We report a novel approach for the efficient computation of solutions of a broad class of large-scale systems of non-linear ordinary differential equations, describing aggregation kinetics. The method is based on a new take on the dimensionality reduction for this class of equations which can be naturally implemented by a cascade of small feed-forward artificial neural networks. We show that this cascade, of otherwise static models, is capable of predicting solutions of the original large-scale system over large intervals of time, using the information about the solution computed over much smaller intervals. The computational cost of the method depends very mildly on the temporal horizon, which is a major improvement over the current state-of-the-art methods, whose complexity increases super-linearly with the system's size and proportionally to the simulation time. In cases when prior information about the values of solutions over a relatively small interval of time is already available, the method's computational complexity does not depend explicitly on the system's size. The successful application of the new method is illustrated for spatially-homogeneous systems, with a source of monomers, for a number of the most representative reaction rates kernels.

翻译：我们报道了一种高效计算描述聚集动力学的大规模非线性常微分方程系统解的新方法。该方法基于对此类方程降维的新思路，可通过级联小型前馈人工神经网络自然实现。我们证明，该级联结构（由静态模型组成）能利用在较小时段内计算的解信息，预测原始大规模系统在长时间间隔内的解。该方法计算成本对时间跨度的依赖非常微弱，这是对现有最先进方法的重大改进——后者复杂度随系统规模超线性增长且与模拟时间成正比。当已预先获得相对小时段内解的先验信息时，该方法的计算复杂度甚至不显式依赖于系统规模。我们通过若干最具代表性的反应速率核，针对具有单体源的空间均匀系统展示了新方法的成功应用。