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At least 91 records · Page 5

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

In this work, we present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system’s governing equations to identify a coordinate transformation in which the system dynamics have quadratic structure. This transformation is called a lifting map because it often adds auxiliary variables to the system state. The lifting map is applied to data obtained by evaluating a model for the original nonlinear system. This lifted data is projected onto its leading principal components, and low-dimensional linear and quadratic matrix operators are fit to the lifted reduced data using a least-squares operator inference procedure. Analysis of our method shows that the Lift & Learn models are able to capture the system physics in the lifted coordinates at least as accurately as traditional intrusive model reduction approaches. This preservation of system physics makes the Lift & Learn models robust to changes in inputs. Numerical experiments on the FitzHugh–Nagumo neuron activation model and the compressible Euler equations demonstrate the generalizability of our model.

97 MATHEMATICS AND COMPUTING↗

Structural bases for stoichiometry‐selective calcium potentiation of a neuronal nicotinic receptor

Background and Purpose α4β2 nicotinic acetylcholine (nACh) receptors assemble in two stoichiometric forms, one of which is potentiated by calcium. The sites of calcium binding that underpin potentiation are not known. Experimental Approach To identify calcium binding sites, we applied cryo‐electron microscopy (cryo‐EM) and molecular dynamics (MD) simulations to each stoichiometric form of the α4β2 nACh receptor in the presence of calcium ions. To test whether the identified calcium sites are linked to potentiation, we generated mutants of anionic residues at the sites, expressed wild type and mutant receptors in clonal mammalian fibroblasts, and recorded ACh‐elicited single‐channel currents with or without calcium. Key Results Both cryo‐EM and MD simulations show calcium bound to a site between the extracellular and transmembrane domains of each α4 subunit (ECD‐TMD site). Substituting alanine for anionic residues at the ECD‐TMD site abolishes stoichiometry‐selective calcium potentiation, as monitored by single‐channel patch clamp electrophysiology. Additionally, MD simulation reveals calcium association at subunit interfaces within the extracellular domain. Substituting alanine for anionic residues at the ECD sites reduces or abolishes stoichiometry‐selective calcium potentiation. Conclusions and Implications Stoichiometry‐selective calcium potentiation of the α4β2 nACh receptor is achieved by calcium association with topographically distinct sites framed by anionic residues within the α4 subunit and between the α4 and β2 subunits. Stoichiometry‐selective calcium potentiation could result from the greater number of calcium sites in the stoichiometric form with three rather than two α4 subunits. The results are relevant to modulation of signalling via α4β2 nACh receptors in physiological and pathophysiological conditions.

Pharmacology & Pharmacy↗

O3BNN-R: An Out-Of-Order Architecture for High-Performance and Regularized BNN Inference

Binarized Neural Networks (BNN) have drawn tremendous attention due to significantly reduced computational complexity and memory demand. They have especially shown great potential in cost- and power-restricted domains, such as IoT and smart edge-devices, where reaching a certain accuracy bar is often sufficient, and real-time is highly desired.In this work, we demonstrate that the highly-condensed BNN model can be shrunk significantly further by dynamically pruning irregular redundant edges. Based on two new observations on BNN-specific properties, an out-of-order (OoO) architecture – O3BNN-R, can curtail edge evaluation in cases where the binary output of a neuron can be determined early. Similar to Instruction-Level-Parallelism(ILP), these fine-grained, irregular, runtime pruning opportunities are traditionally presumed to be difficult to exploit. In order to increase the pruning opportunities, we also optimize the training process by adding 2 regularization items in the loss function (1) for pooling pruning and (2) for threshold pruning. We evaluate our design on an FPGA platform using three well-known networks, including VggNet-16, AlexNet for ImageNet, and a VGG-like network for Cifar-10.

Geng, Tong↗

Organismic materials for beyond von Neumann machines

The elementary basis of intelligence in organisms with a central nervous system includes neurons and synapses and their complex interconnections forming neural circuits. In non-neural organisms such as slime mold with gel-like media, viscosity modulation enables adaptation to changing environments. At a larger scale, collective intelligence emerges via social interactions and feedback in animal colonies. Learning and memory are therefore multi-scale features that evolve as a result of constant interactions with the environment. There is growing interest in emulating such features of intelligence in computing machines and autonomous systems. Materials that can respond to their environment in a manner similar to organisms (referred to as "organismic materials") therefore may be of interest as hardware components in artificial intelligence machines. In this brief review, we present a class of semiconductors called correlated oxides as candidates for learning machines. The term "correlated" refers to the fact that electrons in such lattices strongly interact and the ground state is not what is predicted by classical band theory. Such materials can undergo insulator-metal transitions at near ambient conditions under external stimuli such as thermal or electrical fields, strain, and chemical doping. Depending on the mechanism driving the transition, intermediate states can be metastable with different volatilities, and the time scales of phase change can be controlled over many orders of magnitude. The change in electronic properties can be sharp or gradual, leading to digital or analog behavior. These properties enable the realization of artificial neurons and synapses and emulate the associative and non-associative learning characteristics found in various organisms. We examine microscopic properties concerning electronic and structural transitions leading to collective behavior and theoretical treatments of the ground state and dynamical response, showcasing VO 2 as a model system. Next, we briefly review algorithms designed from the plasticity demonstrated by phase changing systems. Finally, we conclude the brief review with suggestions for future research toward realizing non-von Neumann machines.

42 ENGINEERING↗

Heterosynaptic plasticity in memristive and memcapacitive lipid bilayers: A snapshot review

Synaptic plasticity refers to activity-dependent synaptic strengthening or weakening between neurons. It is usually associated with homosynaptic plasticity, which refers to a synaptic junction controlled by interactions between specific neurons. Heterosynaptic plasticity, on the other hand, lacks this specificity. It involves much larger populations of synapses and neurons and can be associated with changes in synaptic strength due to nonlocal alterations in the ambient electrochemical environment. Here, this paper presents specific examples demonstrating how variations in the ambient electrochemical environment of lipid membranes can impact the nonlinear dynamical behaviors of memristive and memcapacitive systems in droplet interface bilayers (DIBs). Examples include the use of pH as a modulatory factor that alters the voltage-dependent memristive behavior of alamethicin ion channels in DIB lipid bilayers, and the discovery of long-term potentiation (LTP) in a lipid bilayer-only system after application of electrical stimulation protocols.

36 MATERIALS SCIENCE↗

Small molecules disaggregate alpha-synuclein and prevent seeding from patient brain-derived fibrils

The amyloid aggregation of alpha-synuclein within the brain is associated with the pathogenesis of Parkinson’s disease (PD) and other related synucleinopathies, including multiple system atrophy (MSA). Alpha-synuclein aggregates are a major therapeutic target for treatment of these diseases. We identify two small molecules capable of disassembling preformed alpha-synuclein fibrils. The compounds, termed CNS-11 and CNS-11g, disaggregate recombinant alpha-synuclein fibrils in vitro, prevent the intracellular seeded aggregation of alpha-synuclein fibrils, and mitigate alpha-synuclein fibril cytotoxicity in neuronal cells. Furthermore, we demonstrate that both compounds disassemble fibrils extracted from MSA patient brains and prevent their intracellular seeding. They also reduce in vivo alpha-synuclein aggregates in C. elegans . Both compounds also penetrate brain tissue in mice. A molecular dynamics–based computational model suggests the compounds may exert their disaggregating effects on the N terminus of the fibril core. These compounds appear to be promising therapeutic leads for targeting alpha-synuclein for the treatment of synucleinopathies.

60 APPLIED LIFE SCIENCES↗

Single Crystals of Vanadium Oxides as a Lens for Understanding Structural and Electronic Phase Transformations, Ion Transport, Chemo-Mechanical Coupling, and Electrothermal Neuronal Emulation

Vanadium oxides cystallize in a diverse array of structures and compositions arising from the redox versatility of vanadium, variable covalency of V−O bonds, and myriad coordination geometries. Their open frameworks present abundant interstitial sites that enable insertion of guest-ions. In such compounds, V3d electron and spin localization and disorder couple strongly to structural preferences. The rich structural diversity manifests as a “rugged” free energy landscape with multiple interconvertible polymorphs. Such a landscape sets up structural, electronic, and magnetic transitions that underpin the promise of these materials as ion-insertion battery electrodes; compact primitives for brain-inspired computing, and heterogeneous catalysts. Here, we examine the structural and compositional diversity, electronic instabilities, defect dynamics, structure transformations, mechanical properties, and surface structure of vanadium oxides using single crystals as a distinctive lens. Single crystals enable the measurement of structure−function correlations without the ensemble and orientational averaging inevitable in polycrystalline materials. Their well-defined surfaces further enable examination of facet-dependent reactivity toward molecular adsorbates, ion fluxes, and lattice (mis)matched solids. We provide a comprehensive account of vanadium-oxide single-crystal studies, from delineation of common structural motifs to single-crystal growth techniques, topochemical modification strategies, mechanisms underpinning electronic instabilities, and implementation as electrothermal neurons and battery electrode materials.

Ponis, John [Texas A&M University, College Station↗

Mean Field Theory of Self‐Organizing Memristive Connectomes

Abstract Biological neuronal networks are characterized by nonlinear interactions and complex connectivity. Given the growing impetus to build neuromorphic computers, understanding physical devices that exhibit structures and functionalities similar to biological neural networks is an important step toward this goal. Self‐organizing circuits of nanodevices are at the forefront of the research in neuromorphic computing, as their behavior mimics synaptic plasticity features of biological neuronal circuits. However, an effective theory to describe their behavior is lacking. This study provides for the first time an effective mean field theory for the emergent voltage‐induced polymorphism of circuits of a nanowire connectome, showing that the behavior of these circuits can be explained by a low‐dimensional dynamical equation. The equation can be derived from the microscopic dynamics of a single memristive junction in analytical form. The effective model is tested on experiments of nanowire networks and show that it fits both the potentiation and depression of these synapse‐mimicking circuits. It is shown that this theory applies beyond the case of nanowire networks by formulating a general mean‐field theory of conductance transitions in self‐organizing memristive connectomes.

Caravelli, Francesco↗

Operando microscopy for neuromorphic hardware

Microscopy techniques can uncover the physical properties and dynamic behaviours of materials, driving the discovery of emergent phenomena and guiding the design of next-generation computing hardware. As artificial intelligence becomes pervasive, the demand for high-performance materials to support sustainable information technologies is growing. Here, this Review highlights state-of-the-art imaging from electron and X-ray to optical techniques to probe the dynamics of neuromorphic materials, including operando characterization of devices. We examine design principles for neuromorphic materials, along with obstacles that hinder their development. Emphasis is placed on spatially and temporally resolved approaches that capture state changes including phase transitions, ferroic switching and spin-wave propagation that emulate biological components such as neurons, synapses and their connectivity. We discuss challenges in operando characterization and the integration of artificial intelligence-driven analysis for feedback-guided material discovery. Finally, we outline opportunities for real-time imaging of neuromorphic systems, paving the way towards adaptive, brain-inspired hardware.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Variational and phase response analysis for limit cycles with hard boundaries, with applications to neuromechanical control problems

Motor systems show an overall robustness, but because they are highly nonlinear, understanding how they achieve robustness is difficult. In many rhythmic systems, robustness against perturbations involves response of both the shape and the timing of the trajectory. This makes the study of robustness even more challenging. To understand how a motor system produces robust behaviors in a variable environment, we consider a neuromechanical model of motor patterns in the feeding apparatus of the marine mollusk Aplysia californica (Shaw et al. in J Comput Neurosci 38(1):25–51, 2015; Lyttle et al. in Biol Cybern 111(1):25–47, 2017). We established in (Wang et al. in SIAM J Appl Dyn Syst 20(2):701–744, 2021. https://doi.org/10.1137/20M1344974) the tools for studying combined shape and timing responses of limit cycle systems under sustained perturbations and here apply them to study robustness of the neuromechanical model against increased mechanical load during swallowing. Interestingly, we discover that nonlinear biomechanical properties confer resilience by immediately increasing resistance to applied loads. In contrast, the effect of changed sensory feedback signal is significantly delayed by the firing rates’ hard boundary properties. Our analysis suggests that sensory feedback contributes to robustness in swallowing primarily by shifting the timing of neural activation involved in the power stroke of the motor cycle (retraction). This effect enables the system to generate stronger retractor muscle forces to compensate for the increased load, and hence achieve strong robustness. The approaches that we are applying to understanding a neuromechanical model in Aplysia, and the results that we have obtained, are likely to provide insights into the function of other motor systems that encounter changing mechanical loads and hard boundaries, both due to mechanical and neuronal firing properties.

59 BASIC BIOLOGICAL SCIENCES↗

Bypassing Fast Time Scales of the Hodgkin-Huxley Neuron Model via a Thresholded Hard Reset

We propose a modification to the Hodgkin-Huxley model to reduce the numerical stiffness of the equations by introducing an explicit voltage threshold. When this threshold is crossed, the voltage and the gating variables are reset to constant values. It is found that, for all of the current stimuli considered, the proposed model accurately reproduces the behavior of the baseline Hodgkin-Huxley model while bypassing the fast dynamics of spiking. Specifically, the model accurately reproduces the spike times and, between spikes, the time courses of the membrane potential and gating variables.

97 MATHEMATICS AND COMPUTING↗

Superstructured Biomaterials Formed by Exchange Dynamics and Host–Guest Interactions in Supramolecular Polymers

Dynamic and reversible assembly of molecules is ubiquitous in the hierarchical superstructures of living systems and plays a key role in cellular functions. Recent work from the laboratory reported on the reversible formation of such superstructures in systems of peptide amphiphiles conjugated to oligonucleotides and electrostatically complimentary peptide sequences. Here, a supramolecular system is reported upon where exchange dynamics and host–guest interactions between β-cyclodextrin and adamantane on peptide amphiphiles lead to superstructure formation. Superstructure formation with bundled nanoribbons generates a mechanically robust hydrogel with a highly porous architecture that can be 3D printed. Functionalization of the porous superstructured material with a biological signal results in a matrix with significant in vitro bioactivity toward neurons that could be used as a supramolecular model to design novel biomaterials.

36 MATERIALS SCIENCE↗

Probing function in 3D neuronal cultures: a survey of 3D multielectrode array advances

Recent advances in microphysiological systems (MPS) have made significant strides to include design features that reconstruct key elements found in the brain, and in parallel advanced technologies to detect the activity of electrogenic cells that form neural networks. In particular, three-dimensional multielectrode arrays (3D MEAs) are being developed with the increasing levels of spatial and temporal precision, difficult to achieve with current 2D MEAs, insertable MEA probes, and/or optical imaging of calcium dynamics. Thus, providing a means to monitor the flow of neural network activity within all three dimensions (X, Y, and Z) of the engineered tissue. In the last 6 years, 3D MEAs, using either “bottom-up” or “top-down” designs, have been developed to overcome the current technical challenges in monitoring the functionality of the in vitro systems. Herein, we will report on the design and application of novel 3D MEA prototypes for probing neural activity throughout the 3D neural tissue.

59 BASIC BIOLOGICAL SCIENCES↗

Mixed-mode oscillations in a three-timescale coupled Morris–Lecar system

Mixed-mode oscillations (MMOs) are complex oscillatory behaviors of multiple-timescale dynamical systems in which there is an alternation of large-amplitude and small-amplitude oscillations. It is well known that MMOs in two-timescale systems can arise either from a canard mechanism associated with folded node singularities or a delayed Andronov–Hopf bifurcation (DHB) of the fast subsystem. While MMOs in two-timescale systems have been extensively studied, less is known regarding MMOs emerging in three-timescale systems. In this work, we examine the mechanisms of MMOs in coupled Morris–Lecar neurons with three distinct timescales. We investigate two kinds of MMOs occurring in the presence of a singularity known as canard-delayed-Hopf (CDH) and in cases where CDH is absent. In both cases, we examine how features and mechanisms of MMOs vary with respect to variations in timescales. Our analysis reveals that MMOs supported by CDH demonstrate significantly stronger robustness than those in its absence. Moreover, we show that the mere presence of CDH does not guarantee the occurrence of MMOs. This work yields important insights into conditions under which the two separate mechanisms in two-timescale context, canard and DHB, can interact in a three-timescale setting and produce more robust MMOs, particularly against timescale variations.

97 MATHEMATICS AND COMPUTING↗

Leveraging dendritic complexity for neuromorphic computing

Abstract Beyond-von Neumann computing approaches are necessary to sustain the growth of microelectronics and the increasing appetite for artificial intelligence/machine learning algorithms. Neuromorphic computing is an emerging paradigm that takes inspiration from the brain to provide a path forward to improve the computational efficiency and computational density of next-generation computing architectures. In nature, we observe brains performing complex computations with a much smaller energy footprint than conventional computing approaches. Current neuromorphic systems are focused primarily on scalability, namely, increasing the number of computational units (neurons) and connections between units (synapses). However, for brain-like cognition and efficiency in next-generation computing hardware, we need increased complexity in function, as well as improved connection density for scalability. Here, we present our work that aims to incorporate dendrites for ‘compute-on-wire’ in neuromorphic architectures to increase the computational complexity (e.g. number of programmable parameters, nonlinear dynamics) as well as computational efficiency (energy/compute) of artificial neural networks (ANNs). We do this by showcasing neuromorphic dendrite elements that can be leveraged for various applications. We will present examples of neuroscience-inspired direction-selective circuits and an ANN with active dendrites leveraging shunting inhibition. We also demonstrate the benefits of using dendrites in deep neural networks. To conclude, we discuss how we can utilize emerging hardware devices in these systems and design next-generation neuromorphic architectures with dendrites.

Cardwell, Suma G. (ORCID:0000000226575545)↗

Learning emergent partial differential equations in a learned emergent space

We propose an approach to learn effective evolution equations for large systems of interacting agents. This is demonstrated on two examples, a well-studied system of coupled normal form oscillators and a biologically motivated example of coupled Hodgkin-Huxley-like neurons. For such types of systems there is no obvious space coordinate in which to learn effective evolution laws in the form of partial differential equations. In our approach, we accomplish this by learning embedding coordinates from the time series data of the system using manifold learning as a first step. In these emergent coordinates, we then show how one can learn effective partial differential equations, using neural networks, that do not only reproduce the dynamics of the oscillator ensemble, but also capture the collective bifurcations when system parameters vary. The proposed approach thus integrates the automatic, data-driven extraction of emergent space coordinates parametrizing the agent dynamics, with machine-learning assisted identification of an emergent PDE description of the dynamics in this parametrization.

97 MATHEMATICS AND COMPUTING↗

Electrically‐Driven Metal‐Insulator Transitions Emerging from Localizing Current Density and Temperature

Negative differential resistance (NDR) is a key electronic response enabling two‐terminal artificial neurons that can be achieved through different physical phenomena, including phase‐homogeneous current density and temperature (electro‐thermal) localizations and spatially‐localized metal‐insulator phase transitions (MITs). These two effects have been observed to occur sequentially in select electrically‐biased transition metal oxides. However, it is unknown why and under what conditions localizing behaviors precede MITs, particularly as a function of device length scale. To this end, the interplay between phase‐homogeneous electro‐thermal localizations and MITs is investigated in a 3D multiphysics simulation of a lateral thin film device, using the material properties of the prototype MIT material VO 2 . These findings demonstrate that the MIT is nucleated through dynamically localizing current density and temperature. A critical device width (≈0.7 µm in this study) is identified, below which both the electrically‐induced electro‐thermal and phase inhomogeneities cease to appear. It is demonstrated that the formation of spatial inhomogeneities directly relates to device dimensions, and demonstrate the decoupling of NDR from the MIT through device scaling relationships. These results provide insight into the material phenomena underlying the material's electrical responses, clarifying conditions under which spatial inhomogeneities form in electrically‐biased MIT materials.

artificial neuron↗

Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks

Here we propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of activation function is achieved by introducing a scalable parameter in each layer (layer-wise) and for every neuron (neuron-wise) separately, and then optimizing it using a variant of stochastic gradient descent algorithm. In order to further increase the training speed, an activation slope-based slope recovery term is added in the loss function, which further accelerates convergence, thereby reducing the training cost. On the theoretical side, we prove that in the proposed method, the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate, and that the gradient dynamics of the proposed method is not achievable by base methods with any (adaptive) learning rates. We further show that the adaptive activation methods accelerate the convergence by implicitly multiplying conditioning matrices to the gradient of the base method without any explicit computation of the conditioning matrix and the matrix–vector product. The different adaptive activation functions are shown to induce different implicit conditioning matrices. Furthermore, the proposed methods with the slope recovery are shown to accelerate the training process.

97 MATHEMATICS AND COMPUTING↗