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We use Monte Carlo and genetic algorithms to train neural-network feedback-control protocols for simulated fluctuating nanosystems. These protocols convert the information obtained by the feedback process into heat or work, allowing the extraction of work from a colloidal particle pulled by an optical trap and the absorption of entropy by an Ising model undergoing magnetization reversal. The learning framework requires no prior knowledge of the system, depends only upon measurements that are accessible experimentally, and scales to systems of considerable complexity. It could be used in the laboratory to learn protocols for fluctuating nanosystems that convert measurement information into stored work or heat.

Exact analytic calculation shows that optimal control protocols for passive molecular systems often involve rapid variations and discontinuities. However, similar analytic baselines are not generally available for active-matter systems, because it is more difficult to treat active systems exactly. Here we use machine learning to derive efficient control protocols for active-matter systems, and find that they are characterized by sharp features similar to those seen in passive systems. We show that it is possible to learn protocols that effect fast and efficient state-to-state transformations in simulation models of active particles by encoding the protocol in the form of a neural network. We use evolutionary methods to identify protocols that take active particles from one steady state to another, as quickly as possible or with as little energy expended as possible. Our results show that protocols identified by a flexible neural-network ansatz, which allows the optimization of multiple control parameters and the emergence of sharp features, are more efficient than protocols derived recently by constrained analytical methods. Our learning scheme is straightforward to use in experiment, suggesting a way of designing protocols for the efficient manipulation of active matter in the laboratory. Exact analytic calculation shows that optimal control protocols for passive molecular systems often involve rapid variations and discontinuities. However, similar analytic baselines are not generally available for active-matter systems, because it is more difficult to treat active systems exactly. Here, the authors use machine learning to derive efficient control protocols for active-matter systems, and find that they are characterized by sharp features similar to those seen in passive systems.

We present the design for a thermodynamic computer that can perform arbitrary nonlinear calculations in or out of equilibrium. Simple thermodynamic circuits, fluctuating degrees of freedom in contact with a thermal bath and confined by a quartic potential, display an activity that is a nonlinear function of their input. Such circuits can therefore be regarded as thermodynamic neurons, and can serve as the building blocks of networked structures that act as thermodynamic neural networks, universal function approximators whose operation is powered by thermal fluctuations. We simulate a digital model of a thermodynamic neural network, and show that its parameters can be adjusted by genetic algorithm to perform nonlinear calculations at specified observation times, regardless of whether the system has attained thermal equilibrium. This work expands the field of thermodynamic computing beyond the regime of thermal equilibrium, enabling fully nonlinear computations, analogous to those performed by classical neural networks, at specified observation times. To date, thermodynamic computers have been designed to work in thermal equilibrium. Here, the authors show that thermodynamic circuits can perform nonlinear computations, similar to those performed by neural networks, and do so at a specified observation time, whether in or out of equilibrium.

A conceptually simple way to classify images is to directly compare test-set data and training-set data. The accuracy of this approach is limited by the method of comparison used, and by the extent to which the training-set data cover configuration space. Here we show that this coverage can be substantially increased using coarse-graining (replacing groups of images by their centroids) and stochastic sampling (using distinct sets of centroids in combination). We use the MNIST and Fashion-MNIST data sets to show that a principled coarse-graining algorithm can convert training images into fewer image centroids without loss of accuracy of classification of test-set images by nearest-neighbor classification. Distinct batches of centroids can be used in combination as a means of stochastically sampling configuration space, and can classify test-set data more accurately than can the unaltered training set. On the MNIST and Fashion-MNIST data sets this approach converts nearest-neighbor classification from a mid-ranking- to an upper-ranking member of the set of classical machine-learning techniques.

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. Learning the dynamics governing a simulation or experiment usually requires coarse graining or projection, as the number of transition rates typically grows exponentially with system size. The authors show that transformers, neural networks introduced initially for natural language processing, can be used to parameterize the dynamics of large systems without coarse graining.

The growth of colloidal nanocrystal architectures by nanoparticle attachment is frequently reported as an alternative to the conventional growth by monomer attachment. However, the mechanism whereby nanoparticle attachment proceeds microscopically remains unclear. We report real-time transmission electron microscopy (TEM) imaging of the solution growth of Pt₃Fe nanorods from nanoparticle building blocks. Observations revealed growth of winding polycrystalline nanoparticle chains by shape-directed nanoparticle attachment followed by straightening and orientation and shape corrections to yield single-crystal nanorods. Tracking nanoparticle growth trajectories allowed us to distinguish the force fields exerted by single nanoparticles and nanoparticle chains. Such quantification of nanoparticle interaction and understanding the growth pathways are important for the design of hierarchical nanomaterials and controlling nanocrystal self-assembly for functional devices.

Crystals grow in a number a ways, including pathways involving the assembly of other particles and multi-ion complexes. De Yoreo et al. review the mounting evidence for these nonclassical pathways from new observational and computational techniques, and the thermodynamic basis for these growth mechanisms. Developing predictive models for these crystal growth and nucleation pathways will improve materials synthesis strategies. These approaches will also improve fundamental understanding of natural processes such as biomineralization and trace element cycling in aquatic ecosystems. Science , this issue 10.1126/science.aaa6760 Materials nucleate and grow by the assembly of small particles and multi-ion complexes. Field and laboratory observations show that crystals commonly form by the addition and attachment of particles that range from multi-ion complexes to fully formed nanoparticles. The particles involved in these nonclassical pathways to crystallization are diverse, in contrast to classical models that consider only the addition of monomeric chemical species. We review progress toward understanding crystal growth by particle-attachment processes and show that multiple pathways result from the interplay of free-energy landscapes and reaction dynamics. Much remains unknown about the fundamental aspects, particularly the relationships between solution structure, interfacial forces, and particle motion. Developing a predictive description that connects molecular details to ensemble behavior will require revisiting long-standing interpretations of crystal formation in synthetic systems, biominerals, and patterns of mineralization in natural environments.

NRC publication: Yes

Some peptoids—synthetic structural relatives of polypeptides—can assemble into two-dimensional nanometre-scale sheets; simulations and experimental measurements show that these nanosheets contain a motif unique to peptoids, namely zigzag Σ-strands, which interlock and enable the nanosheets to extend in two dimensions only. Bioengineering promise of peptoid nanosheets Peptoids are biomimetic peptide-like oligomers, some of which can assemble into two-dimensional bilayer nanosheets. Now Stephen Whitelam and colleagues present simulations and structural analyses of this recently discovered form. They find that the sheets contain a motif unique to peptoids, zigzag 'Σ-strands', that interlock and enable the assemblies to extend in two dimensions only. The resulting Σ-sheets are analogous to the α-helices and β-sheets found in proteins but are comprised of two distinct rotational states that allow the polymer chains to resist twist so that the nanosheets remain planar over a macroscopic extent. This work could pave the way to rationally designed nanosheets and extended nanomaterials incorporating protein-like functions. A promising route to the synthesis of protein-mimetic materials that are capable of complex functions, such as molecular recognition and catalysis, is provided by sequence-defined peptoid polymers 1 , 2 —structural relatives of biologically occurring polypeptides. Peptoids, which are relatively non-toxic and resistant to degradation 3 , can fold into defined structures through a combination of sequence-dependent interactions 3 , 4 , 5 , 6 , 7 , 8 . However, the range of possible structures that are accessible to peptoids and other biological mimetics is unknown, and our ability to design protein-like architectures from these polymer classes is limited 9 . Here we use molecular-dynamics simulations, together with scattering and microscopy data, to determine the atomic-resolution structure of the recently discovered peptoid nanosheet, an ordered supramolecular assembly that extends macroscopically in only two dimensions. Our simulations show that nanosheets are structurally and dynamically heterogeneous, can be formed only from peptoids of certain lengths, and are potentially porous to water and ions. Moreover, their formation is enabled by the peptoids’ adoption of a secondary structure that is not seen in the natural world. This structure, a zigzag pattern that we call a Σ(‘sigma’)-strand, results from the ability of adjacent backbone monomers to adopt opposed rotational states, thereby allowing the backbone to remain linear and untwisted. Linear backbones tiled in a brick-like way form an extended two-dimensional nanostructure, the Σ-sheet. The binary rotational-state motif of the Σ-strand is not seen in regular protein structures, which are usually built from one type of rotational state. We also show that the concept of building regular structures from multiple rotational states can be generalized beyond the peptoid nanosheet system.

A quantitative understanding of nanocrystal phase transformations would enable more efficient energy conversion and catalysis, but has been hindered by difficulties in directly monitoring well-characterized nanoscale systems in reactive environments. We present a new in situ luminescence-based probe enabling direct quantification of nanocrystal phase transformations, applied here to the hydriding transformation of palladium nanocrystals. Our approach reveals the intrinsic kinetics and thermodynamics of nanocrystal phase transformations, eliminating complications of substrate strain, ligand effects and external signal transducers. Clear size-dependent trends emerge in nanocrystals long accepted to be bulk-like in behaviour. Statistical mechanical simulations show these trends to be a consequence of nanoconfinement of a thermally driven, first-order phase transition: near the phase boundary, critical nuclei of the new phase are comparable in size to the nanocrystal itself. Transformation rates are then unavoidably governed by nanocrystal dimensions. Our results provide a general framework for understanding how nanoconfinement fundamentally impacts broad classes of thermally driven solid-state phase transformations relevant to hydrogen storage, catalysis, batteries and fuel cells. Although quantitative understanding of nanocrystal phase transformations is important for efficient energy conversion and catalysis, difficulties in directly monitoring nanoscale systems in reactive environments remain. Direct quantification of hydriding transformations in palladium nanocrystals now clearly reveals that the transformation rates are governed by nanocrystal dimensions.