Brocke Ekaterina, Djurfeldt Mikael, Bhalla Upinder S, Kotaleski Jeanette Hellgren, Hanke Michael
Science for Life Laboratory, School of Computer Science and Communication, KTH Royal Institute of Technology, Stockholm, Sweden.
National Centre for Biological Sciences, Bangalore, India.
J Comput Neurosci. 2017 Jun;42(3):245-256. doi: 10.1007/s10827-017-0639-7. Epub 2017 Apr 7.
Multiscale modeling by means of co-simulation is a powerful tool to address many vital questions in neuroscience. It can for example be applied in the study of the process of learning and memory formation in the brain. At the same time the co-simulation technique makes it possible to take advantage of interoperability between existing tools and multi-physics models as well as distributed computing. However, the theoretical basis for multiscale modeling is not sufficiently understood. There is, for example, a need of efficient and accurate numerical methods for time integration. When time constants of model components are different by several orders of magnitude, individual dynamics and mathematical definitions of each component all together impose stability, accuracy and efficiency challenges for the time integrator. Following our numerical investigations in Brocke et al. (Frontiers in Computational Neuroscience, 10, 97, 2016), we present a new multirate algorithm that allows us to handle each component of a large system with a step size appropriate to its time scale. We take care of error estimates in a recursive manner allowing individual components to follow their discretization time course while keeping numerical error within acceptable bounds. The method is developed with an ultimate goal of minimizing the communication between the components. Thus it is especially suitable for co-simulations. Our preliminary results support our confidence that the multirate approach can be used in the class of problems we are interested in. We show that the dynamics ofa communication signal as well as an appropriate choice of the discretization order between system components may have a significant impact on the accuracy of the coupled simulation. Although, the ideas presented in the paper have only been tested on a single model, it is likely that they can be applied to other problems without loss of generality. We believe that this work may significantly contribute to the establishment of a firm theoretical basis and to the development of an efficient computational framework for multiscale modeling and simulations.
通过联合仿真进行多尺度建模是解决神经科学中许多重要问题的有力工具。例如，它可应用于大脑学习和记忆形成过程的研究。同时，联合仿真技术使得利用现有工具与多物理模型之间的互操作性以及分布式计算成为可能。然而，多尺度建模的理论基础尚未得到充分理解。例如，需要高效且准确的时间积分数值方法。当模型组件的时间常数相差几个数量级时，每个组件的个体动力学和数学定义共同对时间积分器提出了稳定性、准确性和效率方面的挑战。继我们在Brocke等人（《计算神经科学前沿》，10，97，2016）中的数值研究之后，我们提出了一种新的多速率算法，该算法使我们能够以适合其时间尺度的步长处理大型系统的每个组件。我们以递归方式处理误差估计，允许各个组件遵循其离散化时间进程，同时将数值误差保持在可接受的范围内。该方法的开发最终目标是最小化组件之间的通信。因此，它特别适用于联合仿真。我们的初步结果增强了我们的信心，即多速率方法可用于我们感兴趣的问题类别。我们表明，通信信号的动力学以及系统组件之间离散化阶数的适当选择可能对耦合仿真的准确性产生重大影响。尽管本文中提出的想法仅在单个模型上进行了测试，但很可能它们可以不失一般性地应用于其他问题。我们相信这项工作可能会对建立坚实的理论基础以及开发用于多尺度建模和仿真的高效计算框架做出重大贡献。
