Finding reduced models of spatially distributed chemical reaction networks requires an estimation of which effective dynamics are relevant. We propose a machine learning approach to this coarse graining problem, where a maximum entropy approximation is constructed that evolves slowly in time. The dynamical model governing the approximation is expressed as a functional, allowing a general treatment of spatial interactions. In contrast to typical machine learning approaches which estimate the interaction parameters of a graphical model, we derive Boltzmann-machine like learning algorithms to estimate directly the functionals dictating the time evolution of these parameters. By incorporating analytic solutions from simple reaction motifs, an efficient simulation method is demonstrated for systems ranging from toy problems to basic biologically relevant networks. The broadly applicable nature of our approach to learning spatial dynamics suggests promising applications to multiscale methods for spatial networks, as well as to further problems in machine learning.

中文翻译：

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学习动态玻尔兹曼分布作为空间化学动力学的简化模型


寻找空间分布化学反应网络的简化模型需要估计哪些有效动力学是相关的。我们提出了一种解决这个粗粒度问题的机器学习方法，其中构建了随时间缓慢演化的最大熵近似。控制近似的动态模型被表示为函数，允许对空间相互作用进行一般处理。与估计图模型交互参数的典型机器学习方法相比，我们推导了类似玻尔兹曼机器的学习算法来直接估计指示这些参数的时间演化的函数。通过结合简单反应主题的分析解决方案，为从玩具问题到基本生物相关网络的系统展示了一种有效的模拟方法。我们学习空间动力学方法的广泛适用性表明，它在空间网络的多尺度方法以及机器学习中的进一步问题中具有广阔的应用前景。