Unsupervised learning for local structure detection in colloidal systems

Hydrogen-bond linking is crucial for growing ice VII embryos

We use molecular dynamics simulations to examine the homogeneous nucleation of ice VII from metastable liquid water. An unsupervised machine learning classification identifies two distinct local structures composing Ice VII nuclei. The seeding method, combined with the classical nucleation theory (CNT), predicts the solid-liquid interfacial free energy, consistent with the value from the mold integration method. Meanwhile, the nucleation rates estimated from the CNT framework and brute force spontaneous nucleations are inconsistent, and we discuss the reasons for this discrepancy. Structural and dynamical heterogeneities suggest that the potential birthplace for an ice VII embryo is relatively ordered, although not necessarily relatively immobile. Moreover, we demonstrate that without the formation of hydrogen-bond links, ice VII embryos do not grow.

Revealing the hidden structure of disordered materials by parameterizing their local structural manifold

Durable interest in developing a framework for the detailed structure of glassy materials has produced numerous structural descriptors that trade off between general applicability and interpretability. However, none approach the combination of simplicity and wide-ranging predictive power of the lattice-grain-defect framework for crystalline materials. Working from the hypothesis that the local atomic environments of a glassy material are constrained by enthalpy minimization to a low-dimensional manifold in atomic coordinate space, we develop a generalized distance function, the Gaussian Integral Inner Product (GIIP) distance, in connection with agglomerative clustering and diffusion maps, to parameterize that manifold. Applying this approach to a two-dimensional model crystal and a three-dimensional binary model metallic glass results in parameters interpretable as coordination number, composition, volumetric strain, and local symmetry. In particular, we show that a more slowly quenched glass has a higher degree of local tetrahedral symmetry at the expense of cyclic symmetry. While these descriptors require post-hoc interpretation, they minimize bias rooted in crystalline materials science and illuminate a range of structural trends that might otherwise be missed.

Why neural functionals suit statistical mechanics

We describe recent progress in the statistical mechanical description of many-body systems via machine learning combined with concepts from density functional theory and many-body simulations. We argue that the neural functional theory by Sammülleret al(2023Proc. Natl Acad. Sci.120e2312484120) gives a functional representation of direct correlations and of thermodynamics that allows for thorough quality control and consistency checking of the involved methods of artificial intelligence. Addressing a prototypical system we here present a pedagogical application to hard core particle in one spatial dimension, where Percus' exact solution for the free energy functional provides an unambiguous reference. A corresponding standalone numerical tutorial that demonstrates the neural functional concepts together with the underlying fundamentals of Monte Carlo simulations, classical density functional theory, machine learning, and differential programming is available online athttps://github.com/sfalmo/NeuralDFT-Tutorial.

Neural functional theory for inhomogeneous fluids: Fundamentals and applications

We present a hybrid scheme based on classical density functional theory and machine learning for determining the equilibrium structure and thermodynamics of inhomogeneous fluids. The exact functional map from the density profile to the one-body direct correlation function is represented locally by a deep neural network. We substantiate the general framework for the hard sphere fluid and use grand canonical Monte Carlo simulation data of systems in randomized external environments during training and as reference. Functional calculus is implemented on the basis of the neural network to access higher-order correlation functions via automatic differentiation and the free energy via functional line integration. Thermal Noether sum rules are validated explicitly. We demonstrate the use of the neural functional in the self-consistent calculation of density profiles. The results outperform those from state-of-the-art fundamental measure density functional theory. The low cost of solving an associated Euler-Lagrange equation allows to bridge the gap from the system size of the original training data to macroscopic predictions upon maintaining near-simulation microscopic precision. These results establish the machine learning of functionals as an effective tool in the multiscale description of soft matter.

The prediction of dynamical quantities in granular avalanches based on graph neural networks

The study of granular avalanches in rotating drums is not only essential to understanding various complex behaviors of interest in granular media from a scientific perspective; it also has valuable applications in regard to industrial processes and geological catastrophes. Despite decades of research studies on avalanches, a proper understanding of their dynamic properties still remains a great challenge to scientists due to a lack of state-of-the-art techniques. In this study, we accurately predict the avalanche dynamic features of three-dimensional granular materials in rotating drums, by using graph neural networks on the basis of their initial static microstructures alone. We find that our method is robust to changes in various model parameters, such as the interaction potential, size polydispersity, and noise in particle coordinates. In addition, with the grain-scale velocities obtained either from our network or from numerical simulations, we find an approximately equal and strong correlation between the global velocity and global velocity fluctuation in our 3D granular avalanche systems, which further demonstrates the predictive power of our trained graph neural networks to uncover the fundamental physics of granular avalanches. We expect our method to provide more insight into the avalanche dynamics of granular materials and other amorphous systems in the future.

Ordered ground state configurations of the asymmetric Wigner bilayer system-Revisited with unsupervised learning

We have reanalyzed the rich plethora of ground state configurations of the asymmetric Wigner bilayer system that we had recently published in a related diagram of states [Antlanger et al., Phys. Rev. Lett. 117, 118002 (2016)], comprising roughly 60 000 state points in the phase space spanned by the distance between the plates and the charge asymmetry parameter of the system. In contrast to this preceding contribution where the classification of the emerging structures was carried out "by hand," we have used for the present contribution machine learning concepts, notably based on a principal component analysis and a k-means clustering approach: using a 30-dimensional feature vector for each emerging structure (containing relevant information, such as the composition of the configuration as well as the most relevant order parameters), we were able to reanalyze these ground state configurations in a considerably more systematic and comprehensive manner than we could possibly do in the previously published classification scheme. Indeed, we were now able to identify new structures in previously unclassified regions of the parameter space and could considerably refine the previous classification scheme, thereby identifying a rich wealth of new emerging ground state configurations. Thorough consistency checks confirm the validity of the newly defined diagram of states.

Charting Nanocluster Structures via Convolutional Neural Networks

A general method to obtain a representation of the structural landscape of nanoparticles in terms of a limited number of variables is proposed. The method is applied to a large data set of parallel tempering molecular dynamics simulations of gold clusters of 90 and 147 atoms, silver clusters of 147 atoms, and copper clusters of 147 atoms, covering a plethora of structures and temperatures. The method leverages convolutional neural networks to learn the radial distribution functions of the nanoclusters and distills a low-dimensional chart of the structural landscape. This strategy is found to give rise to a physically meaningful and differentiable mapping of the atom positions to a low-dimensional manifold in which the main structural motifs are clearly discriminated and meaningfully ordered. Furthermore, unsupervised clustering on the low-dimensional data proved effective at further splitting the motifs into structural subfamilies characterized by very fine and physically relevant differences such as the presence of specific punctual or planar defects or of atoms with particular coordination features. Owing to these peculiarities, the chart also enabled tracking of the complex structural evolution in a reactive trajectory. In addition to visualization and analysis of complex structural landscapes, the presented approach offers a general, low-dimensional set of differentiable variables that has the potential to be used for exploration and enhanced sampling purposes.

Symmetry-specific characterization of bond orientation order in DNA-assembled nanoparticle lattices

Bond-orientational order in DNA-assembled nanoparticles lattices is explored with the help of recently introduced Symmetry-specific Bond Order Parameters (SymBOPs). This approach provides a more sensitive analysis of local order than traditional scalar BOPs, facilitating the identification of coherent domains at the single bond level. The present study expands the method initially developed for assemblies of anisotropic particles to the isotropic ones or cases where particle orientation information is unavailable. The SymBOP analysis was applied to experiments on DNA-frame-based assembly of nanoparticle lattices. It proved highly sensitive in identifying coherent crystalline domains with different orientations, as well as detecting topological defects, such as dislocations. Furthermore, the analysis distinguishes individual sublattices within a single crystalline domain, such as pair of interpenetrating FCC lattices within a cubic diamond. The results underscore the versatility and robustness of SymBOPs in characterizing ordering phenomena, making them valuable tools for investigating structural properties in various systems.

In search of a precursor for crystal nucleation of hard and charged colloids

The interplay between crystal nucleation and the structure of the metastable fluid has been a topic of significant debate over recent years. In particular, it has been suggested that even in simple model systems such as hard or charged colloids, crystal nucleation might be foreshadowed by significant fluctuations in local structure around the location where the nucleus first arises. We investigate this using computer simulations of spontaneous nucleation events in both hard and charged colloidal systems. To detect local structural variations, we use both standard and unsupervised machine learning methods capable of finding hidden structures in the metastable fluid phase. We track numerous nucleation events for the face-centered cubic and body-centered cubic crystals on a local level and demonstrate that all signs of crystallinity emerge simultaneously from the very start of the nucleation process. We thus conclude that we observe no precursor for the crystal nucleation of hard and charged colloids.

Controlling crystallization: what liquid structure and dynamics reveal about crystal nucleation mechanisms

Over recent years, molecular simulations have provided invaluable insights into the microscopic processes governing the initial stages of crystal nucleation and growth. A key aspect that has been observed in many different systems is the formation of precursors in the supercooled liquid that precedes the emergence of crystalline nuclei. The structural and dynamical properties of these precursors determine to a large extent the nucleation probability as well as the formation of specific polymorphs. This novel microscopic view on nucleation mechanisms has further implications for our understanding of the nucleating ability and polymorph selectivity of nucleating agents, as these appear to be strongly linked to their ability in modifying structural and dynamical characteristics of the supercooled liquid, namely liquid heterogeneity. In this perspective, we highlight recent progress in exploring the connection between liquid heterogeneity and crystallization, including the effects of templates, and the potential impact for controlling crystallization processes. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Quantifying disorder one atom at a time using an interpretable graph neural network paradigm

Quantifying the level of atomic disorder within materials is critical to understanding how evolving local structural environments dictate performance and durability. Here, we leverage graph neural networks to define a physically interpretable metric for local disorder, called SODAS. This metric encodes the diversity of the local atomic configurations as a continuous spectrum between the solid and liquid phases, quantified against a distribution of thermal perturbations. We apply this methodology to four prototypical examples with varying levels of disorder: (1) grain boundaries, (2) solid-liquid interfaces, (3) polycrystalline microstructures, and (4) tensile failure/fracture. We also compare SODAS to several commonly used methods. Using elemental aluminum as a case study, we show how our paradigm can track the spatio-temporal evolution of interfaces, incorporating a mathematically defined description of the spatial boundary between order and disorder. We further show how to extract physics-preserved gradients from our continuous disorder fields, which may be used to understand and predict materials performance and failure. Overall, our framework provides a simple and generalizable pathway to quantify the relationship between complex local atomic structure and coarse-grained materials phenomena.

Perspective: How to overcome dynamical density functional theory

We argue in favour of developing a comprehensive dynamical theory for rationalizing, predicting, designing, and machine learning nonequilibrium phenomena that occur in soft matter. To give guidance for navigating the theoretical and practical challenges that lie ahead, we discuss and exemplify the limitations of dynamical density functional theory (DDFT). Instead of the implied adiabatic sequence of equilibrium states that this approach provides as a makeshift for the true time evolution, we posit that the pending theoretical tasks lie in developing a systematic understanding of the dynamical functional relationships that govern the genuine nonequilibrium physics. While static density functional theory gives a comprehensive account of the equilibrium properties of many-body systems, we argue that power functional theory is the only present contender to shed similar insights into nonequilibrium dynamics, including the recognition and implementation of exact sum rules that result from the Noether theorem. As a demonstration of the power functional point of view, we consider an idealized steady sedimentation flow of the three-dimensional Lennard-Jones fluid and machine-learn the kinematic map from the mean motion to the internal force field. The trained model is capable of both predicting and designing the steady state dynamics universally for various target density modulations. This demonstrates the significant potential of using such techniques in nonequilibrium many-body physics and overcomes both the conceptual constraints of DDFT as well as the limited availability of its analytical functional approximations.

Correlations between defect propensity and dynamical heterogeneities in supercooled water

A salient feature of supercooled liquids consists in the dramatic dynamical slowdown they undergo as temperature decreases while no significant structural change is evident. These systems also present dynamical heterogeneities (DH): certain molecules, spatially arranged in clusters, relax various orders of magnitude faster than the others. However, again, no static quantity (such as structural or energetic measures) shows strong direct correlations with such fast-moving molecules. In turn, the dynamic propensity approach, an indirect measure that quantifies the tendency of the molecules to move in a given structural configuration, has revealed that dynamical constraints, indeed, originate from the initial structure. Nevertheless, this approach is not able to elicit which structural quantity is, in fact, responsible for such a behavior. In an effort to remove dynamics from its definition in favor of a static quantity, an energy-based propensity has also been developed for supercooled water, but it could only find positive correlations between the lowest-energy and the least-mobile molecules, while no correlations could be found for those more relevant mobile molecules involved in the DH clusters responsible for the system's structural relaxation. Thus, in this work, we shall define a defect propensity measure based on a recently introduced structural index that accurately characterizes water structural defects. We shall show that this defect propensity measure provides positive correlations with dynamic propensity, being also able to account for the fast-moving molecules responsible for the structural relaxation. Moreover, time dependent correlations will show that defect propensity represents an appropriate early-time predictor of the long-time dynamical heterogeneity.

Dimensionality reduction of local structure in glassy binary mixtures

We consider unsupervised learning methods for characterizing the disordered microscopic structure of supercooled liquids and glasses. Specifically, we perform dimensionality reduction of smooth structural descriptors that describe radial and bond-orientational correlations and assess the ability of the method to grasp the essential structural features of glassy binary mixtures. In several cases, a few collective variables account for the bulk of the structural fluctuations within the first coordination shell and also display a clear connection with the fluctuations of particle mobility. Fine-grained descriptors that characterize the radial dependence of bond-orientational order better capture the structural fluctuations relevant for particle mobility but are also more difficult to parameterize and to interpret. We also find that principal component analysis of bond-orientational order parameters provides identical results to neural network autoencoders while having the advantage of being easily interpretable. Overall, our results indicate that glassy binary mixtures have a broad spectrum of structural features. In the temperature range we investigate, some mixtures display well-defined locally favored structures, which are reflected in bimodal distributions of the structural variables identified by dimensionality reduction.

A Deep Learning Framework Discovers Compositional Order and Self-Assembly Pathways in Binary Colloidal Mixtures

Binary colloidal superlattices (BSLs) have demonstrated enormous potential for the design of advanced multifunctional materials that can be synthesized via colloidal self-assembly. However, mechanistic understanding of the three-dimensional self-assembly of BSLs is largely limited due to a lack of tractable strategies for characterizing the many two-component structures that can appear during the self-assembly process. To address this gap, we present a framework for colloidal crystal structure characterization that uses branched graphlet decomposition with deep learning to systematically and quantitatively describe the self-assembly of BSLs at the single-particle level. Branched graphlet decomposition is used to evaluate local structure via high-dimensional neighborhood graphs that quantify both structural order (e.g., body-centered-cubic vs face-centered-cubic) and compositional order (e.g., substitutional defects) of each individual particle. Deep autoencoders are then used to efficiently translate these neighborhood graphs into low-dimensional manifolds from which relationships among neighborhood graphs can be more easily inferred. We demonstrate the framework on in silico systems of DNA-functionalized particles, in which two well-recognized design parameters, particle size ratio and interparticle potential well depth can be adjusted independently. The framework reveals that binary colloidal mixtures with small interparticle size disparities (i.e., A- and B-type particle radius ratios of r _A/r _B = 0.8 to r _A/r _B = 0.95) can promote the self-assembly of defect-free BSLs much more effectively than systems of identically sized particles, as nearly defect-free BCC-CsCl, FCC-CuAu, and IrV crystals are observed in the former case. The framework additionally reveals that size-disparate colloidal mixtures can undergo nonclassical nucleation pathways where BSLs evolve from dense amorphous precursors, instead of directly nucleating from dilute solution. These findings illustrate that the presented characterization framework can assist in enhancing mechanistic understanding of the self-assembly of binary colloidal mixtures, which in turn can pave the way for engineering the growth of defect-free BSLs.

Robust prediction of force chains in jammed solids using graph neural networks

Force chains are quasi-linear self-organised structures carrying large stresses and are ubiquitous in jammed amorphous materials like granular materials, foams or even cell assemblies. Predicting where they will form upon deformation is crucial to describe the properties of such materials, but remains an open question. Here we demonstrate that graph neural networks (GNN) can accurately predict the location of force chains in both frictionless and frictional materials from the undeformed structure, without any additional information. The GNN prediction accuracy also proves to be robust to changes in packing fraction, mixture composition, amount of deformation, friction coefficient, system size, and the form of the interaction potential. By analysing the structure of the force chains, we identify the key features that affect prediction accuracy. Our results and methodology will be of interest for granular matter and disordered systems, e.g. in cases where direct force chain visualisation or force measurements are impossible.

Unsupervised topological learning for identification of atomic structures

We propose an unsupervised learning methodology with descriptors based on topological data analysis (TDA) concepts to describe the local structural properties of materials at the atomic scale. Based only on atomic positions and without a priori knowledge, our method allows for an autonomous identification of clusters of atomic structures through a Gaussian mixture model. We apply successfully this approach to the analysis of elemental Zr in the crystalline and liquid states as well as homogeneous nucleation events under deep undercooling conditions. This opens the way to deeper and autonomous study of complex phenomena in materials at the atomic scale.

Descriptor-free unsupervised learning method for local structure identification in particle packings

Local structure identification is of great importance in many scientific and engineering fields. However, mathematical and supervised learning methods mostly rely on specific descriptors of local structure and can only be applied to particular packing configurations. In this work, we propose an improved unsupervised learning method, which is descriptor-free, for local structure identification in particle packing. The point cloud is used as the input of the improved method, which directly comes from spatial positions of particles and does not rely on specific descriptors. The improved method constructs an autoencoder based on the point cloud network combined with Gaussian mixture models for dimension reduction and clustering. Numerical examples show that the improved method performs well in local structure identification of quasicrystal disk and sphere packings, achieving comparable accuracy with previous methods. For disordered packings which have been considered nearly having no local structures, the improved method identifies a nontrivial 7-neighbor motif in the maximally dense random packing of disks, and finds acentric structural motifs in the random close packing of spheres, which demonstrate the ability on identification of new and unknown local structures. The improved unsupervised learning method would help mining information from massive simulation and experimental results, as well as devising new order parameters for particle packings.

A long-range order in a thermally driven system with temperature-dependent interactions

Aggregation of macro-molecules under an external force is far from being understood. An important driving situation is achieved by temperature difference. Inter-particle interactions in metallic nanoparticles with ligand capping are reported to be sensitive to temperature and the zeta potential of the particles being reduced in the cold region. Such particles form aggregates in the cold region of the system in the presence of temperature difference. Here we study the aggregation of particles in the presence of temperature difference with temperature-dependent interaction parameters using Brownian dynamics simulation. The particle interaction and particle diffusion are considered to be sensitive to the local temperature. We identify a long-range structural order in the cold region of the system using the Avrami equation for crystal growth kinetics. Our observations might be useful in designing ordered structures with macro-molecules under non-equilibrium steady-state conditions.

Phase classification using neural networks: application to supercooled, polymorphic core-softened mixtures

Characterization of phases of soft matter systems is a challenge faced in many physical chemical problems. For polymorphic fluids it is an even greater challenge. Specifically, glass forming fluids, as water, can have, besides solid polymorphism, more than one liquid and glassy phases, and even a liquid-liquid critical point. In this sense, we apply a neural network algorithm to analyze the phase behavior of a mixture of core-softened fluids that interact through the continuous-shouldered well (CSW) potential, which have liquid polymorphism and liquid-liquid critical points, similar to water. We also apply the neural network to mixtures of CSW fluids and core-softened alcohols models. We combine and expand methods based on bond-orientational order parameters to study mixtures, applied to mixtures of hardcore fluids and to supercooled water, to include longer range coordination shells. With this, the trained neural network was able to properly predict the crystalline solid phases, the fluid phases and the amorphous phase for the pure CSW and CSW-alcohols mixtures with high efficiency. More than this, information about the phase populations, obtained from the network approach, can help verify if the phase transition is continuous or discontinuous, and also to interpret how the metastable amorphous region spreads along the stable high density fluid phase. These findings help to understand the behavior of supercooled polymorphic fluids and extend the comprehension of how amphiphilic solutes affect the phases behavior.

Semi-supervised learning for the study of structural formation in colloidal systems via image recognition

The analysis of the structural formation of colloidal systems using machine learning techniques has recently attracted much attention. In many of these studies, local bond-order parameters (LBOPs) were employed as descriptors, where such LBOPs are suitable mainly for the detection of crystal structures. On the other hand, image-based convolutional neural networks (CNNs) are quite effective in detecting not only crystals but also random structures, and the author demonstrated their efficiency in a previous paper. However, in supervised learning, it is difficult to obtain a correct result when there is an unexpected new phase that was unknown when training the CNN. In this paper, we propose a hybrid scheme that consists of supervised and unsupervised learning techniques, employing two different approaches: image-based CNN and generalized LBOP. The proposed method was applied to two-dimensional colloidal systems, and its efficiency was demonstrated.

From predictive modelling to machine learning and reverse engineering of colloidal self-assembly

An overwhelming diversity of colloidal building blocks with distinct sizes, materials and tunable interaction potentials are now available for colloidal self-assembly. The application space for materials composed of these building blocks is vast. To make progress in the rational design of new self-assembled materials, it is desirable to guide the experimental synthesis efforts by computational modelling. Here, we discuss computer simulation methods and strategies used for the design of soft materials created through bottom-up self-assembly of colloids and nanoparticles. We describe simulation techniques for investigating the self-assembly behaviour of colloidal suspensions, including crystal structure prediction methods, phase diagram calculations and enhanced sampling techniques, as well as their limitations. We also discuss the recent surge of interest in machine learning and reverse-engineering methods. Although their implementation in the colloidal realm is still in its infancy, we anticipate that these data-science tools offer new paradigms in understanding, predicting and (inverse) design of novel colloidal materials.

Disentangling Rotational Dynamics and Ordering Transitions in a System of Self-Organizing Protein Nanorods via Rotationally Invariant Latent Representations

The dynamics of complex ordering systems with active rotational degrees of freedom exemplified by protein self-assembly is explored using a machine learning workflow that combines deep learning-based semantic segmentation and rotationally invariant variational autoencoder-based analysis of orientation and shape evolution. The latter allows for disentanglement of the particle orientation from other degrees of freedom and compensates for lateral shifts. The disentangled representations in the latent space encode the rich spectrum of local transitions that can now be visualized and explored via continuous variables. The time dependence of ensemble averages allows insight into the time dynamics of the system and, in particular, illustrates the presence of the potential ordering transition. Finally, analysis of the latent variables along the single-particle trajectory allows tracing these parameters on a single-particle level. The proposed approach is expected to be universally applicable for the description of the imaging data in optical, scanning probe, and electron microscopy seeking to understand the dynamics of complex systems where rotations are a significant part of the process.

Characterising soft matter using machine learning

Machine learning is making a major impact in materials research. I review current progress across a selection of areas of ubiquitous soft matter. When applied to particle tracking, machine learning using convolution neural networks is providing impressive performance but there remain some significant problems to solve. Characterising ordered arrangements of particles is a huge challenge and machine learning has been deployed to create the description, perform the classification and tease out an interpretation using a wide array of techniques often with good success. In glass research, machine learning has proved decisive in quantifying very subtle correlations between the local structure around a site and the susceptibility towards a rearrangement event at that site. There are also beginning to be some impressive attempts to deploy machine learning in the design of composite soft materials. The discovery aspect of this new materials design meets the current interest in teaching algorithms to learn to extrapolate beyond the training data.

A structural study and its relation to dynamic heterogeneity in a polymer glass former

The relationship between structure and dynamical behavior (super-Arrhenius temperature dependence of relaxation time accompanied by heterogeneous dynamics) in glassy materials remains an open issue in the physics of condensed matter. The question of whether this dynamic phenomena have a thermodynamic origin or not still remains unanswered. In this work we analyze several dynamic and structural parameters in a polymer glass-former by means of molecular dynamics simulations. The results obtained in this work indicate that the structure does affect dynamic behavior, whereas structural conditioning becomes noticeable below the temperature at which the non-Arrhenius behavior manifests and increases as the system approaches the glass transition temperature. Moreover, we observed that the short-range order parameters are related to local dynamics at the single-particle level. These results reinforce the idea of a connection between the structure and dynamics and that could indicate the thermodynamic nature of glass transition.

Deep learning for characterizing the self-assembly of three-dimensional colloidal systems

Creating a systematic framework to characterize the structural states of colloidal self-assembly systems is crucial for unraveling the fundamental understanding of these systems' stochastic and non-linear behavior. The most accurate characterization methods create high-dimensional neighborhood graphs that may not provide useful information about structures unless these are well-defined reference crystalline structures. Dimensionality reduction methods are thus required to translate the neighborhood graphs into a low-dimensional space that can be easily interpreted and used to characterize non-reference structures. We investigate a framework for colloidal system state characterization that employs deep learning methods to reduce the dimensionality of neighborhood graphs. The framework next uses agglomerative hierarchical clustering techniques to partition the low-dimensional space and assign physically meaningful classifications to the resulting partitions. We first demonstrate the proposed colloidal self-assembly state characterization framework on a three-dimensional in silico system of 500 multi-flavored colloids that self-assemble under isothermal conditions. We next investigate the generalizability of the characterization framework by applying the framework to several independent self-assembly trajectories, including a three-dimensional in silico system of 2052 colloidal particles that undergo evaporation-induced self-assembly.

Machine learning for condensed matter physics

Condensed matter physics (CMP) seeks to understand the microscopic interactions of matter at the quantum and atomistic levels, and describes how these interactions result in both mesoscopic and macroscopic properties. CMP overlaps with many other important branches of science, such as chemistry, materials science, statistical physics, and high-performance computing. With the advancements in modern machine learning (ML) technology, a keen interest in applying these algorithms to further CMP research has created a compelling new area of research at the intersection of both fields. In this review, we aim to explore the main areas within CMP, which have successfully applied ML techniques to further research, such as the description and use of ML schemes for potential energy surfaces, the characterization of topological phases of matter in lattice systems, the prediction of phase transitions in off-lattice and atomistic simulations, the interpretation of ML theories with physics-inspired frameworks and the enhancement of simulation methods with ML algorithms. We also discuss in detail the main challenges and drawbacks of using ML methods on CMP problems, as well as some perspectives for future developments.

Autonomously revealing hidden local structures in supercooled liquids

Few questions in condensed matter science have proven as difficult to unravel as the interplay between structure and dynamics in supercooled liquids. To explore this link, much research has been devoted to pinpointing local structures and order parameters that correlate strongly with dynamics. Here we use an unsupervised machine learning algorithm to identify structural heterogeneities in three archetypical glass formers—without using any dynamical information. In each system, the unsupervised machine learning approach autonomously designs a purely structural order parameter within a single snapshot. Comparing the structural order parameter with the dynamics, we find strong correlations with the dynamical heterogeneities. Moreover, the structural characteristics linked to slow particles disappear further away from the glass transition. Our results demonstrate the power of machine learning techniques to detect structural patterns even in disordered systems, and provide a new way forward for unraveling the structural origins of the slow dynamics of glassy materials.

The origin of dynamical slowdown in disordered materials remains elusive, especially in the absence of obvious structural changes. Boattini et al. use unsupervised machine learning to reveal correlations between structural and dynamical heterogeneity in supercooled liquids.

Pattern detection in colloidal assembly: A mosaic of analysis techniques

Characterization of the morphology, identification of patterns and quantification of order encountered in colloidal assemblies is essential for several reasons. First of all, it is useful to compare different self-assembly methods and assess the influence of different process parameters on the final colloidal pattern. In addition, casting light on the structures formed by colloidal particles can help to get better insight into colloidal interactions and understand phase transitions. Finally, the growing interest in colloidal assemblies in materials science for practical applications going from optoelectronics to biosensing imposes a thorough characterization of the morphology of colloidal assemblies because of the intimate relationship between morphology and physical properties (e.g. optical and mechanical) of a material. Several image analysis techniques developed to investigate images (acquired via scanning electron microscopy, digital video microscopy and other imaging methods) provide variegated and complementary information on the colloidal structures under scrutiny. However, understanding how to use such image analysis tools to get information on the characteristics of the colloidal assemblies may represent a non-trivial task, because it requires the combination of approaches drawn from diverse disciplines such as image processing, computational geometry and computational topology and their application to a primarily physico-chemical process. Moreover, the lack of a systematic description of such analysis tools makes it difficult to select the ones more suitable for the features of the colloidal assembly under examination. In this review we provide a methodical and extensive description of real-space image analysis tools by explaining their principles and their application to the investigation of two-dimensional colloidal assemblies with different morphological characteristics.

GCIceNet: a graph convolutional network for accurate classification of water phases

We develop GCIceNet, which automatically generates machine-based order parameters for classifying the phases of water molecules via supervised and unsupervised learning with graph convolutional networks.