对于随机动力学的原则模型选择
Andonis Gerardos1, Pierre Ronceray1
1Aix Marseille Université, CNRS, CINAM, Turing Center for Living Systems, Marseille, France.
Physical review letters
|October 31, 2025
概括
我们引入了节的随机推理 (PASTIS),以防止通过随机微分方程建模的复杂动态系统过度拟合. 帕斯蒂斯有效地从数据中识别最小模型,即使有噪音或稀疏采样.
科学领域:
- 动态系统和复杂性 动态系统和复杂性
- 计算统计学 计算统计学
- 理论生态学理论生态学
背景情况:
- 复杂的系统 (从宏分子到生态系统) 通常使用随机微分方程进行建模.
- 从数据中学习这些模型通常涉及从广泛的函数库中进行稀疏选择,这可能导致过度拟合.
- 过度装配源于单个模型的复杂性和潜在模型的组合式爆炸.
研究的目的:
- 从数据中开发一种原则方法来学习复杂动态系统的节模型.
- 解决对随机微分方程稀疏选择方法固有的过拟合问题.
- 在存在噪音和有限数据的情况下,提高模型识别的可靠性和准确性.
主要方法:
- 介绍了节的随机推理 (PASTIS),一个新的统计框架.
- 将概率估计统计与极端价值理论结合起来,以惩罚多余的参数.
- 在各种复杂系统中应用和验证,包括随机局部微分方程.
主要成果:
- 在识别最小模型方面,PASTIS显著优于现有方法.
- 该方法即使采样率低且测量误差很大,也显示出可靠性.
- 对生态网络和反应-扩散动态的成功应用,展示了广泛的适用性.
结论:
- 节的随机推理 (PASTIS) 提供了一个强大而有效的解决方案,用于复杂的动态系统中的过拟合.
- 该方法可以可靠地识别基本模型组件,从而产生更易于解释和通用化的模型.
- 在涉及随机过程的各种科学领域,PASTIS为数据驱动的建模提供了重大进展.
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