IHCV：非线性动力系统中隐藏的随时间变化的控制变量的发现
IHCV: Discovery of Hidden Time-Dependent Control Variables in Non-Linear Dynamical Systems
AI总结：
本文提出数据高效且无需求导的 IHCV 方法，利用范式识别非线性动力系统中控制不同动力学机制间切换的隐藏控制变量，并在多种经典模型上验证了其鲁棒性与可扩展性。
摘要：
从数据中发现非线性动力模型是科学的核心。最近的进展依赖于使用大量候选函数库对可观测量进行稀疏回归。然而，对控制不同动力学机制之间切换的隐藏的不可观测控制变量进行建模仍然具有挑战性。在此，我们开发了一种数据高效且无需求导的方法 IHCV，用于识别隐藏控制变量。首先，通过使用著名的分岔模型（鞍结分岔、跨临界分岔、叉式分岔、Hopf 分岔）对 IHCV 方法进行基准测试，评估了 IHCV 针对噪声的性能和鲁棒性。接下来，我们证明了 IHCV 能够在 Lorenz、van der Pol、Hodgkin-Huxley 和 Fitzhugh-Nagumo 模型中发现隐藏的驱动变量。最后，IHCV 推广到了仅给定部分观测数据的情况，这通过使用拨动开关模型、基因抑制振荡器和 Waddington 景观模型进行了演示。我们的原理验证表明，利用范式可以促进对不同动力学机制和非线性模型之间转换进行控制的隐藏变量的数据高效且可扩展的发现。
英文摘要：
Discovering non-linear dynamical models from data is at the core of science. Recent progress hinges upon sparse regression of observables using extensive libraries of candidate functions. However, it remains challenging to model hidden non-observable control variables governing switching between different dynamical regimes. Here we develop a data-efficient derivative-free method, IHCV, for the Identification of Hidden Control Variables. First, the performance and robustness of IHCV against noise are evaluated by benchmarking the IHCV method using well-known bifurcation models (saddle-node, transcritical, pitchfork, Hopf). Next, we demonstrate that IHCV discovers hidden driver variables in the Lorenz, van der Pol, Hodgkin-Huxley, and Fitzhugh-Nagumo models. Finally, IHCV generalizes to the case when only partial observational is given, as demonstrated using the toggle switch model, the genetic repressilator oscillator, and a Waddington landscape model. Our proof-of-principle illustrates that utilizing normal forms could facilitate the data-efficient and scalable discovery of hidden variables controlling transitions between different dynamical regimes and non-linear models.
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