Programming patchy particles for materials assembly design.

Direct design of complex functional materials would revolutionize technologies ranging from printable organs to novel clean energy devices. However, even incremental steps toward designing functional materials have proven challenging. If the material is constructed from highly complex components, the design space of materials properties rapidly becomes too computationally expensive to search. On the other hand, very simple components such as uniform spherical particles are not powerful enough to capture rich functional behavior. Here, we introduce a differentiable materials design model with components that are simple enough to design yet powerful enough to capture complex materials properties: rigid bodies composed of spherical particles with directional interactions (patchy particles). We showcase the method with self-assembly designs ranging from open lattices to self-limiting clusters, all of which are notoriously challenging design goals to achieve using purely isotropic particles. By directly optimizing over the location and interaction of the patches on patchy particles using gradient descent, we dramatically reduce the computation time for finding the optimal building blocks.

Scaling deep learning for materials discovery.

Novel functional materials enable fundamental breakthroughs across technological applications from clean energy to information processing1-11. From microchips to batteries and photovoltaics, discovery of inorganic crystals has been bottlenecked by expensive trial-and-error approaches. Concurrently, deep-learning models for language, vision and biology have showcased emergent predictive capabilities with increasing data and computation12-14. Here we show that graph networks trained at scale can reach unprecedented levels of generalization, improving the efficiency of materials discovery by an order of magnitude. Building on 48,000 stable crystals identified in continuing studies15-17, improved efficiency enables the discovery of 2.2 million structures below the current convex hull, many of which escaped previous human chemical intuition. Our work represents an order-of-magnitude expansion in stable materials known to humanity. Stable discoveries that are on the final convex hull will be made available to screen for technological applications, as we demonstrate for layered materials and solid-electrolyte candidates. Of the stable structures, 736 have already been independently experimentally realized. The scale and diversity of hundreds of millions of first-principles calculations also unlock modelling capabilities for downstream applications, leading in particular to highly accurate and robust learned interatomic potentials that can be used in condensed-phase molecular-dynamics simulations and high-fidelity zero-shot prediction of ionic conductivity.

Learning molecular dynamics: predicting the dynamics of glasses by a machine learning simulator.

Many-body dynamics of atoms such as glass dynamics is generally governed by complex (and sometimes unknown) physics laws. This challenges the construction of atom dynamics simulations that both (i) capture the physics laws and (ii) run with little computation cost. Here, based on graph neural network (GNN), we introduce an observation-based graph network (OGN) framework to "bypass all physics laws" to simulate complex glass dynamics solely from their static structure. By taking the example of molecular dynamics (MD) simulations, we successfully apply the OGN to predict atom trajectories evolving up to a few hundred timesteps and ranging over different families of complex atomistic systems, which implies that the atom dynamics is largely encoded in their static structure in disordered phases and, furthermore, allows us to explore the capacity of OGN simulations that is potentially generic to many-body dynamics. Importantly, unlike traditional numerical simulations, the OGN simulations bypass the numerical constraint of small integration timestep by a multiplier of ≥5 to conserve energy and momentum until hundreds of timesteps, thus leapfrogging the execution speed of MD simulations for a modest timescale.

Designing self-assembling kinetics with differentiable statistical physics models.

The inverse problem of designing component interactions to target emergent structure is fundamental to numerous applications in biotechnology, materials science, and statistical physics. Equally important is the inverse problem of designing emergent kinetics, but this has received considerably less attention. Using recent advances in automatic differentiation, we show how kinetic pathways can be precisely designed by directly differentiating through statistical physics models, namely free energy calculations and molecular dynamics simulations. We consider two systems that are crucial to our understanding of structural self-assembly: bulk crystallization and small nanoclusters. In each case, we are able to assemble precise dynamical features. Using gradient information, we manipulate interactions among constituent particles to tune the rate at which these systems yield specific structures of interest. Moreover, we use this approach to learn nontrivial features about the high-dimensional design space, allowing us to accurately predict when multiple kinetic features can be simultaneously and independently controlled. These results provide a concrete and generalizable foundation for studying nonstructural self-assembly, including kinetic properties as well as other complex emergent properties, in a vast array of systems.

Machine learning determination of atomic dynamics at grain boundaries.

In polycrystalline materials, grain boundaries are sites of enhanced atomic motion, but the complexity of the atomic structures within a grain boundary network makes it difficult to link the structure and atomic dynamics. Here, we use a machine learning technique to establish a connection between local structure and dynamics of these materials. Following previous work on bulk glassy materials, we define a purely structural quantity (softness) that captures the propensity of an atom to rearrange. This approach correctly identifies crystalline regions, stacking faults, and twin boundaries as having low likelihood of atomic rearrangements while finding a large variability within high-energy grain boundaries. As has been found in glasses, the probability that atoms of a given softness will rearrange is nearly Arrhenius. This indicates a well-defined energy barrier as well as a well-defined prefactor for the Arrhenius form for atoms of a given softness. The decrease in the prefactor for low-softness atoms indicates that variations in entropy exhibit a dominant influence on the atomic dynamics in grain boundaries.

Disconnecting structure and dynamics in glassy thin films.

Nanometrically thin glassy films depart strikingly from the behavior of their bulk counterparts. We investigate whether the dynamical differences between a bulk and thin film polymeric glass former can be understood by differences in local microscopic structure. Machine learning methods have shown that local structure can serve as the foundation for successful, predictive models of particle rearrangement dynamics in bulk systems. By contrast, in thin glassy films, we find that particles at the center of the film and those near the surface are structurally indistinguishable despite exhibiting very different dynamics. Next, we show that structure-independent processes, already present in bulk systems and demonstrably different from simple facilitated dynamics, are crucial for understanding glassy dynamics in thin films. Our analysis suggests a picture of glassy dynamics in which two dynamical processes coexist, with relative strengths that depend on the distance from an interface. One of these processes depends on local structure and is unchanged throughout most of the film, while the other is purely Arrhenius, does not depend on local structure, and is strongly enhanced near the free surface of a film.

Prediction Errors of Molecular Machine Learning Models Lower than Hybrid DFT Error.

We investigate the impact of choosing regressors and molecular representations for the construction of fast machine learning (ML) models of 13 electronic ground-state properties of organic molecules. The performance of each regressor/representation/property combination is assessed using learning curves which report out-of-sample errors as a function of training set size with up to ∼118k distinct molecules. Molecular structures and properties at the hybrid density functional theory (DFT) level of theory come from the QM9 database [ Ramakrishnan et al. Sci. Data 2014 , 1 , 140022 ] and include enthalpies and free energies of atomization, HOMO/LUMO energies and gap, dipole moment, polarizability, zero point vibrational energy, heat capacity, and the highest fundamental vibrational frequency. Various molecular representations have been studied (Coulomb matrix, bag of bonds, BAML and ECFP4, molecular graphs (MG)), as well as newly developed distribution based variants including histograms of distances (HD), angles (HDA/MARAD), and dihedrals (HDAD). Regressors include linear models (Bayesian ridge regression (BR) and linear regression with elastic net regularization (EN)), random forest (RF), kernel ridge regression (KRR), and two types of neural networks, graph convolutions (GC) and gated graph networks (GG). Out-of sample errors are strongly dependent on the choice of representation and regressor and molecular property. Electronic properties are typically best accounted for by MG and GC, while energetic properties are better described by HDAD and KRR. The specific combinations with the lowest out-of-sample errors in the ∼118k training set size limit are (free) energies and enthalpies of atomization (HDAD/KRR), HOMO/LUMO eigenvalue and gap (MG/GC), dipole moment (MG/GC), static polarizability (MG/GG), zero point vibrational energy (HDAD/KRR), heat capacity at room temperature (HDAD/KRR), and highest fundamental vibrational frequency (BAML/RF). We present numerical evidence that ML model predictions deviate from DFT (B3LYP) less than DFT (B3LYP) deviates from experiment for all properties. Furthermore, out-of-sample prediction errors with respect to hybrid DFT reference are on par with, or close to, chemical accuracy. The results suggest that ML models could be more accurate than hybrid DFT if explicitly electron correlated quantum (or experimental) data were available.

Relationship between local structure and relaxation in out-of-equilibrium glassy systems.

The dynamical glass transition is typically taken to be the temperature at which a glassy liquid is no longer able to equilibrate on experimental timescales. Consequently, the physical properties of these systems just above or below the dynamical glass transition, such as viscosity, can change by many orders of magnitude over long periods of time following external perturbation. During this progress toward equilibrium, glassy systems exhibit a history dependence that has complicated their study. In previous work, we bridged the gap between structure and dynamics in glassy liquids above their dynamical glass transition temperatures by introducing a scalar field called "softness," a quantity obtained using machine-learning methods. Softness is designed to capture the hidden patterns in relative particle positions that correlate strongly with dynamical rearrangements of particle positions. Here we show that the out-of-equilibrium behavior of a model glass-forming system can be understood in terms of softness. To do this we first demonstrate that the evolution of behavior following a temperature quench is a primarily structural phenomenon: The structure changes considerably, but the relationship between structure and dynamics remains invariant. We then show that the relaxation time can be robustly computed from structure as quantified by softness, with the same relation holding both in equilibrium and as the system ages. Together, these results show that the history dependence of the relaxation time in glasses requires knowledge only of the softness in addition to the usual state variables.

Structural Properties of Defects in Glassy Liquids.

At zero temperature a disordered solid corresponds to a local minimum in the energy landscape. As the temperature is raised or the system is driven with a mechanical load, the system explores different minima via dynamical events in which particles rearrange their relative positions. We have shown recently that the dynamics of particle rearrangements are strongly correlated with a structural quantity associated with each particle, "softness", which we can identify using supervised machine learning. Particles of a given softness have a well-defined energy scale that governs local rearrangements; because of this property, softness greatly simplifies our understanding of glassy dynamics. Here we investigate the correlation of softness with other commonly used structural quantities, such as coordination number and local potential energy. We show that although softness strongly correlates with these properties, its predictive power for rearrangement dynamics is much higher. We introduce a useful metric for quantifying the quality of structural quantities as predictors of dynamics. We hope that, in the future, authors introducing new structural measures of dynamics will compare their proposals quantitatively to softness using this metric. We also show how softness correlations give insight into rearrangements. Finally, we explore the physical meaning of softness using unsupervised dimensionality reduction and reduced curve-fitting models, and show that softness can be recast in a form that is amenable to analytical treatment.

Strain fluctuations and elastic moduli in disordered solids.

Recently there has been a surge in interest in using video-microscopy techniques to infer the local mechanical properties of disordered solids. One common approach is to minimize the difference between particle vibrational displacements in a local coarse-graining volume and the displacements that would result from a best-fit affine deformation. Effective moduli are then inferred under the assumption that the components of this best-fit affine deformation tensor have a Boltzmann distribution. In this paper, we combine theoretical arguments with experimental and simulation data to demonstrate that the above does not reveal information about the true elastic moduli of jammed packings and colloidal glasses.

Predicting plasticity with soft vibrational modes: from dislocations to glasses.

We show that quasilocalized low-frequency modes in the vibrational spectrum can be used to construct soft spots, or regions vulnerable to rearrangement, which serve as a universal tool for the identification of flow defects in solids. We show that soft spots not only encode spatial information, via their location, but also directional information, via directors for particles within each soft spot. Single crystals with isolated dislocations exhibit low-frequency phonon modes that localize at the core, and their polarization pattern predicts the motion of atoms during elementary dislocation glide in two and three dimensions in exquisite detail. Even in polycrystals and disordered solids, we find that the directors associated with particles in soft spots are highly correlated with the direction of particle displacements in rearrangements.

Phonon dispersion and elastic moduli of two-dimensional disordered colloidal packings of soft particles with frictional interactions.

Particle tracking and displacement covariance matrix techniques are employed to investigate the phonon dispersion relations of two-dimensional colloidal glasses composed of soft, thermoresponsive microgel particles whose temperature-sensitive size permits in situ variation of particle packing fraction. Bulk, B, and shear, G, moduli of the colloidal glasses are extracted from the dispersion relations as a function of packing fraction, and variation of the ratio G/B with packing fraction is found to agree quantitatively with predictions for jammed packings of frictional soft particles. In addition, G and B individually agree with numerical predictions for frictional particles. This remarkable level of agreement enabled us to extract an energy scale for the interparticle interaction from the individual elastic constants and to derive an approximate estimate for the interparticle friction coefficient.

Phonons in two-dimensional soft colloidal crystals.

The vibrational modes of pristine and polycrystalline monolayer colloidal crystals composed of thermosensitive microgel particles are measured using video microscopy and covariance matrix analysis. At low frequencies, the Debye relation for two-dimensional harmonic crystals is observed in both crystal types; at higher frequencies, evidence for van Hove singularities in the phonon density of states is significantly smeared out by experimental noise and measurement statistics. The effects of these errors are analyzed using numerical simulations. We introduce methods to correct for these limitations, which can be applied to disordered systems as well as crystalline ones, and we show that application of the error correction procedure to the experimental data leads to more pronounced van Hove singularities in the pristine crystal. Finally, quasilocalized low-frequency modes in polycrystalline two-dimensional colloidal crystals are identified and demonstrated to correlate with structural defects such as dislocations, suggesting that quasilocalized low-frequency phonon modes may be used to identify local regions vulnerable to rearrangements in crystalline as well as amorphous solids.