Enhanced sampling methods, such as forward flux sampling (FFS), have great capacity for accelerating stochastic simulations of nonequilibrium biochemical systems involving rare events. However, the description of the tradeoffs between simulation efficiency and error in FFS remains incomplete. We present a novel and mathematically rigorous analysis of the errors in FFS that, for the first time, covers the contribution of every phase of the simulation. We derive a closed form expression for the optimally efficient count of samples to take in each FFS phase in terms of a fixed constraint on sampling error. We introduce a new method, forward flux pilot sampling (FFPilot), that is designed to take full advantage of our optimizing equation without prior information or assumptions about the phase weights and costs along the transition path. In simulations of both single and multidimensional gene regulatory networks, FFPilot is able to completely control sampling error. We then discuss how memory effects can introduce additional error when relaxation along the transition path is slow. This extra error can be traced to correlations between the FFS phases and can be controlled by monitoring the covariance between them. Finally, we show that, in sets of simulations with matched error, FFPilot is on the order of tens-to-hundreds of times faster than direct sampling and noticeably more efficient than previous FFS methods.

中文翻译：

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在主方程模型中对稀有事件进行正向通量采样期间的自动误差控制。

增强的采样方法（例如正向通量采样（FFS））具有加速涉及罕见事件的非平衡生化系统随机模拟的强大能力。但是，FFS中的仿真效率和误差之间的折衷描述仍然不完整。我们对FFS中的错误进行了新颖且数学上严格的分析，这首次涵盖了模拟每个阶段的贡献。我们根据固定的采样误差约束，导出了一个封闭形式的表达式，以获取每个FFS阶段中采样的最佳有效计数。我们引入了一种新方法，即前向通量导频采样（FFPilot），该方法旨在充分利用我们的优化方程，而无需事先了解或假设沿过渡路径的相位权重和成本。在单维和多维基因调控网络的仿真中，FFPilot能够完全控制采样误差。然后，我们讨论了当沿过渡路径的松弛缓慢时，记忆效应如何会引入附加错误。这种额外的误差可以追溯到FFS相位之间的相关性，并且可以通过监视它们之间的协方差来控制。最后，我们证明，在具有匹配误差的仿真组中，FFPilot的速度比直接采样快数十到数百倍，并且比以前的FFS方法有效得多。这种额外的误差可以追溯到FFS相位之间的相关性，并且可以通过监视它们之间的协方差来控制。最后，我们证明，在具有匹配误差的仿真组中，FFPilot的速度比直接采样快数十到数百倍，并且比以前的FFS方法有效得多。这种额外的误差可以追溯到FFS相位之间的相关性，并且可以通过监视它们之间的协方差来控制。最后，我们证明，在具有匹配误差的仿真组中，FFPilot的速度比直接采样快数十到数百倍，并且比以前的FFS方法有效得多。