Parameter estimation for macroscopic pedestrian dynamics models from microscopic data

In this paper we develop a framework for parameter estimation in macroscopic pedestrian models using individual trajectories -- microscopic data. We consider a unidirectional flow of pedestrians in a corridor and assume that the velocity decreases with the average density according to the fundamental diagram. Our model is formed from a coupling between a density dependent stochastic differential equation and a nonlinear partial differential equation for the density, and is hence of McKean--Vlasov type. We discuss identifiability of the parameters appearing in the fundamental diagram from trajectories of individuals, and we introduce optimization and Bayesian methods to perform the identification. We analyze the performance of the developed methodologies in various situations, such as for different in- and outflow conditions, for varying numbers of individual trajectories and for differing channel geometries

Confederated Modular Differential Equation APIs for Accelerated Algorithm Development and Benchmarking

Performant numerical solving of differential equations is required for large-scale scientific modeling. In this manuscript we focus on two questions: (1) how can researchers empirically verify theoretical advances and consistently compare methods in production software settings and (2) how can users (scientific domain experts) keep up with the state-of-the-art methods to select those which are most appropriate? Here we describe how the confederated modular API of DifferentialEquations.jl addresses these concerns. We detail the package-free API which allows numerical methods researchers to readily utilize and benchmark any compatible method directly in full-scale scientific applications. In addition, we describe how the complexity of the method choices is abstracted via a polyalgorithm. We show how scientific tooling built on top of DifferentialEquations.jl, such as packages for dynamical systems quantification and quantum optics simulation, both benefit from this structure and provide themselves as convenient benchmarking tools.Comment: 4 figures, 3 algorithm

SODECL: An Open-Source Library for Calculating Multiple Orbits of a System of Stochastic Differential Equations in Parallel

This is the final version. Available on open access from ACM via the DOI in this recordStochastic differential equations (SDEs) are widely used to model systems affected by random processes. In general, the analysis of an SDE model requires numerical solutions to be generated many times over multiple parameter combinations. However, this process often requires considerable computational resources to be practicable. Due to the embarrassingly parallel nature of the task, devices such as multi-core processors and graphics processing units (GPUs) can be employed for acceleration. Here, we present SODECL (https://github.com/avramidis/sodecl), a software library that utilizes such devices to calculate multiple orbits of an SDE model. To evaluate the acceleration provided by SODECL, we compared the time required to calculate multiple orbits of an exemplar stochastic model when one CPU core is used, to the time required when using all CPU cores or a GPU. In addition, to assess scalability, we investigated how model size affected execution time on different parallel compute devices. Our results show that when using all 32 CPU cores of a high-end high-performance computing node, the task is accelerated by a factor of up to ≈ 6.7, compared to when using a single CPU core. Executing the task on a high-end GPU yielded accelerations of up to ≈ 4.5, compared to a single CPU core.Engineering and Physical Sciences Research Council (EPSRC

Stochastic Intra-Cellular Modeling

Air Force personnel may sometimes come into contact with potentially harmful chemicals while performing their duties. Of course the Air Force desires to keep any potential health risks to its members to a minimum. To this end the Air Force would like to identify which chemicals are toxic, their level of toxicity, and the processes by which these chemicals disrupt normal biological activities at the cellular level. The development of mathematical models can be of great benefit to toxicity studies. Because real world systems involve randomness, that is noise, and the desire is to create mathematical models to represent those systems, it is necessary to study approaches used to add noise to mathematical models. This document examines different methods for incorporating noise into biochemical systems. The various quantities involved in the reactions are treated as random variables. The methods can be separated into two categories: those which treat the random variable as having a continuous state space and those which treat the random variable as having a discrete state space. These different approaches are compared in order to better understand what type of method would be best used for adding noise to a model and how the model is affected