Biological neurons can be modeled with different levels of biophysical/biochemical details. The accuracy with which a model reflects the actual physiological processes and ultimately the information function of a neuron, can range from very detailed to a schematic phenomenological representation. This range exists due to the common problem: one needs to find an optimal trade-off between the level of details needed to capture the necessary information processing in a neuron and the computational load needed to compute one second of model time. An increase in modeled network size or model-time, for which the solution should be obtained, makes this trade-off pivotal in model development. Numerical simulations become incredibly challenging when an extensive network with a detailed representation of each neuron needs to be modeled over a long time interval to study slow evolving processes, e.g. development of the thalamocortical circuits. Here we suggest a simple, powerful and flexible approach in which we approximate the right-hand sides of differential equations by combinations of functions from three families: Polynomial, piecewise-Linear, Step (PLS). To obtain a single coherent framework, we provide four core principles in which PLS functions should be combined. We show the rationale behind each of the core principles. Two examples illustrate how to build a conductance-based or phenomenological model using the PLS-framework. We use the first example as a benchmark on three different computational platforms: CPU, GPU, and mobile system-on-chip devices. We show that the PLS-framework speeds up computations without increasing the memory footprint and maintains high model fidelity comparable to the fully-computed model or with lookup-table approximation. We are convinced that the full range of neuron models: from biophysical to phenomenological and even to abstract models, may benefit from using the PLS-framework.

中文翻译：

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多项式分段线性步骤（PLS）：一个简单，可扩展且有效的神经元建模框架。

可以用不同水平的生物物理/生化细节对生物神经元进行建模。模型反映实际生理过程并最终反映神经元信息功能的准确性，可以从非常详细的现象学到示意性的现象学表示。存在此范围是由于常见问题：需要在神经元中捕获必要信息处理所需的详细程度与计算模型时间的一秒所需的计算负荷之间找到最佳折衷。要获得解决方案的模型化网络规模或模型时间的增加，使得这种权衡在模型开发中至关重要。当需要在很长的时间间隔内对每个神经元的详细表示进行建模的广泛网络来研究缓慢发展的过程（例如，丘脑皮层回路的发展）时，数值模拟将变得异常困难。在这里，我们建议一种简单，强大且灵活的方法，在该方法中，我们通过组合以下三个族的函数来近似微分方程的右侧：多项式，分段线性，阶跃（PLS）。为了获得一个统一的框架，我们提供了将PLS功能组合在一起的四个核心原则。我们展示了每个核心原则的基本原理。两个示例说明了如何使用PLS框架建立基于电导或现象学的模型。我们将第一个示例用作三个不同计算平台上的基准：CPU，GPU，和移动片上系统设备。我们表明，PLS框架在不增加内存占用的情况下加快了计算速度，并保持了与完全计算模型或查找表近似值相当的高模型保真度。我们坚信，从生物物理模型到现象学乃至抽象模型，整个神经元模型都可以从使用PLS框架中受益。