Unsupervised hyperspectral stimulated Raman microscopy image enhancement: denoising and segmentation via one-shot deep learning.

Hyperspectral stimulated Raman scattering (SRS) microscopy is a label-free technique for biomedical and mineralogical imaging which can suffer from low signal-to-noise ratios. Here we demonstrate the use of an unsupervised deep learning neural network for rapid and automatic denoising of SRS images: UHRED (Unsupervised Hyperspectral Resolution Enhancement and Denoising). UHRED is capable of "one-shot" learning; only one hyperspectral image is needed, with no requirements for training on previously labelled datasets or images. Furthermore, by applying a k-means clustering algorithm to the processed data, we demonstrate automatic, unsupervised image segmentation, yielding, without prior knowledge of the sample, intuitive chemical species maps, as shown here for a lithium ore sample.

Neuroevolutionary Learning of Particles and Protocols for Self-Assembly.

Within simulations of molecules deposited on a surface we show that neuroevolutionary learning can design particles and time-dependent protocols to promote self-assembly, without input from physical concepts such as thermal equilibrium or mechanical stability and without prior knowledge of candidate or competing structures. The learning algorithm is capable of both directed and exploratory design: it can assemble a material with a user-defined property, or search for novelty in the space of specified order parameters. In the latter mode it explores the space of what can be made, rather than the space of structures that are low in energy but not necessarily kinetically accessible.

Dynamical Large Deviations of Two-Dimensional Kinetically Constrained Models Using a Neural-Network State Ansatz.

We use a neural-network ansatz originally designed for the variational optimization of quantum systems to study dynamical large deviations in classical ones. We use recurrent neural networks to describe the large deviations of the dynamical activity of model glasses, kinetically constrained models in two dimensions. We present the first finite size-scaling analysis of the large-deviation functions of the two-dimensional Fredrickson-Andersen model, and explore the spatial structure of the high-activity sector of the South-or-East model. These results provide a new route to the study of dynamical large-deviation functions, and highlight the broad applicability of the neural-network state ansatz across domains in physics.

Neural evolution structure generation: High entropy alloys.

We propose a neural evolution structure (NES) generation methodology combining artificial neural networks and evolutionary algorithms to generate high entropy alloy structures. Our inverse design approach is based on pair distribution functions and atomic properties and allows one to train a model on smaller unit cells and then generate a larger cell. With a speed-up factor of ∼1000 with respect to the special quasi-random structures (SQSs), the NESs dramatically reduce computational costs and time, making possible the generation of very large structures (over 40 000 atoms) in few hours. Additionally, unlike the SQSs, the same model can be used to generate multiple structures with the same fractional composition.

Evolutionary reinforcement learning of dynamical large deviations.

We show how to bound and calculate the likelihood of dynamical large deviations using evolutionary reinforcement learning. An agent, a stochastic model, propagates a continuous-time Monte Carlo trajectory and receives a reward conditioned upon the values of certain path-extensive quantities. Evolution produces progressively fitter agents, potentially allowing the calculation of a piece of a large-deviation rate function for a particular model and path-extensive quantity. For models with small state spaces, the evolutionary process acts directly on rates, and for models with large state spaces, the process acts on the weights of a neural network that parameterizes the model's rates. This approach shows how path-extensive physics problems can be considered within a framework widely used in machine learning.

Emergent rhombus tilings from molecular interactions with M-fold rotational symmetry.

We show that model molecules with particular rotational symmetries can self-assemble into network structures equivalent to rhombus tilings. This assembly happens in an emergent way, in the sense that molecules spontaneously select irregular fourfold local coordination from a larger set of possible local binding geometries. The existence of such networks can be rationalized by simple geometrical arguments, but the same arguments do not guarantee a network's spontaneous self-assembly. This class of structures must in certain regimes of parameter space be able to reconfigure into networks equivalent to triangular tilings.

A density functional tight binding model with an extended basis set and three-body repulsion for hydrogen under extreme thermodynamic conditions.

We present a new DFTB-p3b density functional tight binding model for hydrogen at extremely high pressures and temperatures, which includes a polarizable basis set (p) and a three-body environmentally dependent repulsive potential (3b). We find that use of an extended basis set is necessary under dissociated liquid conditions to account for the substantial p-orbital character of the electronic states around the Fermi energy. The repulsive energy is determined through comparison to cold curve pressures computed from density functional theory (DFT) for the hexagonal close-packed solid, as well as pressures from thermally equilibrated DFT-MD simulations of the liquid phase. In particular, we observe improved agreement in our DFTB-p3b model with previous theoretical and experimental results for the shock Hugoniot of hydrogen up to 100 GPa and 25000 K, compared to a standard DFTB model using pairwise interactions and an s-orbital basis set, only. The DFTB-p3b approach discussed here provides a general method to extend the DFTB method for a wide variety of materials over a significantly larger range of thermodynamic conditions than previously possible.

Learning stochastic dynamics and predicting emergent behavior using transformers.

We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior under conditions not observed during training. We consider a lattice model of active matter undergoing continuous-time Monte Carlo dynamics, simulated at a density at which its steady state comprises small, dispersed clusters. We train a neural network called a transformer on a single trajectory of the model. The transformer, which we show has the capacity to represent dynamical rules that are numerous and nonlocal, learns that the dynamics of this model consists of a small number of processes. Forward-propagated trajectories of the trained transformer, at densities not encountered during training, exhibit motility-induced phase separation and so predict the existence of a nonequilibrium phase transition. Transformers have the flexibility to learn dynamical rules from observation without explicit enumeration of rates or coarse-graining of configuration space, and so the procedure used here can be applied to a wide range of physical systems, including those with large and complex dynamical generators.

Efficient determination of Born-effective charges, LO-TO splitting, and Raman tensors of solids with a real-space atom-centered deep learning approach.

We introduce a deep neural network (DNN) framework called theReal-spaceAtomicDecompositionNETwork (radnet), which is capable of making accurate predictions of polarization and of electronic dielectric permittivity tensors in solids and aims to address limitations of previously available machine learning models for Raman predictions in periodic systems. This framework builds on previous, atom-centered approaches while utilizing deep convolutional neural networks. We report excellent accuracies on direct predictions for two prototypical examples: GaAs and BN. We then use automatic differentiation to efficiently calculate the Born-effective charges, longitudinal optical-transverse optical (LO-TO) splitting frequencies, and Raman tensors of these materials. We compute the Raman spectra, and find agreement withab initioresults. Lastly, we explore ways to generalize the predictions of polarization while taking into account periodic boundary conditions and symmetries.

Competing thermodynamic and dynamic factors select molecular assemblies on a gold surface.

Controlling the self-assembly of surface-adsorbed molecules into nanostructures requires understanding physical mechanisms that act across multiple length and time scales. By combining scanning tunneling microscopy with hierarchical ab initio and statistical mechanical modeling of 1,4-substituted benzenediamine (BDA) molecules adsorbed on a gold (111) surface, we demonstrate that apparently simple nanostructures are selected by a subtle competition of thermodynamics and dynamics. Of the collection of possible BDA nanostructures mechanically stabilized by hydrogen bonding, the interplay of intermolecular forces, surface modulation, and assembly dynamics select at low temperature a particular subset: low free energy oriented linear chains of monomers and high free energy branched chains.

Prebiotic chemistry within a simple impacting icy mixture.

We present results of prebiotic organic synthesis in shock compressed mixtures of simple ices from quantum molecular dynamics (MD) simulations extended to close to equilibrium time scales. Given the likelihood of an inhospitable prebiotic atmosphere on early Earth, it is possible that impact processes of comets or other icy bodies were a source of prebiotic chemical compounds on the primitive planet. We observe that moderate shock pressures and temperatures within a CO2-rich icy mixture (36 GPa and 2800 K) produce a number of nitrogen containing heterocycles, which dissociate to form functionalized aromatic hydrocarbons upon expansion and cooling to ambient conditions. In contrast, higher shock conditions (48-60 GPa, 3700-4800 K) resulted in the synthesis of long carbon-chain molecules, CH4, and formaldehyde. All shock compression simulations at these conditions have produced significant quantities of simple C-N bonded compounds such as HCN, HNC, and HNCO upon expansion and cooling to ambient conditions. Our results elucidate a mechanism for impact synthesis of prebiotic molecules at realistic impact conditions that is independent of external constraints such as the presence of a catalyst, illuminating UV radiation, or pre-existing conditions on a planet.

Cellular automata can classify data by inducing trajectory phase coexistence.

We show that cellular automata can classify data by inducing a form of dynamical phase coexistence. We use Monte Carlo methods to search for general two-dimensional deterministic automata that classify images on the basis of activity, the number of state changes that occur in a trajectory initiated from the image. When the number of time steps of the automaton is a trainable parameter, the search scheme identifies automata that generate a population of dynamical trajectories displaying high or low activity, depending on initial conditions. Automata of this nature behave as nonlinear activation functions with an output that is effectively binary, resembling an emergent version of a spiking neuron.

Random and ordered phases of off-lattice rhombus tiles.

We study the covering of the plane by nonoverlapping rhombus tiles, a problem well studied only in the limiting case of dimer coverings of regular lattices. We go beyond this limit by allowing tiles to take any position and orientation on the plane, to be of irregular shape, and to possess different types of attractive interactions. Using extensive numerical simulations, we show that at large tile densities there is a phase transition from a fluid of rhombus tiles to a solid packing with broken rotational symmetry. We observe self-assembly of broken-symmetry phases, even at low densities, in the presence of attractive tile-tile interactions. Depending on the tile shape and interactions, the solid phase can be random, possessing critical orientational fluctuations, or crystalline. Our results suggest strategies for controlling tiling order in experiments involving "molecular rhombi."

Machine Learning Diffusion Monte Carlo Energies.

We present two machine learning methodologies that are capable of predicting diffusion Monte Carlo (DMC) energies with small data sets (≈60 DMC calculations in total). The first uses voxel deep neural networks (VDNNs) to predict DMC energy densities using Kohn-Sham density functional theory (DFT) electron densities as input. The second uses kernel ridge regression (KRR) to predict atomic contributions to the DMC total energy using atomic environment vectors as input (we used atom-centered symmetry functions, atomic environment vectors from the ANI models, and smooth overlap of atomic positions). We first compare the methodologies on pristine graphene lattices, where we find that the KRR methodology performs best in comparison to gradient boosted decision trees, random forest, Gaussian process regression, and multilayer perceptrons. In addition, KRR outperforms VDNNs by an order of magnitude. Afterward, we study the generalizability of KRR to predict the energy barrier associated with a Stone-Wales defect. Lastly, we move from 2D to 3D materials and use KRR to predict total energies of liquid water. In all cases, we find that the KRR models are more accurate than Kohn-Sham DFT and all mean absolute errors are less than chemical accuracy.

Toward Orbital-Free Density Functional Theory with Small Data Sets and Deep Learning.

We use voxel deep neural networks to predict energy densities and functional derivatives of electron kinetic energies for the Thomas-Fermi model and Kohn-Sham density functional theory calculations. We show that the ground-state electron density can be found via direct minimization for a graphene lattice without any projection scheme using a voxel deep neural network trained with the Thomas-Fermi model. Additionally, we predict the kinetic energy of a graphene lattice within chemical accuracy after training from only two Kohn-Sham density functional theory (DFT) calculations. We identify an important sampling issue inherent in Kohn-Sham DFT calculations and propose future work to rectify this problem. Furthermore, we demonstrate an alternative, functional derivative-free, Monte Carlo based orbital-free density functional theory algorithm to calculate an accurate two-electron density in a double inverted Gaussian potential with a machine-learned kinetic energy functional.

High-Throughput Evaluation of Emission and Structure in Reduced-Dimensional Perovskites.

High-throughput experimentation (HTE) seeks to accelerate the exploration of materials space by uniting robotics, combinatorial methods, and parallel processing. HTE is particularly relevant to metal halide perovskites (MHPs), a diverse class of optoelectronic materials with a large chemical space. Here we develop an HTE workflow to synthesize and characterize light-emitting MHP single crystals, allowing us to generate the first reported data set of experimentally derived photoluminescence spectra for low-dimensional MHPs. We leverage the accelerated workflow to optimize the synthesis and emission of a new MHP, methoxy-phenethylammonium lead iodide ((4-MeO-PEAI)2-PbI2). We then synthesize 16 000 MHP single crystals and measure their photoluminescence to study the effects of synthesis parameters and compositional engineering on the emission intensity of 54 distinct MHPs: we achieve an acceleration factor of more than 100 times over previously reported HTE MHP synthesis and characterization methods. Using insights derived from this analysis, we screen an existing database for new, potentially emissive MHPs. On the basis of the Tanimoto similarity of the bright available emitters, we present our top candidates for future exploration. As a proof of concept, we use one of these (3,4-difluorophenylmethanamine) to synthesize an MHP which we find has a photoluminescence quantum yield of 10%.

Electronic level alignment at a metal-molecule interface from a short-range hybrid functional.

Hybrid functionals often exhibit a marked improvement over semi-local functionals in the description of the electronic structure of organic materials. Because short-range hybrid functionals, notably the Heyd-Scuseria-Ernzerhof (HSE) functional, can also describe the electronic structure of metals reasonably well, it is interesting to examine to which extent they can correctly describe the electronic structure at metal-organic interfaces. Here, we address this question by comparing HSE calculations with many-body perturbation theory calculations in the GW approximation, or with experimental photoemission data, for two prototypical systems: benzene on graphite and benzene diamine on gold. For both cases, we find that while HSE yields results that are somewhat closer to experiment than those of semi-local functionals, the HSE prediction is still lacking quantitatively by ∼1 eV. We show that this quantitative failure arises because HSE does not correctly capture the fundamental gap of the organic or its renormalization by the metal. These discrepancies are traced back to missing long-range exchange and correlation components, an explanation which applies to any conventional or short-range hybrid functional.

Correspondence between neuroevolution and gradient descent.

We show analytically that training a neural network by conditioned stochastic mutation or neuroevolution of its weights is equivalent, in the limit of small mutations, to gradient descent on the loss function in the presence of Gaussian white noise. Averaged over independent realizations of the learning process, neuroevolution is equivalent to gradient descent on the loss function. We use numerical simulation to show that this correspondence can be observed for finite mutations, for shallow and deep neural networks. Our results provide a connection between two families of neural-network training methods that are usually considered to be fundamentally different.

Optimizing thermodynamic trajectories using evolutionary and gradient-based reinforcement learning.

Using a model heat engine, we show that neural-network-based reinforcement learning can identify thermodynamic trajectories of maximal efficiency. We consider both gradient and gradient-free reinforcement learning. We use an evolutionary learning algorithm to evolve a population of neural networks, subject to a directive to maximize the efficiency of a trajectory composed of a set of elementary thermodynamic processes; the resulting networks learn to carry out the maximally efficient Carnot, Stirling, or Otto cycles. When given an additional irreversible process, this evolutionary scheme learns a previously unknown thermodynamic cycle. Gradient-based reinforcement learning is able to learn the Stirling cycle, whereas an evolutionary approach achieves the optimal Carnot cycle. Our results show how the reinforcement learning strategies developed for game playing can be applied to solve physical problems conditioned upon path-extensive order parameters.