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DOE OSTI2026

FunDiff: diffusion models over function spaces for physics-informed generative modeling

Recent advances in generative modeling-particularly diffusion models and flow matching-have been widely used for synthesizing discrete data such as images and videos. However, adapting these models to physical applications remains challenging, as the quantities of interest are continuous functions governed by complex physical laws. To address this, we introduce FunDiff, an efficient and robust framework for generative modeling in function spaces. FunDiff combines a latent diffusion process with a function autoencoder architecture to handle input functions with varying discretizations, generates continuous functions that can be evaluated at arbitrary locations, and seamlessly incorporate physical priors. These priors are enforced through architectural constraints or physics-informed loss functions, ensuring that generated samples satisfy fundamental physical laws. We theoretically establish minimax optimality guarantees for density estimation in function spaces, demonstrating that diffusion-based estimators achieve optimal convergence rates under suitable regularity conditions. We further demonstrate the practical effectiveness of FunDiff across diverse applications in fluid dynamics and solid mechanics. Empirical results indicate that our method can generate physically consistent samples with high fidelity to the target distribution, and exhibit robustness to noisy and low-resolution data.

Wang, Sifan [Yale University, New Haven, CT (Unite↗

NASA NTRS2000

Fluid Physics and Macromolecular Crystal Growth in Microgravity

The first protein crystallization experiment in microgravity was launched in April, 1981 and used Germany's Technologische Experimente unter Schwerelosigkeit (TEXUS 3) sounding rocket. The protein P-galactosidase (molecular weight 465Kda) was chosen as the sample with a liquid-liquid diffusion growth method. A sliding device brought the protein, buffer and salt solution into contact when microgravity was reached. The sounding rocket gave six minutes of microgravity time with a cine camera and schlieren optics used to monitor the experiment, a single growth cell. In microgravity a strictly laminar diffusion process was observed in contrast to the turbulent convection seen on the ground. Several single crystals, approx 100micron in length, were formed in the flight which were of inferior but of comparable visual quality to those grown on the ground over several days. A second experiment using the same protocol but with solutions cooled to -8C (kept liquid with glycerol antifreeze) again showed laminar diffusion. The science of macromolecular structural crystallography involves crystallization of the macromolecule followed by use of the crystal for X-ray diffraction experiments to determine the three dimensional structure of the macromolecule. Neutron protein crystallography is employed for elucidation of H/D exchange and for improved definition of the bound solvent (D20). The structural information enables an understanding of how the molecule functions with important potential for rational drug design, improved efficiency of industrial enzymes and agricultural chemical development. The removal of turbulent convection and sedimentation in microgravity, and the assumption that higher quality crystals will be produced, has given rise to the growing number of crystallization experiments now flown. Many experiments can be flown in a small volume with simple, largely automated, equipment - an ideal combination for a microgravity experiment. The term "protein crystal growth" is often historically used to describe these microgravity experiments. This is somewhat inaccurate as the field involves the study of many varied biological molecules including viruses, proteins, DNA, RNA and complexes of those structures. For this reason we use the term macromolecular crystal growth. In this chapter we review a series of diagnostic microgravity crystal growth experiments carried out principally using the European Space Agency (ESA) Advanced Protein Crystallization Facility (APCF). We also review related research, both experimental and theoretical, on the aspects of microgravity fluid physics that affect microgravity protein crystal growth. Our experiments have revealed some surprises that were not initially expected. We discuss them here in the context of practical lessons learnt and how to maximize the limited microgravity opportunities available.

Helliwell, John R.↗

NASA NTRS2007

Isotopic Measurements in CAIs with the Nanosims: Implications to the understanding of the Formation process of Ca, Al-Rich Inclusions

Ca, Al-rich Inclusions (CAIs) preserve evidence of thermal events that they experienced during their formation in the early solar system. Most CAIs from CV and CO chondrites are characterized by large variations in O-isotopic compositions of primary minerals, with spinel, hibonite, and pyroxene being more O-16-rich than melilite and anorthite, with delta 17, O-18 = approx. -40%o (DELTA O-17 = delta O-17 - 0.52 x delta O-18 = approx. - 20%o ). These anomalous compositions cannot be accounted for by standard mass dependent fractionation and diffusive process of those minerals. It requires the presence of an anomalous oxygen reservoir of nucleosynthetic origin or mass independent fractionations before the formation of CAIs in the early solar system. The CAMECA NanoSIMS is a new generation ion microprobe that offers high sensitivity isotopic measurements with sub 100 nm spatial resolution. The NanoSIMS has significantly improved abilities in the study of presolar grains in various kind of meteorites and the decay products of extinct nuclides in ancient solar system matter. This instrument promises significant improvements over other conventional ion probes in the precision isotopic characterization of sub-micron scales. We report the results of our first O isotopic measurements of various CAI minerals from EK1-6-3 and 7R19-1(a) utilizing the JSC NanoSIMS 50L ion microprobe. We evaluate the measurement conditions, the instrumental mass fractionation factor (IMF) for O isotopic measurement and the accuracy of the isotopic ratio through the analysis of a San Carlos olivine standard and CAI sample of 7R19-1(a).

Ito, M.↗

NASA NTRS1999

Fluid Physics in a Fluctuating Acceleration Environment

Our program of research aims at developing a stochastic description of the residual acceleration field onboard spacecraft (g-jitter) to describe in quantitative detail its effect on fluid motion. Our main premise is that such a statistical description is necessary in those cases in which the characteristic time scales of the process under investigation are long compared with the correlation time of g-jitter. Although a clear separation between time scales makes this approach feasible, there remain several difficulties of practical nature: (i), g-jitter time series are not statistically stationary but rather show definite dependences on factors such as active or rest crew periods; (ii), it is very difficult to extract reliably the low frequency range of the power spectrum of the acceleration field. This range controls the magnitude of diffusive processes; and (iii), models used to date are Gaussian, but there is evidence that large amplitude disturbances occur much more frequently than a Gaussian distribution would predict. The lack of stationarity does not constitute a severe limitation in practice, since the intensity of the stochastic components changes very slowly during space missions (perhaps over times of the order of hours). A separate analysis of large amplitude disturbances has not been undertaken yet, but it does not seem difficult a priori to devise models that may describe this range better than a Gaussian distribution. The effect of low frequency components, on the other hand, is more difficult to ascertain, partly due to the difficulty associated with measuring them, and partly because they may be indistinguishable from slowly changing averages. This latter effect is further complicated by the lack of statistical stationarity of the time series. Recent work has focused on the effect of stochastic modulation on the onset of oscillatory instabilities as an example of resonant interaction between the driving acceleration and normal modes of the system, and on cavity flow as an example of how an oscillatory response under periodic driving becomes diffusive if the forcing is random instead. This paper describes three different topics that illustrate behavior that is peculiar to a stochastic acceleration field. In the first case, we show that g-jitter can induce effective attractive or repulsive forces between a pair of spherical particles that are suspended in an incompressible fluid of different density provided that the momentum diffusion length is larger than the interparticle separation (as in the case in most colloidal suspensions). Second, a stochastic modulation of the control parameter in the vicinity of a pitchfork or supercritical bifurcation is known not to affect the location of the threshold. We show, however, that resonance between the modulation and linearly stable modes close to onset can lead to a shift in threshold. Finally, we discuss the classical problem of vorticity diffusion away from a plane boundary that is being vibrated along its own plane. Periodic motion with zero average vorticity production results in an exponential decay of the vorticity away from the boundary. Random vibration, on the other hand, results in power law decay away from the boundary even if vorticity production averages to zero.

Drolet, Francois↗

NASA NTRS1980

Empirical study of the interaction of silicon substrate thinness, device design, and solar cell processing

Processing experiments using wire-saw techniques to slice thin silicon wafers are described. Substrates were sliced directly to 17 mil, 8 mil, and 5 mil thicknesses. Some of the 8 mil substrates and all of the 5 mil substrates were chemically etched to 7 and 4 mils, respectively, to guarantee removal of any saw damage. The wafers wire sawed to 17 mil thicknesses were processed as reference cells. A baseline process which results in an n(+)-p cell structure, and two advanced processes which provide n(+)-p-p(+) structures were utilized. By using a p(+) enhancement layer on the solar cell back surface, the performance of the 7 mil wafers was increased to exceed that of the 17 mil solar cells with simple n(+)-p structures. Cells fabricated by an ion implantation sequence utilizing elemental boron and phosphorus implants were shown to be capable of equalling or exceeding the performance of cells fabricated by an equivalent all-diffusion process.

Pryor, R. A.↗

NASA NTRS1981

Advances in high output voltage silicon solar cells

Solar cells have been fabricated from 0.1 ohm-cm, p-type silicon by means of a two-step diffusion process of emitter formation in order to delineate the factors limiting V(oc) in conventionally structured cells with the goal of achieving 700 mV. The cells are 200 microns thick and 2 x 2 cm in area with a planar front surface that has an anti-reflection coating of tantalum oxide, as well as Cr-Au-Ag contact metallization on both sides of the cell. The Cr-Au-Ag is applied over an aluminum diffused layer on the back, while it is applied through small holes in the anti-reflection coating on the front. Results show that the best of these cells exhibits an open-circuit voltage of 654 mV under AMO illumination.

Arndt, R. A.↗

NASA NTRS1982

Ion-beam-induced topography and surface diffusion

It is pointed out that the development of surface topography along with enhanced surface and bulk diffusion processes accompanying ion bombardment have generated growing interest among users of ion beams and plasmas for thin film or material processing. Interest in these processes stems both from attempts to generate topographic changes for specific studies or applications and from the need to suppress or control undesirable changes. The present investigation provides a summary of the current status of impurity-induced texturing, with emphasis on recent developments. Particular attention is given to the texturing accompanying deposition of an impurity material onto a solid surface while simultaneously etching the surface with an ion beam. A description of experimental considerations is provided, and a thermal-diffusion model is discussed along with the development of sputter cones, and aspects of impact-enhanced surface diffusion.

Robinson, R. S.↗

NASA NTRS1990

On neglect of nonlinear momentum terms in solar nebula accretion disk models

The standard model for accretion disks (e.g., Pringle, 1981; Lin and Papaloizou, 1985) parameterizes the radial eddy angular momentum flux which is quadratically nonlinear in velocity, solely by a viscous diffusion process which is linear in velocity. This paper shows that the eddy angular momentum flux, in addition to a gradient dissipative (viscous) flux, involves a countergradient accelerating flux. Therefore, the momentum parameterization in the standard model is in general unjustified. The formalism of the parameterization can be justified only by recognizing that the eddy viscosity used in the standard model is in fact a pseudoviscosity which includes the effects of countergradient fluxes, and which therefore may have a magnitude less than the eddy diffusivity K for mixing trace constituents in the disk.

Prinn, Ronald G.↗

NASA NTRS1992

NASA/DoD Aerospace Knowledge Diffusion Research Project. Paper 30: The electronic transfer of information and aerospace knowledge diffusion

Increasing reliance on and investment in information technology and electronic networking systems presupposes that computing and information technology will play a major role in the diffusion of aerospace knowledge. Little is known, however, about actual information technology needs, uses, and problems within the aerospace knowledge diffusion process. The authors state that the potential contributions of information technology to increased productivity and competitiveness will be diminished unless empirically derived knowledge regarding the information-seeking behavior of the members of the social system - those who are producing, transferring, and using scientific and technical information - is incorporated into a new technology policy framework. Research into the use of information technology and electronic networks by U.S. aerospace engineers and scientists, collected as part of a research project designed to study aerospace knowledge diffusion, is presented in support of this assertion.

Pinelli, Thomas E.↗

NASA NTRS1992

The electronic transfer of information and aerospace knowledge diffusion

Increasing reliance on and investment in information technology and electronic networking systems presupposes that computing and information technology will play a motor role in the diffusion of aerospace knowledge. Little is known, however, about actual information technology needs, uses, and problems within the aerospace knowledge diffusion process. The authors state that the potential contributions of information technology to increased productivity and competitiveness will be diminished unless empirically derived knowledge regarding the information-seeking behavior of the members of the social system - those who are producing, transferring, and using scientific and technical information - is incorporated into a new technology policy framework. Research into the use of information technology and electronic networks by U.S. aerospace engineers and scientists, collected as part of a research project designed to study aerospace knowledge diffusion, is presented in support of this assertion.

Pinelli, Thomas E.↗

NASA NTRS1985

Double-injection, deep-impurity switch development

The overall objective of this program was the development of device design and process techniques for the fabrication of a double-injection, deep-impurity (DI) sup 2 silicon switch that operates in the 2-10 kV range with conduction current values of 5 A at 2 kV and 1 A at 10 kV. Other major specifications include a holding voltage of 10 V with no gate current, 10 microsec switching time, and power dissipation of 50 W at 75 C. It was decided to concentrate on the lateral circular devices in order to optimize the gold diffusion. This resulted in devices that are much better switches (approx.1 micro sec switching time), and in a gold diffusion process that is much more controllable than those previously developed. Some results with injection-gated devices were also obtained. The current conduction for V less than VT was analyzed and seen to agree, for the most part, with Lampert's theory. Various sections of this report describe the device designs, wafer-processing techniques, and various measurements which include ac and dc characteristics and four-point probe.

Whitson, D. W.↗

NASA NTRS2000

The Turbulent/Non-Turbulent Interface Bounding a Far-Wake

The velocity fields of a turbulent wake behind a flat plate obtained from the direct numerical simulations of Moser et al. are used to study the structure of the flow in the intermittent zone where there are, alternately, regions of fully turbulent flow and non-turbulent velocity fluctuations either side of a thin randomly moving interface. Comparisons are made with a wake that is 'forced' by amplifying initial velocity fluctuations. There is also a random temperature field T in the flow; T varies between constant values of 0.0 and 1.0 on the sides of the wake. The value of the Reynolds number based on the centreplane mean velocity defect and halfwidth b of the wake is Re approx. = 2000. It is found that the thickness of the continuous interface is about equal to 0.07b, whereas the amplitude of fluctuations of the instantaneous interface displacement y(sub I)(t) is an order of magnitude larger, being about 0.5b. This explains why the mean statistics of vorticity in the intermittent zone can be calculated in terms of the probability distribution of y(sub I) and the instantaneous discontinuity in vorticity across the interface. When plotted as functions of y - y(sub I), the conditional mean velocity (U) and temperature (T) profiles show sharp jumps Delta(U) and Delta(T) at the interface adjacent to a thick zone where (U) and (T) vary much more slowly. Statistics for the vorticity and velocity variances, available in such detail only from DNS data, show how streamwise and spanwise components of vorticity are generated by vortex stretching in the bulges of the interface. Flow fields around the interface, analyzed in terms of the local streamline pattern, confirm previous results that the advancement of the vortical interface into the irrotational flow is driven by large-scale eddy motion. It is argued that because this is an inviscid mechanism the entrainment process is not sensitive to the value of Re, and that small-scale nibbling only plays a subsidiary role. While mean Reynolds stresses decrease gradually in the intermittent zone, conditional stresses are found to decrease sharply towards zero at the interface. Using one-point turbulence models applied to either unconditional or conditional statistics for the turbulent region and then averaged, the entrainment rate E(sub b) would, if calculated exactly, be zero. But if computed with standard computational methods, E(sub b) would be non-zero because of numerical diffusion. It is concluded that the current practice in statistical models of approximating entrainment by a diffusion process is computationally arbitrary and physically incorrect. An analysis shows how E(sub b) is related to Delta(U) and the jump in shear stress at the interface, and correspondingly to Delta(T) and the heat flux.

Bisset, David K.↗

NASA NTRS1994

Microencapsulation of anti-tumor, antibiotic and thrombolytic drugs in microgravity

Encapsulation of cytotoxic or labile drugs enables targeted delivery and sustained release kinetics that are not available with intravenous injection. A new liquid-liquid diffusion process has been developed for forming unique microcapsules that contain both aqueous and hydrocarbon soluble drugs. Microgravity experiments, on sounding rockets (1989-92) and Shuttle missions STS-52 (1992) and STS-56 (1993) using an automated Materials Dispersion Apparatus, produced multi-lamellar microcapsules containing both Cis-platinum (anti-tumor drug) and iodinated poppy seed oil (a radiocontrast medium), surrounded by a polyglyceride skin. Microcapsules formed with amoxicillin (antibiotic) or urokinase (a clot dissolving enzyme), co-encapsulated with IPO, are still intact after two years. Microcapsules were formed with the drug so concentrated that crystals formed inside. Multi-layered microspheres, with both hydrophobic drug compartments, can enable diffusion of complementary drugs from the same microcapsule, e.g. antibiotics and immuno-stimulants to treat resistant infections or multiple fibrinolytic drugs to dissolve emboli. Co-encapsulation of enough radio-contrast medium enables oncologists to monitor the delivery of anti-tumor microcapsules to target tumors using computerized tomography and radiography that would track the distribution of microcapsules after release from the intra-arterial catheter. These microcapsules could have important applications in chemotheraphy of certain liver, kidney, brain and other tumors.

Morrison, Dennis R.↗

DOE OSTI2024

Controlled patterning of crystalline domains by frontal polymerization

Materials with hierarchical architectures that combine soft and hard material domains with coalesced interfaces possess superior properties compared with their homogeneous counterparts. These architectures in synthetic materials have been achieved through deterministic manufacturing strategies such as 3D printing, which require an a priori design and active intervention throughout the process to achieve architectures spanning multiple length scales. Here we harness frontal polymerization spin mode dynamics to autonomously fabricate patterned crystalline domains in poly(cyclooctadiene) with multiscale organization. This rapid, dissipative processing method leads to the formation of amorphous and semi-crystalline domains emerging from the internal interfaces generated between the solid polymer and the propagating cure front. The size, spacing and arrangement of the domains are controlled by the interplay between the reaction kinetics, thermochemistry and boundary conditions. Small perturbations in the fabrication conditions reproducibly lead to remarkable changes in the patterned microstructure and the resulting strength, elastic modulus and toughness of the polymer. Furthermore, this ability to control mechanical properties and performance solely through the initial conditions and the mode of front propagation represents a marked advancement in the design and manufacturing of advanced multiscale materials. Drawing inspiration from biological systems in which structural complexity develops through dissipative reaction–diffusion processes, this study explores a transformative synthetic manufacturing strategy aimed at harnessing the principles underpinning morphogenic growth, unlocking new avenues for advanced materials design and fabrication. Synthetic coupled reaction-transport processes offer a versatile yet relatively underexplored method to manipulate the spatial attributes of synthetic materials10. Here we introduce an innovative manufacturing approach based on frontal ring-opening metathesis polymerization (FROMP) that draws parallels with morphogenic growth and development, enabling the formation of patterned microstructures within polymeric materials.

36 MATERIALS SCIENCE↗

NASA NTRS1998

Multiple-breath washin of helium and sulfur hexafluoride in sustained microgravity

We performed multiple-breath washouts of N2 and simultaneous washins of He and SF6 with fixed tidal volume (approximately 1,250 ml) and preinspiratory lung volume (approximately the subject's functional residual capacity in the standing position) in four normal subjects (mean age 40 yr) standing and supine in normal gravity (1 G) and during exposure to sustained microgravity (microG). The primary objective was to examine the influence of diffusive processes on the residual, nongravitational ventilatory inhomogeneity in the lung in microG. We calculated several indexes of convective ventilatory inhomogeneity from each gas species. A normal degree of ventilatory inhomogeneity was seen in the standing position at 1 G that was largely unaltered in the supine position. When we compared the standing position in 1 G with microG, there were reductions in phase III slope in all gases, consistent with a reduction in convection-dependent inhomogeneity in the lung in microG, although considerable convective inhomogeneity persisted in microG. The reductions in the indexes of convection-dependent inhomogeneity were greater for He than for SF6, suggesting that the distances between remaining nonuniformly ventilated compartments in microG were short enough for diffusion of He to be an effective mechanism to reduce gas concentration differences between them.

NASA Discipline Cardiopulmonary↗

NASA NTRS1990

Chemical reaction of atomic oxygen with evaporated films of copper, part 4

Evaporated copper films were exposed to an atomic oxygen flux of 1.4 x 10(exp 17) atoms/sq cm per sec at temperatures in the range 285 to 375 F (140 to 191 C) for time intervals between 2 and 50 minutes. Rutherford backscattering spectroscopy (RBS) was used to determine the thickness of the oxide layers formed and the ratio of the number of copper to oxygen atoms in the layers. Oxide film thicknesses ranged from 50 to 3000 A (0.005 to 0.3 microns, or equivalently, 5 x 10(exp -9) to 3 x 10(exp -7); it was determined that the primary oxide phase was Cu2O. The growth law was found to be parabolic (L(t) varies as t(exp 1/2)), in which the oxide thickness L(t) increases as the square root of the exposure time t. The analysis of the data is consistent with either of the two parabolic growth laws. (The thin-film parabolic growth law is based on the assumption that the process is diffusion controlled, with the space charge within the growing oxide layer being negligible. The thick-film parabolic growth law is also based on a diffusion controlled process, but space-charge neutrality prevails locally within very thick oxides.) In the absence of a voltage measurement across the growing oxide, a distinction between the two mechanisms cannot be made, nor can growth by the diffusion of neutral atomic oxygen be entirely ruled out. The activation energy for the reaction is on the order of 1.1 eV (1.76 x 10(exp -19) joule, or equivalently, 25.3 kcal/mole).

Fromhold, A. T.↗

NASA NTRS1978

Research on solar-wind and magnetospheric electric fields and plasmas

Attempts were made to determine the role of the interplanetary magnetic field in controlling: (1) particle acceleration processes in the earth's polar cap; (2) plasma convection patterns at high latitudes; and, (3) the topology of magnetic field lines in the earth's polar cusps. The primary result of the study on polar-cap particle acceleration regions was that they tend to occur in only one polar cap at a time, and that they occur in the hemisphere for which the magnetospheric tail-lobe field lines have solar-magnetospheric x components that are antiparallel to those of the interplanetary and tail-lobe magnetic field. Southward-directed interplanetary magnetic fields give rise to broad convection throats which cover several hours of local time across the dayside cleft. Under such conditions, solar-wind plasma is channeled efficiently through the polar cusps to populate the plasma mantle and dayside boundary layer. On the other hand, the appearance of strong northward components in the interplanetary magnetic field result in a very constricted throat, resulting in inefficient plasma entry at the cusps by diffusion processes.

Burch, J. L.↗

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↗