标题： 学习动态玻尔兹曼分布作为空间化学动力学的简化模型 显示英文标题

标题： Learning Dynamic Boltzmann Distributions as Reduced Models of Spatial Chemical Kinetics

摘要： 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。 我们提出了一种机器学习方法来解决这种粗粒化问题，其中构建了一个最大熵近似，该近似随时间缓慢演变。 支配该近似的行为模型被表示为一个泛函，允许对空间相互作用进行一般性处理。 与典型机器学习方法估计图形模型的相互作用参数不同，我们推导了类似玻尔兹曼机的学习算法，以直接估计决定这些参数时间演化的泛函。 通过结合简单反应基序的解析解，展示了一种高效的模拟方法，适用于从玩具问题到基本生物相关网络的系统。 我们的方法在学习空间动力学中的广泛适用性表明，它在空间网络的多尺度方法以及机器学习中的其他问题中具有广阔的应用前景。 显示英文摘要

摘要： 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.