Directed aging, memory, and nature's greed

Training allostery-inspired mechanical response in disordered elastic networks

Disordered elastic networks are a model material system in which it is possible to achieve tunable and trainable functions. This work investigates the modification of local mechanical properties in disordered networks inspired by allosteric interactions in proteins: applying strain locally to a set of source nodes triggers a strain response at a distant set of target nodes. This is demonstrated first by using directed aging to modify the existing mechanical coupling between pairs of distant source and target nodes, and later as a means for inducing coupling between formerly isolated source-target pairs. The experimental results are compared with those predicted by simulations.

Physical Networks Become What They Learn

Physical networks can develop tuned responses, or functions, by design, by evolution, or by learning via local rules. In all of these cases, tunable degrees of freedom characterizing internal interactions are modified to lower a cost penalizing deviations from desired outputs. An important class of such networks follows dynamics that minimize a global physical quantity, or Lyapunov function, with respect to physical degrees of freedom. In such networks, learning is a "double optimization" process in which two quantities, one defined by the task and the other prescribed by physics, are minimized with respect to different but coupled sets of variables. Here, we show how this learning process couples the high-dimensional "cost landscape" to the "physical landscape," linking the physical and cost Hessian matrices. Physical responses of trained networks to random perturbations thus reveal the functions to which they were tuned. Our results, illustrated using electrical networks with adaptable resistors, are generic to networks that perform tasks in the linear response regime.

Kovacs-like memory effect in a sheared colloidal glass: role of non-affine flows

Memory effect reflects a system's ability to encode, retain and retrieve information about its past. Such effects are essentially an out-of-equilibrium phenomenon providing insight into the complex structural and dynamical behavior of the system. Kovacs effect is one such memory effect that is traditionally associated with thermal history. Although studies on the Kovacs-like memory effect have been extended to mechanical perturbations such as compression-decompression, whether such effects can also be observed under volume-conserving perturbations like shear, remains unclear. Combining experiments, simulations and linear response theory we demonstrate Kovacs-like memory effect in a sheared colloidal glass. Moreover, we explore the influence of non-linear perturbations and establish a correlation between the deviation from linear response prediction and microscopic non-affine flows generated due to such large deformations in affecting the memory effect. Our study not only extends Kovacs-like memory effect in the domain of volume-conserving mechanical perturbations, it also highlights the importance of the nature of underlying microscopic flows in controlling the bulk stress relaxation, affecting the Kovacs-like memory effect in amorphous materials.

Temporal Contrastive Learning through implicit non-equilibrium memory

The backpropagation method has enabled transformative uses of neural networks. Alternatively, for energy-based models, local learning methods involving only nearby neurons offer benefits in terms of decentralized training, and allow for the possibility of learning in computationally-constrained substrates. One class of local learning methods contrasts the desired, clamped behavior with spontaneous, free behavior. However, directly contrasting free and clamped behaviors requires explicit memory. Here, we introduce 'Temporal Contrastive Learning', an approach that uses integral feedback in each learning degree of freedom to provide a simple form of implicit non-equilibrium memory. During training, free and clamped behaviors are shown in a sawtooth-like protocol over time. When combined with integral feedback dynamics, these alternating temporal protocols generate an implicit memory necessary for comparing free and clamped behaviors, broadening the range of physical and biological systems capable of contrastive learning. Finally, we show that non-equilibrium dissipation improves learning quality and determine a Landauer-like energy cost of contrastive learning through physical dynamics.

Controlling multistimuli elastic response by bistable micromodules

Controlling the elastic response of materials to multiple stimuli is a key prerequisite for the design of adaptive soft matter, e.g., for applications in medicine or soft robotics. Here, we discuss a statistical mechanics model in which the nonlinear elastic response is governed by mechanically coupled bistable micromodules which can be switched by external stimuli. Exact analytical solutions show complex stimuli-mediated, nonlinear stiffening/softening responses tuneable by the microscopic switching parameters. Importantly, we report up to two maxima in the softness (compliance) originating from cooperative transitions and show how to control their existence and properties. We demonstrate the usefulness of the model by fitting it to experimental extension-force data on various scales. We further illustrate how to explore the entire nonlinear response map as a function of multiple stimuli, utilizing distinct pathways to either cancel/reset or amplify the elastic responses through a combination of these stimuli. Our analysis should be useful for the design of nonlinear elasticity, e.g., in bistable microgel networks or mechanical metamaterials.

Harnessing plasticity in sequential metamaterials for ideal shock absorption

Mechanical metamaterials exhibit interesting properties such as high stiffness at low density1-3, enhanced energy absorption3,4, shape morphing5-7, sequential deformations8-11, auxeticity12-14 and robust waveguiding15,16. Until now, metamaterial design has primarily relied on geometry, and materials nonlinearities such as viscoelasticity, fracture and plasticity have been largely left out of the design rationale. In fact, plastic deformations have been traditionally seen as a failure mode and thereby carefully avoided1,3,17,18. Here we embrace plasticity instead and discover a delicate balance between plasticity and buckling instability, which we term 'yield buckling'. We exploit yield buckling to design metamaterials that buckle sequentially in an arbitrary large sequence of steps whilst keeping a load-bearing capacity. We make use of sequential yield buckling to create metamaterials that combine stiffness and dissipation-two properties that are usually incompatible-and that can be used several times. Hence, our metamaterials exhibit superior shock-absorption performance. Our findings add plasticity to the metamaterial toolbox and make mechanical metamaterials a burgeoning technology with serious potential for mass production.

Training physical matter to matter

Biological systems offer a great many examples of how sophisticated, highly adapted behavior can emerge from training. Here we discuss how training might be used to impart similarly adaptive properties in physical matter. As a special form of materials processing, training differs in important ways from standard approaches of obtaining sought after material properties. In particular, rather than designing or programming the local configurations and interactions of constituents, training uses externally applied stimuli to evolve material properties. This makes it possible to obtain different functionalities from the same starting material (pluripotency). Furthermore, training evolves a material in situ or under conditions similar to those during the intended use; thus, material performance can improve rather than degrade over time. We discuss requirements for trainability, outline recently developed training strategies for creating soft materials with multiple, targeted and adaptable functionalities, and provide examples where the concept of training has been applied to materials on length scales from the molecular to the macroscopic.

Machine learning without a processor: Emergent learning in a nonlinear analog network

Standard deep learning algorithms require differentiating large nonlinear networks, a process that is slow and power-hungry. Electronic contrastive local learning networks (CLLNs) offer potentially fast, efficient, and fault-tolerant hardware for analog machine learning, but existing implementations are linear, severely limiting their capabilities. These systems differ significantly from artificial neural networks as well as the brain, so the feasibility and utility of incorporating nonlinear elements have not been explored. Here, we introduce a nonlinear CLLN-an analog electronic network made of self-adjusting nonlinear resistive elements based on transistors. We demonstrate that the system learns tasks unachievable in linear systems, including XOR (exclusive or) and nonlinear regression, without a computer. We find our decentralized system reduces modes of training error in order (mean, slope, curvature), similar to spectral bias in artificial neural networks. The circuitry is robust to damage, retrainable in seconds, and performs learned tasks in microseconds while dissipating only picojoules of energy across each transistor. This suggests enormous potential for fast, low-power computing in edge systems like sensors, robotic controllers, and medical devices, as well as manufacturability at scale for performing and studying emergent learning.

The fluidic memristor as a collective phenomenon in elastohydrodynamic networks

Fluid flow networks are ubiquitous and can be found in a broad range of contexts, from human-made systems such as water supply networks to living systems like animal and plant vasculature. In many cases, the elements forming these networks exhibit a highly non-linear pressure-flow relationship. Although we understand how these elements work individually, their collective behavior remains poorly understood. In this work, we combine experiments, theory, and numerical simulations to understand the main mechanisms underlying the collective behavior of soft flow networks with elements that exhibit negative differential resistance. Strikingly, our theoretical analysis and experiments reveal that a minimal network of nonlinear resistors, which we have termed a 'fluidic memristor', displays history-dependent resistance. This new class of element can be understood as a collection of hysteresis loops that allows this fluidic system to store information, and it can be directly used as a tunable resistor in fluidic setups. Our results provide insights that can inform other applications of fluid flow networks in soft materials science, biomedical settings, and soft robotics, and may also motivate new understanding of the flow networks involved in animal and plant physiology.

Physical effects of learning

Interacting many-body physical systems ranging from neural networks in the brain to folding proteins to self-modifying electrical circuits can learn to perform diverse tasks. This learning, both in nature and in engineered systems, can occur through evolutionary selection or through dynamical rules that drive active learning from experience. Here, we show that learning in linear physical networks with weak input signals leaves architectural imprints on the Hessian of a physical system. Compared to a generic organization of the system components, (a) the effective physical dimension of the response to inputs decreases, (b) the response of physical degrees of freedom to random perturbations (or system "susceptibility") increases, and (c) the low-eigenvalue eigenvectors of the Hessian align with the task. Overall, these effects embody the typical scenario for learning processes in physical systems in the weak input regime, suggesting ways of discovering whether a physical network may have been trained.

Drive-specific selection in multistable mechanical networks

Systems with many stable configurations abound in nature, both in living and inanimate matter, encoding a rich variety of behaviors. In equilibrium, a multistable system is more likely to be found in configurations with lower energy, but the presence of an external drive can alter the relative stability of different configurations in unexpected ways. Living systems are examples par excellence of metastable nonequilibrium attractors whose structure and stability are highly dependent on the specific form and pattern of the energy flow sustaining them. Taking this distinctively lifelike behavior as inspiration, we sought to investigate the more general physical phenomenon of drive-specific selection in nonequilibrium dynamics. To do so, we numerically studied driven disordered mechanical networks of bistable springs possessing a vast number of stable configurations arising from the two stable rest lengths of each spring, thereby capturing the essential physical properties of a broad class of multistable systems. We found that there exists a range of forcing amplitudes for which the attractor states of driven disordered multistable mechanical networks are fine-tuned with respect to the pattern of external forcing to have low energy absorption from it. Additionally, we found that these drive-specific attractor states are further stabilized by precise matching between the multidimensional shape of their orbit and that of the potential energy well they inhabit. Lastly, we showed evidence of drive-specific selection in an experimental system and proposed a general method to estimate the range of drive amplitudes for drive-specific selection.

Learning to learn by using nonequilibrium training protocols for adaptable materials

Evolution in time-varying environments naturally leads to adaptable biological systems that can easily switch functionalities. Advances in the synthesis of environmentally responsive materials therefore open up the possibility of creating a wide range of synthetic materials which can also be trained for adaptability. We consider high-dimensional inverse problems for materials where any particular functionality can be realized by numerous equivalent choices of design parameters. By periodically switching targets in a given design algorithm, we can teach a material to perform incompatible functionalities with minimal changes in design parameters. We exhibit this learning strategy for adaptability in two simulated settings: elastic networks that are designed to switch deformation modes with minimal bond changes and heteropolymers whose folding pathway selections are controlled by a minimal set of monomer affinities. The resulting designs can reveal physical principles, such as nucleation-controlled folding, that enable such adaptability.

Systematic modification of functionality in disordered elastic networks through free energy surface tailoring

A combined machine learning-physics-based approach is explored for molecular and materials engineering. Specifically, collective variables, akin to those used in enhanced sampled simulations, are constructed using a machine learning model trained on data gathered from a single system. Through the constructed collective variables, it becomes possible to identify critical molecular interactions in the considered system, the modulation of which enables a systematic tailoring of the system's free energy landscape. To explore the efficacy of the proposed approach, we use it to engineer allosteric regulation and uniaxial strain fluctuations in a complex disordered elastic network. Its successful application in these two cases provides insights regarding how functionality is governed in systems characterized by extensive connectivity and points to its potential for design of complex molecular systems.

Competition between Energy and Dynamics in Memory Formation

Bistable objects that are pushed between states by an external field are often used as a simple model to study memory formation in disordered materials. Such systems, called hysterons, are typically treated quasistatically. Here, we generalize hysterons to explore the effect of dynamics in a simple spring system with tunable bistability and study how the system chooses a minimum. Changing the timescale of the forcing allows the system to transition between a situation where its fate is determined by following the local energy minimum to one where it is trapped in a shallow well determined by the path taken through configuration space. Oscillatory forcing can lead to transients lasting many cycles, a behavior not possible for a single quasistatic hysteron.

Training precise stress patterns

We introduce a training rule that enables a network composed of springs and dashpots to learn precise stress patterns. Our goal is to control the tensions on a fraction of "target" bonds, which are chosen randomly. The system is trained by applying stresses to the target bonds, causing the remaining bonds, which act as the learning degrees of freedom, to evolve. Different criteria for selecting the target bonds affects whether frustration is present. When there is at most a single target bond per node the error converges to computer precision. Additional targets on a single node may lead to slow convergence and failure. Nonetheless, training is successful even when approaching the limit predicted by the Maxwell Calladine theorem. We demonstrate the generality of these ideas by considering dashpots with yield stresses. We show that training converges, albeit with a slower, power-law decay of the error. Furthermore, dashpots with yielding stresses prevent the system from relaxing after training, enabling to encode permanent memories.

Memory capacity of adaptive flow networks

Biological flow networks adapt their network morphology to optimize flow while being exposed to external stimuli from different spatial locations in their environment. These adaptive flow networks retain a memory of the stimulus location in the network morphology. Yet, what limits this memory and how many stimuli can be stored are unknown. Here, we study a numerical model of adaptive flow networks by applying multiple stimuli subsequently. We find strong memory signals for stimuli imprinted for a long time into young networks. Consequently, networks can store many stimuli for intermediate stimulus duration, which balance imprinting and aging.

Reprogrammable allosteric metamaterials from disordered networks

Prior works on disordered mechanical metamaterial networks-consisting of fixed nodes connected by discrete bonds-have shown that auxetic and allosteric responses can be achieved by pruning a specific set of the bonds from an originally random network. However, bond pruning is irreversible and yields a single bulk response. Using material stiffness as a tunable design parameter, we create metamaterial networks where allosteric responses are achieved without bond removal. Such systems are experimentally realized through variable stiffness bonds that can strengthen and weaken on-demand. In a disordered mechanical network with variable stiffness bonds, different subsets of bonds can be strategically softened to achieve different bulk responses, enabling a multiplicity of reprogrammable input/output allosteric responses.

Learning to self-fold at a bifurcation

Disordered mechanical systems can deform along a network of pathways that branch and recombine at special configurations called bifurcation points. Multiple pathways are accessible from these bifurcation points; consequently, computer-aided design algorithms have been sought to achieve a specific structure of pathways at bifurcations by rationally designing the geometry and material properties of these systems. Here, we explore an alternative physical training framework in which the topology of folding pathways in a disordered sheet is changed in a desired manner due to changes in crease stiffnesses induced by prior folding. We study the quality and robustness of such training for different "learning rules," that is, different quantitative ways in which local strain changes the local folding stiffness. We experimentally demonstrate these ideas using sheets with epoxy-filled creases whose stiffnesses change due to folding before the epoxy sets. Our work shows how specific forms of plasticity in materials enable them to learn nonlinear behaviors through their prior deformation history in a robust manner.

Transient learning degrees of freedom for introducing function in materials

SignificanceMany protocols used in material design and training have a common theme: they introduce new degrees of freedom, often by relaxing away existing constraints, and then evolve these degrees of freedom based on a rule that leads the material to a desired state at which point these new degrees of freedom are frozen out. By creating a unifying framework for these protocols, we can now understand that some protocols work better than others because the choice of new degrees of freedom matters. For instance, introducing particle sizes as degrees of freedom to the minimization of a jammed particle packing can lead to a highly stable state, whereas particle stiffnesses do not have nearly the same impact.

Desynchronous learning in a physics-driven learning network

In a neuron network, synapses update individually using local information, allowing for entirely decentralized learning. In contrast, elements in an artificial neural network are typically updated simultaneously using a central processor. Here, we investigate the feasibility and effect of desynchronous learning in a recently introduced decentralized, physics-driven learning network. We show that desynchronizing the learning process does not degrade the performance for a variety of tasks in an idealized simulation. In experiment, desynchronization actually improves the performance by allowing the system to better explore the discretized state space of solutions. We draw an analogy between desynchronization and mini-batching in stochastic gradient descent and show that they have similar effects on the learning process. Desynchronizing the learning process establishes physics-driven learning networks as truly fully distributed learning machines, promoting better performance and scalability in deployment.

Insight into redox regulation of apoptosis in cancer cells with multiparametric live-cell microscopy

Cellular redox status and the level of reactive oxygen species (ROS) are important regulators of apoptotic potential, playing a crucial role in the growth of cancer cell and their resistance to apoptosis. However, the relationships between the redox status and ROS production during apoptosis remain poorly explored. In this study, we present an investigation on the correlations between the production of ROS, the redox ratio FAD/NAD(P)H, the proportions of the reduced nicotinamide cofactors NADH and NADPH, and caspase-3 activity in cancer cells at the level of individual cells. Two-photon excitation fluorescence lifetime imaging microscopy (FLIM) was applied to monitor simultaneously apoptosis using the genetically encoded sensor of caspase-3, mKate2-DEVD-iRFP, and the autofluorescence of redox cofactors in colorectal cancer cells upon stimulation of apoptosis with staurosporine, cisplatin or hydrogen peroxide. We found that, irrespective of the apoptotic stimulus used, ROS accumulation correlated well with both the elevated pool of mitochondrial, enzyme-bound NADH and caspase-3 activation. Meanwhile, a shift in the contribution of bound NADH could develop independently of the apoptosis, and this was observed in the case of cisplatin. An increase in the proportion of bound NADPH was detected only in staurosporine-treated cells, this likely being associated with a high level of ROS production and their resulting detoxification. The results of the study favor the discovery of new therapeutic strategies based on manipulation of the cellular redox balance, which could help improve the anti-tumor activity of drugs and overcome apoptotic resistance.

Profusion of transition pathways for interacting hysterons

The response, pathways, and memory effects of cyclically driven complex media can be captured by hysteretic elements called hysterons. Here we demonstrate the profound impact of hysteron interactions on pathways and memory. Specifically, while the Preisach model of independent hysterons features a restricted class of pathways which always satisfy return point memory, we show that three interacting hysterons generate more than 15 000 transition graphs, with most violating return point memory and having features completely distinct from the Preisach model. Exploring these opens a route to designer pathways and information processing in complex matter.

The structural, vibrational, and mechanical properties of jammed packings of deformable particles in three dimensions

We investigate the structural, vibrational, and mechanical properties of jammed packings of deformable particles with shape degrees of freedom in three dimensions (3D). Each 3D deformable particle is modeled as a surface-triangulated polyhedron, with spherical vertices whose positions are determined by a shape-energy function with terms that constrain the particle surface area, volume, and curvature, and prevent interparticle overlap. We show that jammed packings of deformable particles without bending energy possess low-frequency, quartic vibrational modes, whose number decreases with increasing asphericity and matches the number of missing contacts relative to the isostatic value. In contrast, jammed packings of deformable particles with non-zero bending energy are isostatic in 3D, with no quartic modes. We find that the contributions to the eigenmodes of the dynamical matrix from the shape degrees of freedom are significant over the full range of frequency and shape parameters for particles with zero bending energy. We further show that the ensemble-averaged shear modulus 〈G〉 scales with pressure P as 〈G〉 ∼ Pβ, with β ≈ 0.75 for jammed packings of deformable particles with zero bending energy. In contrast, β ≈ 0.5 for packings of deformable particles with non-zero bending energy, which matches the value for jammed packings of soft, spherical particles with fixed shape. These studies underscore the importance of incorporating particle deformability and shape change when modeling the properties of jammed soft materials.

Molecular and micro-scale heterogeneities in Raman modes of a relaxing polymer glass

We have used Raman spectroscopy to study relaxation dynamics at two different length scales, molecular level and micro-scale in order to probe the presence of cooperative rearranging regions in a polymer glass. Response to slow thermal cycles and fast quench through the glass transition temperature (T_g) is analyzed for film and unprocessed forms of polyvinyl acetate (PVAc). In PVAc film, enhanced disorder and molecular mobility lead to peak broadening by about a factor of 10 compared to unprocessed PVAc. Thermal cycles (10 K min^-1) produce hysteresis in integrated Raman peak intensity (loop areaAINTI).AINTIvalues of film are two orders of magnitude more than unprocessed, indicating more configurational mosaics with higher interfacial energy dissipations. Ageing after 60 K min^-1quench manifests as heterogeneous molecular dynamics of film Raman modes with significant peak-width variations, differentiating high mobility and low mobility modes. Two-dimensional mapping of film Raman modes after quench reveal micro-scale clusters of average size ≈250 molecules having fractal boundaries with fractal dimensiond_f= 1.5, resemblingd_fof percolation clusters below percolation threshold. During thermal cycling and relaxation after a quench, cooperative segmental dynamics with large correlations between skeletal C-C stretch and side branch modes is observed. The observations are analyzed in the context of the random first order transition theory of glasses, which attributes heterogeneous relaxations in glasses to the presence of clusters of variable configurational states.

Training nonlinear elastic functions: nonmonotonic, sequence dependent and bifurcating

The elastic behavior of materials operating in the linear regime is constrained, by definition, to operations that are linear in the imposed deformation. Although the nonlinear regime holds promise for new functionality, the design in this regime is challenging. In this paper, we demonstrate that a recent approach based on training [Hexner et al., PNAS 2020, 201922847] allows responses that are inherently non-linear. By applying designer strains, a disordered solid evolves through plastic deformations that alter its response. We show examples of elaborate nonlinear training paths that lead to the following functions: (1) frequency conversion, (2) logic gate and (3) expansion or contraction along one axis, depending on the sequence of imposed transverse compressions. We study the convergence rate and find that it depends on the trained function.

Overexpression of Stat3 increases circulating cfDNA in breast cancer

PURPOSE

Current studies on circulating cell-free DNA (cfDNA) have been focusing on its potential as biomarkers in liquid biopsy by detecting its content or genetic and epigenetic changes for the evaluation of tumor burden and therapeutic efficacy. However, the regulatory mechanism of cfDNA release remains unclear. Stat3 has been documented as an oncogene for the development and metastasis of breast cancer cells. In this study, we investigated whether Stat3 affects the release of cfDNA into blood and its association with the number of circulating tumor cells (CTCs).

METHODS

The cfDNA level in plasma of patients with breast cancer and healthy volunteers were determined by quantitative real-time PCR. Three mouse breast cancer models with different Stat3 expression were generated and used to established three breast cancer orthotopic animal models to examine the effect of Stat3 on cfDNA release in vivo. Stat3 mediated Epithelial-mesenchymal phenotype transition of CTCs was determined by immunofluorescence assay and Western blot assay.

RESULTS

The data showed that Stat3 increased circulating cfDNA, which is correlated with the increased volume of primary tumors and number of CTCs, accompanied with the dynamic EMT changes regulated by Snail induction. Furthermore, the high level of total circulating cfDNA and Stat3-cfDNA in patients with breast cancer were detected by quantitative real-time PCR using GAPDH and Stat3 primers.

CONCLUSION

Our results suggested that Stat3 increases the circulating cfDNA and CTCs in breast cancer.

Clinical characteristics of subjective idiopathic tinnitus and preliminarily analyses for the effect of tinnitus multielement integration sound therapy

OBJECTIVE

To study the psychoacoustic and audiological characteristics of patients with chronic subjective tinnitus and provide basis for the personalized diagnosis and treatment of tinnitus through a single tinnitus multielement integration sound therapy (T-MIST) and analysis of efficacy preliminarily.

METHODS

145 patients with tinnitus were assessed by systematic medical history collection, professional examination of otolaryngology, audiology examination, full precision test (FPT), residual inhibition test (RIT), tinnitus handicap inventory (THI) and visual analog scale (VAS) annoyance. The correlation among factors was performed.

RESULTS

The frequency of tinnitus was correlated with the frequency of maximum hearing loss (P < 0.05). The loudness of tinnitus was correlated with the loudness of maximum hearing loss (P < 0.05). In this study, T-MIST was used to treat tinnitus. After treatment, tinnitus alleviated VAS annoyance (P < 0.05). The results of RIT were correlated with the effect of T-MIST (P < 0.05).

CONCLUSION

There was a correlation between tinnitus and hearing loss. The RIT may indicate the effectiveness of acoustic therapy in patients. The FPT can find the hidden hearing loss without display on routine pure tone audiometry, so as to provide a clinical reference for the detection of early hearing loss in tinnitus patients.

Periodic training of creeping solids

We consider disordered solids in which the microscopic elements can deform plastically in response to stresses on them. We show that by driving the system periodically, this plasticity can be exploited to train in desired elastic properties, both in the global moduli and in local "allosteric" interactions. Periodic driving can couple an applied "source" strain to a "target" strain over a path in the energy landscape. This coupling allows control of the system's response, even at large strains well into the nonlinear regime, where it can be difficult to achieve control simply by design.

Supervised learning through physical changes in a mechanical system

Mechanical metamaterials are usually designed to show desired responses to prescribed forces. In some applications, the desired force-response relationship is hard to specify exactly, but examples of forces and desired responses are easily available. Here, we propose a framework for supervised learning in thin, creased sheets that learn the desired force-response behavior by physically experiencing training examples and then, crucially, respond correctly (generalize) to previously unseen test forces. During training, we fold the sheet using training forces, prompting local crease stiffnesses to change in proportion to their experienced strain. We find that this learning process reshapes nonlinearities inherent in folding a sheet so as to show the correct response for previously unseen test forces. We show the relationship between training error, test error, and sheet size (model complexity) in learning sheets and compare them to counterparts in machine-learning algorithms. Our framework shows how the rugged energy landscape of disordered mechanical materials can be sculpted to show desired force-response behaviors by a local physical learning process.

Embedding orthogonal memories in a colloidal gel through oscillatory shear

It has recently been shown that in a broad class of disordered systems oscillatory shear training can embed memories of specific shear protocols in relevant physical parameters such as the yield strain. These shear protocols can be used to change the physical properties of the system and memories of the protocol can later be "read" out. Here we investigate shear training memories in colloidal gels, which include an attractive interaction and network structure, and discover that such systems can support memories both along and orthogonal to the training flow direction. We use oscillatory shear protocols to set and read out the yield strain memories and confocal microscopy to analyze the rearranging gel structure throughout the shear training. We find that the gel bonds remain largely isotropic in the shear-vorticity plane throughout the training process suggesting that structures formed to support shear along the training shear plane are also able to support shear along the orthogonal plane. Orthogonal memory extends the usefulness of shear memories to more applications and should apply to many other disordered systems as well.

Shear Controls Frictional Aging by Erasing Memory

We simultaneously measure the static friction and the real area of contact between two solid bodies. These quantities are traditionally considered equivalent, and under static conditions both increase logarithmically in time, a phenomenon coined aging. Here we show that the frictional aging rate is determined by the combination of the aging rate of the real area of contact and two memory-erasure effects that occur when shear is changed (e.g., to measure static friction.) The application of a static shear load accelerates frictional aging while the aging rate of the real area of contact is unaffected. Moreover, a negative static shear-pulling instead of pushing-slows frictional aging, but similarly does not affect the aging of contacts. The origin of this shear effect on aging is geometrical. When shear load is increased, minute relative tilts between the two blocks prematurely erase interfacial memory prior to sliding, negating the effect of aging. Modifying the loading point of the interface eliminates these tilts and as a result frictional aging rate becomes insensitive to shear. We also identify a secondary memory-erasure effect that remains even when all tilts are eliminated and show that this effect can be leveraged to accelerate aging by cycling between two static shear loads.