Fast and Exact Simulation Methods Applied on a Broad Range of Neuron Models

2010 ◽  
Vol 22 (6) ◽  
pp. 1468-1472 ◽  
Author(s):  
Michiel D'Haene ◽  
Benjamin Schrauwen
Keyword(s):  
Linear Models ◽  
Iteration Scheme ◽  
Integration Scheme ◽  
State Variables ◽  
Neuron Models ◽  
Time Constants ◽  
Highly Nonlinear ◽  
Wide Range ◽  
Computation Scheme ◽  
Event Based

Recently van Elburg and van Ooyen ( 2009 ) published a generalization of the event-based integration scheme for an integrate-and-fire neuron model with exponentially decaying excitatory currents and double exponential inhibitory synaptic currents, introduced by Carnevale and Hines. In the paper, it was shown that the constraints on the synaptic time constants imposed by the Newton-Raphson iteration scheme, can be relaxed. In this note, we show that according to the results published in D'Haene, Schrauwen, Van Campenhout, and Stroobandt ( 2009 ), a further generalization is possible, eliminating any constraint on the time constants. We also demonstrate that in fact, a wide range of linear neuron models can be efficiently simulated with this computation scheme, including neuron models mimicking complex neuronal behavior. These results can change the way complex neuronal spiking behavior is modeled: instead of highly nonlinear neuron models with few state variables, it is possible to efficiently simulate linear models with a large number of state variables.

Exact Subthreshold Integration with Continuous Spike Times in Discrete-Time Neural Network Simulations

2007 ◽  
Vol 19 (1) ◽  
pp. 47-79 ◽  
Author(s):  
Abigail Morrison ◽  
Sirko Straube ◽  
Hans Ekkehard Plesser ◽  
Markus Diesmann
Keyword(s):  
Grid Point ◽  
Propagation Delay ◽  
Integration Scheme ◽  
The Novel ◽  
Neuron Models ◽  
Exact Integration ◽  
Wide Range ◽  
Network Simulations ◽  
Adequate Representation ◽  
Grid Points

Very large networks of spiking neurons can be simulated efficiently in parallel under the constraint that spike times are bound to an equidistant time grid. Within this scheme, the subthreshold dynamics of a wide class of integrate-and-fire-type neuron models can be integrated exactly from one grid point to the next. However, the loss in accuracy caused by restricting spike times to the grid can have undesirable consequences, which has led to interest in interpolating spike times between the grid points to retrieve an adequate representation of network dynamics. We demonstrate that the exact integration scheme can be combined naturally with off-grid spike events found by interpolation. We show that by exploiting the existence of a minimal synaptic propagation delay, the need for a central event queue is removed, so that the precision of event-driven simulation on the level of single neurons is combined with the efficiency of time-driven global scheduling. Further, for neuron models with linear subthreshold dynamics, even local event queuing can be avoided, resulting in much greater efficiency on the single-neuron level. These ideas are exemplified by two implementations of a widely used neuron model. We present a measure for the efficiency of network simulations in terms of their integration error and show that for a wide range of input spike rates, the novel techniques we present are both more accurate and faster than standard techniques.

Accelerating Event-Driven Simulation of Spiking Neurons with Multiple Synaptic Time Constants

2009 ◽  
Vol 21 (4) ◽  
pp. 1068-1099 ◽  
Author(s):  
Michiel D'Haene ◽  
Benjamin Schrauwen ◽  
Jan Van Campenhout ◽  
Dirk Stroobandt
Keyword(s):  
Neuron Model ◽  
Driving Forces ◽  
Firing Time ◽  
State Variables ◽  
Neuron Models ◽  
Time Constants ◽  
Simulation Speed ◽  
Event Driven ◽  
Spiking Neuron Models ◽  
Algorithmic Techniques

The simulation of spiking neural networks (SNNs) is known to be a very time-consuming task. This limits the size of SNN that can be simulated in reasonable time or forces users to overly limit the complexity of the neuron models. This is one of the driving forces behind much of the recent research on event-driven simulation strategies. Although event-driven simulation allows precise and efficient simulation of certain spiking neuron models, it is not straightforward to generalize the technique to more complex neuron models, mostly because the firing time of these neuron models is computationally expensive to evaluate. Most solutions proposed in literature concentrate on algorithms that can solve this problem efficiently. However, these solutions do not scale well when more state variables are involved in the neuron model, which is, for example, the case when multiple synaptic time constants for each neuron are used. In this letter, we show that an exact prediction of the firing time is not required in order to guarantee exact simulation results. Several techniques are presented that try to do the least possible amount of work to predict the firing times. We propose an elegant algorithm for the simulation of leaky integrate-and-fire (LIF) neurons with an arbitrary number of (unconstrained) synaptic time constants, which is able to combine these algorithmic techniques efficiently, resulting in very high simulation speed. Moreover, our algorithm is highly independent of the complexity (i.e., number of synaptic time constants) of the underlying neuron model.

Exact Simulation of Integrate-and-Fire Models with Exponential Currents

2007 ◽  
Vol 19 (10) ◽  
pp. 2604-2609 ◽  
Author(s):  
Romain Brette
Keyword(s):  
The State ◽  
State Variables ◽  
Neuron Models ◽  
Time Constants ◽  
Exact Simulation ◽  
Explicit Test ◽  
Root Finding ◽  
Integrate And Fire ◽  
Fire Models ◽  
Polynomial Root Finding

Neural networks can be simulated exactly using event-driven strategies, in which the algorithm advances directly from one spike to the next spike. It applies to neuron models for which we have (1) an explicit expression for the evolution of the state variables between spikes and (2) an explicit test on the state variables that predicts whether and when a spike will be emitted. In a previous work, we proposed a method that allows exact simulation of an integrate-and-fire model with exponential conductances, with the constraint of a single synaptic time constant. In this note, we propose a method, based on polynomial root finding, that applies to integrate-and-fire models with exponential currents, with possibly many different synaptic time constants. Models can include biexponential synaptic currents and spike-triggered adaptation currents.

scholarly journals Optimal control methods for nonlinear parameter estimation in biophysical neuron models

2022 ◽  
Author(s):  
Nirag Kadakia
Keyword(s):  
Optimal Control ◽  
State Space ◽  
Measurement Noise ◽  
State Variables ◽  
Neuron Models ◽  
Unknown Parameters ◽  
Space Modeling ◽  
Wide Range ◽  
Functional Forms ◽  
Realistic Neuron

Functional forms of biophysically-realistic neuron models are constrained by neurobiological and anatomical considerations, such as cell morphologies and the presence of known ion channels. Despite these constraints, neurons models still contain unknown static parameters which must be inferred from experiment. This inference task is most readily cast into the framework of state-space models, which systematically takes into account partial observability and measurement noise. Inferring only dynamical state variables such as membrane voltages is a well-studied problem, and has been approached with a wide range of techniques beginning with the well-known Kalman filter. Inferring both states and fixed parameters, on the other hand, is less straightforward. Here, we develop a method for joint parameter and state inference that combines traditional state space modeling with chaotic synchronization and optimal control. Our methods are tailored particularly to situations with considerable measurement noise, sparse observability, very nonlinear or chaotic dynamics, and highly uninformed priors. We illustrate our approach both in a canonical chaotic model and in a phenomenological neuron model, showing that many unknown parameters can be uncovered reliably and accurately from short and noisy observed time traces. Our method holds promise for estimation in larger-scale systems, given ongoing improvements in calcium reporters and genetically-encoded voltage indicators.

scholarly journals Generalization of the Event-Based Carnevale-Hines Integration Scheme for Integrate-and-Fire Models

2009 ◽  
Vol 21 (7) ◽  
pp. 1913-1930 ◽  
Author(s):  
Ronald A. J. van Elburg ◽  
Arjen van Ooyen
Keyword(s):  
Neuron Model ◽  
Formal Proof ◽  
Integration Scheme ◽  
Synaptic Currents ◽  
General Applicability ◽  
Time Constants ◽  
Integrate And Fire ◽  
Double Exponential ◽  
Event Based ◽  
Integrate And Fire Neuron

An event-based integration scheme for an integrate-and-fire neuron model with exponentially decaying excitatory synaptic currents and double exponential inhibitory synaptic currents has been introduced by Carnevale and Hines. However, the integration scheme imposes nonphysiological constraints on the time constants of the synaptic currents, which hamper its general applicability. This letter addresses this problem in two ways. First, we provide physical arguments demonstrating why these constraints on the time constants can be relaxed. Second, we give a formal proof showing which constraints can be abolished. As part of our formal proof, we introduce the generalized Carnevale-Hines lemma, a new tool for comparing double exponentials as they naturally occur in many cascaded decay systems, including receptor-neurotransmitter dissociation followed by channel closing. Through repeated application of the generalized lemma, we lift most of the original constraints on the time constants. Thus, we show that the Carnevale-Hines integration scheme for the integrate-and-fire model can be employed for simulating a much wider range of neuron and synapse types than was previously thought.

scholarly journals Machine learning for multi-dimensional optimisation and predictive visualisation of laser machining

2021 ◽  
Author(s):  
Michael D. T. McDonnell ◽  
Daniel Arnaldo ◽  
Etienne Pelletier ◽  
James A. Grant-Jacob ◽  
Matthew Praeger ◽  
...  
Keyword(s):  
Short Pulse ◽  
Surface Texturing ◽  
Laser Surface Texturing ◽  
Laser Machining ◽  
Laser Materials ◽  
Parameter Optimisation ◽  
Short Pulse Laser ◽  
Alternative Approach ◽  
Highly Nonlinear ◽  
Wide Range

AbstractInteractions between light and matter during short-pulse laser materials processing are highly nonlinear, and hence acutely sensitive to laser parameters such as the pulse energy, repetition rate, and number of pulses used. Due to this complexity, simulation approaches based on calculation of the underlying physical principles can often only provide a qualitative understanding of the inter-relationships between these parameters. An alternative approach such as parameter optimisation, often requires a systematic and hence time-consuming experimental exploration over the available parameter space. Here, we apply neural networks for parameter optimisation and for predictive visualisation of expected outcomes in laser surface texturing with blind vias for tribology control applications. Critically, this method greatly reduces the amount of experimental laser machining data that is needed and associated development time, without negatively impacting accuracy or performance. The techniques presented here could be applied in a wide range of fields and have the potential to significantly reduce the time, and the costs associated with laser process optimisation.

scholarly journals Parameters Estimation and Prediction of Water Movement and Solute Transport in Layered, Variably Saturated Soils Using the Ensemble Kalman Filter

Water ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 1520
Author(s):  
Zheng Jiang ◽  
Quanzhong Huang ◽  
Gendong Li ◽  
Guangyong Li
Keyword(s):  
Kalman Filter ◽  
Solute Transport ◽  
Ensemble Kalman Filter ◽  
Water Movement ◽  
Parameters Estimation ◽  
Saturated Soils ◽  
Hydrological Models ◽  
State Variables ◽  
Ensemble Size ◽  
Highly Nonlinear

The parameters of water movement and solute transport models are essential for the accurate simulation of soil moisture and salinity, particularly for layered soils in field conditions. Parameter estimation can be achieved using the inverse modeling method. However, this type of method cannot fully consider the uncertainties of measurements, boundary conditions, and parameters, resulting in inaccurate estimations of parameters and predictions of state variables. The ensemble Kalman filter (EnKF) is well-suited to data assimilation and parameter prediction in Situations with large numbers of variables and uncertainties. Thus, in this study, the EnKF was used to estimate the parameters of water movement and solute transport in layered, variably saturated soils. Our results indicate that when used in conjunction with the HYDRUS-1D software (University of California Riverside, California, CA, USA) the EnKF effectively estimates parameters and predicts state variables for layered, variably saturated soils. The assimilation of factors such as the initial perturbation and ensemble size significantly affected in the simulated results. A proposed ensemble size range of 50–100 was used when applying the EnKF to the highly nonlinear hydrological models of the present study. Although the simulation results for moisture did not exhibit substantial improvement with the assimilation, the simulation of the salinity was significantly improved through the assimilation of the salinity and relative solutetransport parameters. Reducing the uncertainties in measured data can improve the goodness-of-fit in the application of the EnKF method. Sparse field condition observation data also benefited from the accurate measurement of state variables in the case of EnKF assimilation. However, the application of the EnKF algorithm for layered, variably saturated soils with hydrological models requires further study, because it is a challenging and highly nonlinear problem.

scholarly journals Event-based minimum-time control of oscillatory neuron models

2009 ◽  
Vol 101 (5-6) ◽  
pp. 387-399 ◽  
Author(s):  
Per Danzl ◽  
João Hespanha ◽  
Jeff Moehlis
Keyword(s):  
Minimum Time ◽  
Neuron Models ◽  
Time Control ◽  
Event Based

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

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