Bézier插值改进了从数据中推断动力学模型
Bézier interpolation improves the inference of dynamical models from data
摘要：
许多动力学系统，从量子多体系统到进化种群到金融市场，都是由随机过程描述的。表征这种过程的参数通常可以使用随机路径上的信息来推断。然而，从有限时间分辨率的真实数据中估计时间积分量是具有挑战性的。在这里，我们提出了一个框架，准确地估计时间积分量使用贝塞尔插值。我们将我们的方法应用于两个动态推理问题：确定适应度参数不断变化的人口和推断驱动Ornstein-Uhlenbeck过程的力量。我们发现，贝塞尔插值减少了估计偏差的两个动态推理问题。这种改进对于时间分辨率有限的数据集尤其明显。我们的方法可以广泛地应用于提高精度的其他动态推理问题，使用非线性采样数据。
英文摘要：
Many dynamical systems, from quantum many-body systems to evolving populations to financial markets, are described by stochastic processes. Parameters characterizing such processes can often be inferred using information integrated over stochastic paths. However, estimating time-integrated quantities from real data with limited time resolution is challenging. Here, we propose a framework for accurately estimating time-integrated quantities using Bézier interpolation. We applied our approach to two dynamical inference problems: determining fitness parameters for evolving populations and inferring forces driving Ornstein-Uhlenbeck processes. We found that Bézier interpolation reduces the estimation bias for both dynamical inference problems. This improvement was especially noticeable for data sets with limited time resolution. Our method could be broadly applied to improve accuracy for other dynamical inference problems using finitely sampled data.
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