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DOE OSTI2026

Ether of Orbifolds

The orbifold lattice has been proposed as a route to practical quantum simulation of Yang--Mills theory, with claims of exponential speedup over all known approaches. Through analytical derivations, Monte Carlo simulation, and explicit circuit construction, we identify compounding costs entirely absent in Kogut--Susskind formulations: a mass-dependent Trotter overhead that scales as $m^4$, non-singlet contamination that grows as $m^2$ and worsens with penalty terms, and a mandatory mass extrapolation. Monte Carlo simulations of SU(3) establish a universal scaling: the continuum limit forces $m^2 \propto 1/a$, binding the Trotter step to the lattice spacing through a cost unique to orbifolds. For a fiducial $10^3$ calculation, the orbifold is $10^4$--$10^{10}$ times more expensive than every published alternative. These results indicate that the claimed computational advantages do not at present survive quantitative scrutiny.

Lamm, Henry [Fermilab] (ORCID:0000000330330791)↗

NASA NTRS2005

Constraint-based Temporal Reasoning with Preferences

Often we need to work in scenarios where events happen over time and preferences are associated to event distances and durations. Soft temporal constraints allow one to describe in a natural way problems arising in such scenarios. In general, solving soft temporal problems require exponential time in the worst case, but there are interesting subclasses of problems which are polynomially solvable. In this paper we identify one of such subclasses giving tractability results. Moreover, we describe two solvers for this class of soft temporal problems, and we show some experimental results. The random generator used to build the problems on which tests are performed is also described. We also compare the two solvers highlighting the tradeoff between performance and robustness. Sometimes, however, temporal local preferences are difficult to set, and it may be easier instead to associate preferences to some complete solutions of the problem. To model everything in a uniform way via local preferences only, and also to take advantage of the existing constraint solvers which exploit only local preferences, we show that machine learning techniques can be useful in this respect. In particular, we present a learning module based on a gradient descent technique which induces local temporal preferences from global ones. We also show the behavior of the learning module on randomly-generated examples.

Khatib, Lina↗

DOE OSTI2023

Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods

Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree–Fock and density functional theory but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first-quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree–Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the k-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first-quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite-temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1986

Statistical performance of the intensified charged coupled device

The first analysis of the statistical performance of the intensified charge coupled device (CCD) is presented. The Poisson statistics of the arriving photons, the exponential pulse height distribution of the microchannel plate in the image intensifier, and the effects of discrete digitization of the charge in reading the CCD are included. A range of intensifier gains from the high levels that permit pulse counting to the low levels that can be used with the accumulation of charge on the CCD is considered. As a tool for this analysis, an analytical model of the performance of the detector system that is generally useful for predicting many aspects of system performance under a wide range of conditions is developed. The statistical penalty for operating the intensified CCD in the charge accumulation mode is not severe, and in some applications it may be desirable to accept this penalty to gain the advantages of increased dynamic range through charge accumulation. This investigation has revealed no pathological aspects of the operation of the detector system.

Sandel, B. R.↗

NASA NTRS1990

Low NO(x) potential of gas turbine engines

The purpose is to correlate emission levels of gas turbine engines. The predictions of NO(x) emissions are based on a review of the literature of previous low NO(x) combustor programs and analytical chemical kinetic calculations. Concepts included in the literature review consisted of lean-premixed-prevaporized (LPP), rich burn/quick quench/lean burn (RQL), and direct injection. The NO(x) emissions were found to be an exponential function of adiabatic combustion temperature over a wide range of inlet temperatures, pressures and (lean) fuel-air ratios. A simple correlation of NO(x) formation with time was not found. The LPP and direct injection (using gaseous fuels) concepts have the lowest NO(x) emissions of the three concepts. The RQL data has higher values of NO(x) than the LPP concept, probably due to the stoichiometric temperatures and NO(x) production that occur during the quench step. Improvements in the quick quench step could reduce the NO(x) emissions to the LPP levels. The low NO(x) potential of LPP is offset by the operational disadvantages of its narrow stability limits and its susceptibility to autoignition/flashback. The Rich-Burn/Quick-Quench/Lean-Burn (RQL) and the direct injection concepts have the advantage of wider stability limits comparable to conventional combustors.

Tacina, Robert R.↗

DOE OSTI2026

A Tensor Network-Based Quantum Algorithm for the Nonlinear 1D Burgers' Equation

In this work, we implement a tensor network-based quantum algorithm to solve unsteady, nonlinear partial differential equations (PDEs). The challenge lies in how to effectively represent, encode, process, and evolve the nonlinear system of PDEs on quantum computers. We will discuss the new techniques using the compressible 1-dimensional (1D) Burgers' equation as an example, because it represents the fundamental nonlinear feature and yet removes certain complexity in physics, allowing us to focus on the design of quantum algorithms. Previous attempts to solve nonlinear PDEs in quantum computation have often involved storing multiple copies of solutions or employing linearizations. Neither is practical due to exponential scaling with evolution time or insufficient solution accuracy. Our framework is based on matrix product states (MPSs) and matrix product operators (MPOs). For example, the velocity field is represented by MPS, whereas the linear and nonlinear spatial differential terms of the velocity field are processed by MPOs. Our primary focus herein is to verify and validate the various tensor network components of the algorithm using solutions obtained by the classical algorithms on high performance computing (HPC) architectures. We use a classical time marching method to demonstrate the functionality of the tensor network operations to model the PDE and their robustness with the time evolution of the system. Our classical simulation results demonstrate the utility of tensor network-based operations in modeling nonlinear PDEs and highlight the necessity as well as potential advantages of using quantum simulations for these techniques.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗

NASA NTRS1995

The correlated k-distribution technique as applied to the AVHRR channels

Correlated k-distributions have been created to account for the molecular absorption found in the spectral ranges of the five Advanced Very High Resolution Radiometer (AVHRR) satellite channels. The production of the k-distributions was based upon an exponential-sum fitting of transmissions (ESFT) technique which was applied to reference line-by-line absorptance calculations. To account for the overlap of spectral features from different molecular species, the present routines made use of the multiplication transmissivity property which allows for considerable flexibility, especially when altering relative mixing ratios of the various molecular species. To determine the accuracy of the correlated k-distribution technique as compared to the line-by-line procedure, atmospheric flux and heating rate calculations were run for a wide variety of atmospheric conditions. For the atmospheric conditions taken into consideration, the correlated k-distribution technique has yielded results within about 0.5% for both the cases where the satellite spectral response functions were applied and where they were not. The correlated k-distribution's principal advantages is that it can be incorporated directly into multiple scattering routines that consider scattering as well as absorption by clouds and aerosol particles.

Kratz, David P.↗

DOE OSTI2020

Closing the Loops on Solar Photovoltaics Modules: An Agent-Based Modeling Approach for the Study of Circular Economy Strategies

Solar photovoltaics (PV) installed capacity have grown exponentially since the early 2000s (average annual growth rate of 50%). With 4,700 GW projected installed capacity by 2050, the volume of PV panels waste is also expected to become substantial. Though renewables are a sine qua non to the establishment of a truly circular economy (CE), the issue arising from their end-of-life management needs to be resolved. The management of PV end-of-life also represent a singular opportunity to create value, from recovered valuable, rare or critical materials (e.g. silver, tellurium, indium). Moreover, the PV case illustrates some of the current barriers to CE; for instance, the need for a common definition of waste (PV are defined as e-waste in the European Union but as general waste in the United States) and potential loss of innovations' advantages (PV average efficiency has continuously grown the past 10 years). In this study, an agent-based modeling (ABM) approach is proposed to simulate PV end-of-life management in the United States. The model explores how the decisions of the various actors involved in handling PV waste affect the quantities of PV that are reused, recycled, or land-filled. In the model, manufacturers, residential, and nonresidential PV owners, installers, and recyclers are represented by agents while governmental policies and regulations are treated as exogenous variables. PV-market data are used to define agents' characteristics (e.g., installed PV capacities or producing costs). Agents' decision rules draw on the literature related to industrial symbiosis (IS) and peoples' waste behaviors as they appear as the most widely used model to implement CE principles at a meso level. Specifically, the concepts of mutual trust between IS actors and knowledge about the IS philosophy are yielded to define the agents' decision process. The primary outputs of the ABM are the costs and volume of waste associated with each end-of-life pathway. Preliminaries results indicate recycling of residential PV is affected by the cost, perceived difficulty of recycling behaviors, and social norms. Moreover, the type of network connecting agents and the initial recycling rate strongly influence results. The model also highlights the crucial role of recycling behavior adoption: in case of early failure of PV, recycled volumes increase by about 40%. This represents an additional 5.7 billion USD from potential recovered silver. Finally, although results for the PV case are presented here, the developed ABM aims at being a general tool for the study of CE strategies and the CE transition. Furthermore, steps of this research include extending the model to encompass circular economy strategies (e.g., design for recycling or lifetime extension) and validating its general architecture from various case studies.

14 SOLAR ENERGY↗

DOE OSTI2025

Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker–Planck Equations

The Fokker-Planck (FP) equation is a foundational partial differential equation (PDE) in stochastic processes involving Brownian motions. However, the curse of dimensionality (CoD) poses a formidable challenge when dealing with high-dimensional FP equations. Although Monte Carlo simulation and (vanilla) Physics-Informed Neural Networks (PINNs) have shown the potential to tackle CoD, both methods exhibit significant numerical errors in high dimensions when dealing with the probability density function (PDF) associated with Brownian motion. The point-wise PDF values tend to decrease exponentially as dimensionality increases, surpassing the precision of numerical simulations and resulting in substantial errors. In addition, due to its massive sampling, Monte Carlo fails to offer fast sampling. Modeling the logarithm likelihood (LL) via vanilla PINNs transforms the FP equation into a notoriously difficult Hamilton-Jacobi-Bellman (HJB) equation, which is impractical for PINN learning, whose error grows rapidly with dimension. To this end, we propose a novel approach utilizing a score-based solver to fit the score function in stochastic differential equations (SDEs). The score function, defined as the gradient of the LL, plays a fundamental role in inferring LL and PDF and enables fast SDE sampling, offering an effective means to overcome the CoD. Three fitting methods, Score Matching (SM), Sliced Score Matching (SSM), and Score-PINN, are introduced, each contributing unique advantages in computational complexity, accuracy, and generality. The proposed score-based SDE solver operates in two stages: first, employing score matching or Score-PINN to acquire the score function; and second, solving the LL via an ordinary differential equation (ODE) using the obtained score function. Comparative evaluations across these methods showcase varying trade-offs. The proposed methodology is evaluated across diverse SDEs, including anisotropic Ornstein-Uhlenbeck processes, geometric Brownian motion, and Brownian motion with varying eigenspace. We also test various distributions, including Gaussian, Log-normal, Laplace, and Cauchy distributions. The numerical results demonstrate the score-based SDE solver’s stability, speed, and performance across different experimental settings, solidifying its potential as a solution to CoD for high-dimensional FP equations.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2008

Recent Insights into the Nature of Turbulence in the Solar Wind

During the past several years, studies of solar wind turbulence using data from Cluster and other spacecraft, and results from new numerical simulations, have revealed new aspects of solar wind turbulence. I will try to highlight some of that research. At the shortest length scales and highest frequencies, there is renewed interest in determining how the turbulence dissipates, e.g., whether by kinetic Alfven waves or whistler turbulence. Finding observational evidence for exponential damping of solar wind fluctuations has proven challenging. New studies using a combination of flux gate and search coil magnetometer data from Cluster have extended this search (in the spacecraft frame of reference) to more than 10 Hertz. New models and simulations are also being used to study the dissipation. A detailed study of fluctuations in the magnetosheath suggests that turbulent dissipation could be occurring at very thin current sheets as had been suggested by two-dimensional MHD simulations more than 20 years ago. Data from the four Cluster spacecraft, now at their maximum separation of 10,000 km provide new opportunities to investigate the symmetry properties, scale lengths, and the relative proportion of magnetic energy in parallel and perpendicular wave numbers of solar wind turbulence. By utilizing well-calibrated electron data, it has been possible to take advantage of the tetrahedral separation of Cluster in the solar wind near apogee to measure directly the compressibility and vorticity of the solar wind plasma.

Goldstein, Melvun L.↗

NASA NTRS2005

Developing a Framework for Effective Network Capacity Planning

As Internet traffic continues to grow exponentially, developing a clearer understanding of, and appropriately measuring, network's performance is becoming ever more critical. An important challenge faced by the Information Resources Directorate (IRD) at the Johnson Space Center in this context remains not only monitoring and maintaining a secure network, but also better understanding the capacity and future growth potential boundaries of its network. This requires capacity planning which involves modeling and simulating different network alternatives, and incorporating changes in design as technologies, components, configurations, and applications change, to determine optimal solutions in light of IRD's goals, objectives and strategies. My primary task this summer was to address this need. I evaluated network-modeling tools from OPNET Technologies Inc. and Compuware Corporation. I generated a baseline model for Building 45 using both tools by importing "real" topology/traffic information using IRD's various network management tools. I compared each tool against the other in terms of the advantages and disadvantages of both tools to accomplish IRD's goals. I also prepared step-by-step "how to design a baseline model" tutorial for both OPNET and Compuware products.

Yaprak, Ece↗

DOE OSTI2024

Scanning electrochemical probe microscopy investigation of two-dimensional materials

Research interests in two-dimensional (2D) materials have seen exponential growth owing to their unique and fascinating properties. The highly exposed lattice planes coupled with tunable electronic states of 2D materials have created manifold opportunities in the design of new platforms for energy conversion and sensing applications. Still, challenges in understanding the electrochemical (EC) characteristics of these materials arise from the complexity of both intrinsic and extrinsic heterogeneities that can obscure structure–activity correlations. Scanning EC probe microscopic investigations offer unique benefits in disclosing local EC reactivities at the nanoscale level that are otherwise inaccessible with macroscale methods. This review summarizes recent progress in applying techniques of scanning EC microscopy (SECM) and scanning EC cell microscopy (SECCM) to obtain distinctive insights into the fundamentals of 2D electrodes. We showcase the capabilities of EC microscopies in addressing the roles of defects, thickness, environments, strain, phase, stacking, and many other aspects in the heterogeneous electron transfer, ion transport, electrocatalysis, and photoelectrochemistry of representative 2D materials and their derivatives. Perspectives for the advantages, challenges, and future opportunities of scanning EC probe microscopy investigation of 2D structures are discussed.

36 MATERIALS SCIENCE↗

NASA NTRS2007

Generative Representations for Automated Design of Robots

A method of automated design of complex, modular robots involves an evolutionary process in which generative representations of designs are used. The term generative representations as used here signifies, loosely, representations that consist of or include algorithms, computer programs, and the like, wherein encoded designs can reuse elements of their encoding and thereby evolve toward greater complexity. Automated design of robots through synthetic evolutionary processes has already been demonstrated, but it is not clear whether genetically inspired search algorithms can yield designs that are sufficiently complex for practical engineering. The ultimate success of such algorithms as tools for automation of design depends on the scaling properties of representations of designs. A nongenerative representation (one in which each element of the encoded design is used at most once in translating to the design) scales linearly with the number of elements. Search algorithms that use nongenerative representations quickly become intractable (search times vary approximately exponentially with numbers of design elements), and thus are not amenable to scaling to complex designs. Generative representations are compact representations and were devised as means to circumvent the above-mentioned fundamental restriction on scalability. In the present method, a robot is defined by a compact programmatic form (its generative representation) and the evolutionary variation takes place on this form. The evolutionary process is an iterative one, wherein each cycle consists of the following steps: 1. Generative representations are generated in an evolutionary subprocess. 2. Each generative representation is a program that, when compiled, produces an assembly procedure. 3. In a computational simulation, a constructor executes an assembly procedure to generate a robot. 4. A physical-simulation program tests the performance of a simulated constructed robot, evaluating the performance according to a fitness criterion to yield a figure of merit that is fed back into the evolutionary subprocess of the next iteration. In comparison with prior approaches to automated evolutionary design of robots, the use of generative representations offers two advantages: First, a generative representation enables the reuse of components in regular and hierarchical ways and thereby serves a systematic means of creating more complex modules out of simpler ones. Second, the evolved generative representation may capture intrinsic properties of the design problem, so that variations in the representations move through the design space more effectively than do equivalent variations in a nongenerative representation. This method has been demonstrated by using it to design some robots that move, variously, by walking, rolling, or sliding. Some of the robots were built (see figure). Although these robots are very simple, in comparison with robots designed by humans, their structures are more regular, modular, hierarchical, and complex than are those of evolved designs of comparable functionality synthesized by use of nongenerative representations.

Homby, Gregory S.↗

NASA NTRS2014

Phase Transitions in Planning Problems: Design and Analysis of Parameterized Families of Hard Planning Problems

There are two common ways to evaluate algorithms: performance on benchmark problems derived from real applications and analysis of performance on parametrized families of problems. The two approaches complement each other, each having its advantages and disadvantages. The planning community has concentrated on the first approach, with few ways of generating parametrized families of hard problems known prior to this work. Our group's main interest is in comparing approaches to solving planning problems using a novel type of computational device - a quantum annealer - to existing state-of-the-art planning algorithms. Because only small-scale quantum annealers are available, we must compare on small problem sizes. Small problems are primarily useful for comparison only if they are instances of parametrized families of problems for which scaling analysis can be done. In this technical report, we discuss our approach to the generation of hard planning problems from classes of well-studied NP-complete problems that map naturally to planning problems or to aspects of planning problems that many practical planning problems share. These problem classes exhibit a phase transition between easy-to-solve and easy-to-show-unsolvable planning problems. The parametrized families of hard planning problems lie at the phase transition. The exponential scaling of hardness with problem size is apparent in these families even at very small problem sizes, thus enabling us to characterize even very small problems as hard. The families we developed will prove generally useful to the planning community in analyzing the performance of planning algorithms, providing a complementary approach to existing evaluation methods. We illustrate the hardness of these problems and their scaling with results on four state-of-the-art planners, observing significant differences between these planners on these problem families. Finally, we describe two general, and quite different, mappings of planning problems to QUBOs, the form of input required for a quantum annealing machine such as the D-Wave II.

Problems↗

DOE OSTI2024

Challenges in Tracking Waste Reduction Performance Improvement in Manufacturing Plants

The recently released Circularity Gap Report 2023 by Circle Economy Foundation found that the circularity score for the global economy is declining. This indicates that material extraction from virgin sources is climbing over earlier years. As per data released by US Geological Survey, material use in the US economy has increased exponentially with the expanding US economy over last century. EPA tracked municipal solid waste from 1960 to 2018 and found that 50% of the waste is destined for landfills. EPA estimates that US industry is responsible for 2.7 billion ton of solid non-hazardous waste annually in our mostly linear economy model. The circular economy framework aims at decoupling economic value generation from virgin materials extraction from nature. The linear model of material extraction and disposal at end of life is highly unsustainable. Manufacturing companies have realized this and in their commitments to sustainability are adopting ambitious waste reduction targets. Through Better Plants program US Department of Energy has established Waste Reduction Network where it is offering technical assistance to partners to achieve these ambitious waste reduction goals. Basic requirements of establishing a target include identifying a baseline, quantifying waste performance, and measuring progress over time. One problem faced by industry is the unstandardized metrics to quantify waste performance that may not be well suited to demonstrate progress. In this paper, we research methods traditionally used to measure waste performance and highlight advantages, gaps and limitations of each method. Suitability of the methods applicable to different manufacturing circumstances are also examined. Finally, we present a case study of a large manufacturer that faced inconsistencies in their tracked measurement metric. A solution was proposed to alter the methodology to enable more accurate waste performance tracking against a baseline.

Chaudhari, Subodh↗

NASA NTRS2010

Hidden Statistics Approach to Quantum Simulations

Recent advances in quantum information theory have inspired an explosion of interest in new quantum algorithms for solving hard computational (quantum and non-quantum) problems. The basic principle of quantum computation is that the quantum properties can be used to represent structure data, and that quantum mechanisms can be devised and built to perform operations with this data. Three basic non-classical properties of quantum mechanics superposition, entanglement, and direct-product decomposability were main reasons for optimism about capabilities of quantum computers that promised simultaneous processing of large massifs of highly correlated data. Unfortunately, these advantages of quantum mechanics came with a high price. One major problem is keeping the components of the computer in a coherent state, as the slightest interaction with the external world would cause the system to decohere. That is why the hardware implementation of a quantum computer is still unsolved. The basic idea of this work is to create a new kind of dynamical system that would preserve the main three properties of quantum physics superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. In other words, such a system would reinforce the advantages and minimize limitations of both quantum and classical aspects. Based upon a concept of hidden statistics, a new kind of dynamical system for simulation of Schroedinger equation is proposed. The system represents a modified Madelung version of Schroedinger equation. It preserves superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. Such an optimal combination of characteristics is a perfect match for simulating quantum systems. The model includes a transitional component of quantum potential (that has been overlooked in previous treatment of the Madelung equation). The role of the transitional potential is to provide a jump from a deterministic state to a random state with prescribed probability density. This jump is triggered by blowup instability due to violation of Lipschitz condition generated by the quantum potential. As a result, the dynamics attains quantum properties on a classical scale. The model can be implemented physically as an analog VLSI-based (very-large-scale integration-based) computer, or numerically on a digital computer. This work opens a way of developing fundamentally new algorithms for quantum simulations of exponentially complex problems that expand NASA capabilities in conducting space activities. It has been illustrated that the complexity of simulations of particle interaction can be reduced from an exponential one to a polynomial one.

Zak, Michail↗

DOE OSTI2022

Performance Evaluations of Noisy Approximate Quantum Fourier Arithmetic

The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route towards a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor’s algorithm, weighted sum optimization problems in data processing and machine learning and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM’s superconducting qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands’ superposed integer states. We analyze performance, and identify the most effective approximation depths for quantum add and quantum multiply within the given context. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges - relevant to signed, unsigned, modular and non-modular versions - that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. Here, we analyze performance trends in our results and speculate on possible future development within this computational paradigm.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2008

Spiking Neurons for Analysis of Patterns

Artificial neural networks comprising spiking neurons of a novel type have been conceived as improved pattern-analysis and pattern-recognition computational systems. These neurons are represented by a mathematical model denoted the state-variable model (SVM), which among other things, exploits a computational parallelism inherent in spiking-neuron geometry. Networks of SVM neurons offer advantages of speed and computational efficiency, relative to traditional artificial neural networks. The SVM also overcomes some of the limitations of prior spiking-neuron models. There are numerous potential pattern-recognition, tracking, and data-reduction (data preprocessing) applications for these SVM neural networks on Earth and in exploration of remote planets. Spiking neurons imitate biological neurons more closely than do the neurons of traditional artificial neural networks. A spiking neuron includes a central cell body (soma) surrounded by a tree-like interconnection network (dendrites). Spiking neurons are so named because they generate trains of output pulses (spikes) in response to inputs received from sensors or from other neurons. They gain their speed advantage over traditional neural networks by using the timing of individual spikes for computation, whereas traditional artificial neurons use averages of activity levels over time. Moreover, spiking neurons use the delays inherent in dendritic processing in order to efficiently encode the information content of incoming signals. Because traditional artificial neurons fail to capture this encoding, they have less processing capability, and so it is necessary to use more gates when implementing traditional artificial neurons in electronic circuitry. Such higher-order functions as dynamic tasking are effected by use of pools (collections) of spiking neurons interconnected by spike-transmitting fibers. The SVM includes adaptive thresholds and submodels of transport of ions (in imitation of such transport in biological neurons). These features enable the neurons to adapt their responses to high-rate inputs from sensors, and to adapt their firing thresholds to mitigate noise or effects of potential sensor failure. The mathematical derivation of the SVM starts from a prior model, known in the art as the point soma model, which captures all of the salient properties of neuronal response while keeping the computational cost low. The point-soma latency time is modified to be an exponentially decaying function of the strength of the applied potential. Choosing computational efficiency over biological fidelity, the dendrites surrounding a neuron are represented by simplified compartmental submodels and there are no dendritic spines. Updates to the dendritic potential, calcium-ion concentrations and conductances, and potassium-ion conductances are done by use of equations similar to those of the point soma. Diffusion processes in dendrites are modeled by averaging among nearest-neighbor compartments. Inputs to each of the dendritic compartments come from sensors. Alternatively or in addition, when an affected neuron is part of a pool, inputs can come from other spiking neurons. At present, SVM neural networks are implemented by computational simulation, using algorithms that encode the SVM and its submodels. However, it should be possible to implement these neural networks in hardware: The differential equations for the dendritic and cellular processes in the SVM model of spiking neurons map to equivalent circuits that can be implemented directly in analog very-large-scale integrated (VLSI) circuits.

Huntsberger, Terrance↗