2021) https://doi.org/10.1016/j.commatsci.2021.110307

    Mathesan, S., Mordehai, D.: On the yielding and densification of nanoporous au nanopillars in molecular dynamics simulations. Computational Materials Science 191, 110307 (2021) https://doi.org/10.1016/j.commatsci.2021.110307

    work page doi:10.1016/j.commatsci.2021.110307 2021

  53. [54]

    Materials13(2020) https://doi.org/10.3390/ ma13153307

    Richert, C., Huber, N.: A review of experimentally informed micromechani- cal modeling of nanoporous metals: From structural descriptors to predictive structure–property relationships. Materials13(2020) https://doi.org/10.3390/ ma13153307

    work page 2020

  54. [55]

    Thompson, A.P., Aktulga, H.M., Berger, R., Bolintineanu, D.S., Brown, W.M., Crozier, P.S., Veld, P.J., Kohlmeyer, A., Moore, S.G., Nguyen, T.D., Shan, R., 37 Stevens, M.J., Tranchida, J., Trott, C., Plimpton, S.J.: LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comp. Phys. Comm.271, 108...

    work page arXiv 2022

  55. [56]

    The Journal of chemical physics 123(20) (2005)

    Grochola, G., Russo, S.P., Snook, I.K.: On fitting a gold embedded atom method potential using the force matching method. The Journal of chemical physics 123(20) (2005)

    work page 2005

  56. [57]

    MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications

    Howard, A.G.: Mobilenets: Efficient convolutional neural networks for mobile vision applications. arXiv preprint arXiv:1704.04861 (2017)

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  57. [58]

    In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp

    Huang, G., Liu, Z., Van Der Maaten, L., Weinberger, K.Q.: Densely connected convolutional networks. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 4700–4708 (2017)

    work page 2017

  58. [59]

    Journal of Big data3, 1–40 (2016)

    Weiss, K., Khoshgoftaar, T.M., Wang, D.: A survey of transfer learning. Journal of Big data3, 1–40 (2016)

    work page 2016

  59. [60]

    Multimedia Tools and Applications79, 25763–25783 (2020)

    Khan, M.A., Akram, T., Sharif, M., Saba, T.: Fruits diseases classification: exploiting a hierarchical framework for deep features fusion and selection. Multimedia Tools and Applications79, 25763–25783 (2020)

    work page 2020

  60. [61]

    In: 2020 IEEE International Conference on Image Processing (ICIP), pp

    Zhang, K., Cao, Z., Wu, J.: Circular shift: An effective data augmentation method for convolutional neural network on image classification. In: 2020 IEEE International Conference on Image Processing (ICIP), pp. 1676–1680 (2020). https://doi.org/10.1109/ICIP40778.2020.9191303

    work page doi:10.1109/icip40778.2020.9191303 2020

  61. [62]

    Advances in neural information processing systems31(2018)

    Prokhorenkova, L., Gusev, G., Vorobev, A., Dorogush, A.V., Gulin, A.: Catboost: unbiased boosting with categorical features. Advances in neural information processing systems31(2018)

    work page 2018

  62. [63]

    Grinsztajn, L., Oyallon, E., Varoquaux, G.: Why do tree-based models still out- perform deep learning on typical tabular data? Advances in neural information processing systems35, 507–520 (2022)

    work page 2022

  63. [64]

    Information Fusion81, 84–90 (2022)

    Shwartz-Ziv, R., Armon, A.: Tabular data: Deep learning is not all you need. Information Fusion81, 84–90 (2022)

    work page 2022

  64. [65]

    Journal of Applied Physics138(7) (2025)

    Zorkaltsev, S., Haranczyk, M.: A molecular dynamics study of chemistry-inspired nanoporous aluminum structures. Journal of Applied Physics138(7) (2025)

    work page 2025

  65. [66]

    CVGIP: Graphical Models and Image Process- ing56(1994) https://doi.org/10.1006/cgip.1994.1042

    Lee, T.-C., Kashyap, R.L., Chu, C.-N.: Building skeleton models via 3-d medial surface/axis thinning algorithms. CVGIP: Graphical Models and Image Process- ing56(1994) https://doi.org/10.1006/cgip.1994.1042

    work page doi:10.1006/cgip.1994.1042 1994

  66. [67]

    A Unified Approach to Interpreting Model Predictions

    Lundberg, S., Lee, S.-I.: A Unified Approach to Interpreting Model Predictions 38 (2017). https://arxiv.org/abs/1705.07874

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  67. [68]

    Learning important features through propagating activation differences

    Shrikumar, A., Greenside, P., Kundaje, A.: Learning Important Features Through Propagating Activation Differences (2019). https://arxiv.org/abs/1704.02685 39

    work page arXiv 2019