"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."
Tikidji-Hamburyan RA, Colonnese MT (2021) Polynomial, piecewise-Linear, Step (PLS): a simple, scalable and efficient framework for modeling neurons Frontiers in Neuroinformatics