The critical step in a molecular process is often a rare-event and has to be simulated by an enhanced sampling protocol. Recovering accurate dynamical estimates from such biased simulation is challenging. Girsanov reweighting is a method to reweight dynamic properties formulated as path expected values. The path probability is calculated at the time-step resolution of the molecular-dynamics integrator. But the theory is largely limited to overdamped Langevin dynamics. For underdamped Langevin dynamics, the absolute continuity of the path probability ratio for the biased and unbiased potential is not guaranteed, but it depends on the Langevin integrator. We develop a general approach to derive the path probability ratio for Langevin integrators and to analyze whether absolute continuity is fulfilled. We demonstrate our approach on symmetric splitting methods for underdamped Langevin dynamics. For methods that obey absolute continuity, and thus can be used for Girsanov reweighting, we provide an expression for the relative path probability. %

中文翻译：

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Girsanov 重新加权以模拟欠阻尼 Langevin 动力学。理论

分子过程中的关键步骤通常是罕见事件，必须通过增强的采样协议来模拟。从这种有偏差的模拟中恢复准确的动力学估计具有挑战性。Girsanov 重新加权是一种重新加权作为路径期望值制定的动态属性的方法。路径概率是在分子动力学积分器的时间步分辨率下计算的。但该理论在很大程度上仅限于过阻尼朗之万动力学。对于欠阻尼 Langevin 动力学，无法保证有偏和无偏势的路径概率比的绝对连续性，但这取决于 Langevin 积分器。我们开发了一种通用方法来推导 Langevin 积分器的路径概率比，并分析是否满足绝对连续性。我们展示了我们关于欠阻尼 Langevin 动力学的对称分裂方法的方法。对于遵循绝对连续性并因此可用于 Girsanov 重新加权的方法，我们提供了相对路径概率的表达式。%