Revealing hidden medium-range order in amorphous materials using topological data analysis

Sørensen, Søren Strandskov; Biscio, Christophe Ange Napoléon; Bauchy, Mathieu; Fajstrup, Lisbeth; Smedskjær, Morten Mattrup

doi:10.1126/sciadv.abc2320

Cited by 58 publications

(55 citation statements)

References 43 publications

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“…While criticism has been levelled at persistence diagrams for how much they rely on qualitative analysis (see refs. Sørensen et al (2020); Ormrod ; Wasserman (2018)), if that is what's desired they can be extremely useful. The analysis of persistence diagrams is simplified if instead we track whether particular features in a network persistent across time instead of length scale.…”

Section: Persistence Diagramsmentioning

confidence: 99%

“…Persistence diagrams have been criticised (see, for example, refs. Sørensen et al (2020) and Ormrod Morley et al ( 2021)) as they may be hard to interpret quantitatively, and they often reflect properties of a network that are difficult to visualise. Furthermore, analysing biological networks as a function of a length scale at a single point in time can potentially lose critical information.…”

Section: Introductionmentioning

confidence: 99%

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Persistence Diagrams to Visualise Damage to Biological Networks

Bailey

Wilson

2022

Preprint

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One of the critical tools of persistent homology is the persistence diagram. We demonstrate the applicability of a persistence diagram showing the existence of topological features (here rings in a 2D network) generated over time instead of space as a tool to analyse trajectories of biological networks. We show how the time persistence diagram is useful in order to identify critical phenomena such as rupturing and to visualise important features in 2D biological networks; they are particularly useful to highlight patterns of damage and to identify if particular patterns are significant or ephemeral. Persistence diagrams are also used to analyse repair phenomena, and we explore how the measured properties of a dynamical phenomenon change according to the sampling frequency. This shows that the persistence diagrams are robust and still provide useful information even for data of low temporal resolution. Finally, we combine persistence diagrams across many trajectories to show how the technique highlights the existence of sharp transitions at critical points in the rupturing process.

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Section: Persistence Diagramsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Persistence Diagrams to Visualise Damage to Biological Networks

Bailey

Wilson

2022

Preprint

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“…Such representations have also been used in materials discovery where both geometric and chemical information is incorporated to predict properties of materials [46]. Persistent homology has also been used to understand hidden structures in materials [47] and the Mapper method has been used to visualize the network of the solubility space of molecules. In terms of generative modeling, only recently has there been some exploration in using topological priors to regularize the generation of general point cloud data [48].…”

Section: Related Workmentioning

confidence: 99%

Augmenting Molecular Deep Generative Models with Topological Data Analysis Representations

Schiff¹,

Chenthamarakshan²,

Hoffman³

et al. 2021

Preprint

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Deep generative models have emerged as a powerful tool for learning informative molecular representations and designing novel molecules with desired properties, with applications in drug discovery and material design. Deep generative auto-encoders defined over molecular SMILES strings have been a popular choice for that purpose. However, capturing salient molecular properties like quantumchemical energies remains challenging and requires sophisticated neural net models of molecular graphs or geometry-based information. As a simpler and more efficient alternative, we present a SMILES Variational Auto-Encoder (VAE) augmented with topological data analysis (TDA) representations of molecules, known as persistence images. Our experiments show that this TDA augmentation enables a SMILES VAE to capture the complex relation between 3D geometry and electronic properties, and allows generation of novel, diverse, and valid molecules with geometric features consistent with the training data, which exhibit a varying range of global electronic structural properties, such as a small HOMO-LUMO gap -a critical property for designing organic solar cells. We demonstrate that our TDA augmentation yields better success in downstream tasks compared to models trained without these representations and can assist in targeted molecule discovery.

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“…Any process that can elucidate as yet hidden structure in materials, or improve its description, naturally has potential to be extremely useful. In this vein, persistent homology has already been applied to diverse topics such as granular matter [3], porous media [4], water networks [5], fullerenes [6] and, of particular importance to this work, amorphous materials [7][8][9][10][11]. The latter studies claim to highlight structures that are not available using more conventional techniques, quantify the medium range order in glass, and explain phenom-ena such as the origin of the first sharp diffraction peak 39 in disordered materials.…”

Section: Introductionmentioning

confidence: 99%

Persistent homology in two-dimensional atomic networks

Morley

Salmon

Wilson

2021

The Journal of Chemical Physics

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The topology of two-dimensional network materials is investigated by persistent homology analysis. The constraint of two dimensions allows for a direct comparison of key persistent homology metrics (persistence diagrams, cycles, Betti numbers) with more traditional metrics such as the ring-size distributions. Two different types of networks are employed in which the topology is manipulated systematically. In the first, comparatively rigid networks are generated for a triangle-raft model, which are representative of materials such as silica bilayers. In the second, more flexible networks are generated using a bond-switching algorithm, which are representative of materials such as graphene. Bands are identified in the persistence diagrams by reference to the length-scales associated with distorted polygons. The triangle-raft models with the largest ordering allow specific bands Bn (n = 1, 2, 3,. . . ) to be allocated to configurations of atoms separated by n bonds. The persistence diagrams for the more disordered network models also display bands albeit less pronounced. The persistent homology method thereby provides information on n-body correlations that is not accessible from structure factors or radial distribution functions. An analysis of the persistent cycles gives the primitive ring statistics, provided the level of disorder is not too large. The method also gives information on the regularity of rings that is unavailable from a ring-statistics analysis. The utility of the persistent homology method is demonstrated by its application to experimentally-obtained configurations of silica bilayers and graphene. 42In this paper the utility of persistent homology will 43 be assessed using two-dimensional amorphous materials. 44The interpretation of the properties of these reduced di-45 mensional systems is simpler compared to three dimen-46 sional networks, and should bring insight to the analysis 47 of the latter. The paper begins by outlining the relevant 48 theory to persistent homology, with the aid of small ex-49 ample systems. Persistent homology is then calculated 50 for triangle rafts (a proxy for amorphous bilayers of, e.g., 51 silica), systematically generated with increasing levels of 52 disorder. The results are contrasted with those obtained 53 from generic random-networks as produced from bond 54 switching. In addition, the persistence diagrams are dis-55 cussed for configurations obtained directly from experi-56 ments on silica bilayers and graphene. Finally, the con-57 clusions of these investigations are assessed in the con-58 text of more complex systems, and the potential utility 59 of persistent homology as an analytic tool for materials 60 characterisation is examined. 61 II. OVERVIEW OF TRADITIONAL METHODS 62 Amorphous network-forming materials are usually 63 built from simple local-structural-units such as the SiO 4 64 tetrahedron in amorphous silica. Bond-length and bond-65 bending flexibility leads, however, to structural complex-66 ity as these units connect to form configurations on lon...

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Revealing hidden medium-range order in amorphous materials using topological data analysis

Cited by 58 publications

References 43 publications

Persistence Diagrams to Visualise Damage to Biological Networks

Persistence Diagrams to Visualise Damage to Biological Networks

Augmenting Molecular Deep Generative Models with Topological Data Analysis Representations

Persistent homology in two-dimensional atomic networks

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