Title: Characterizing nonlinear dynamics by contrastive cartography Show Chinese title

Title: 通过对比制图表征非线性动力学

Abstract: The qualitative study of dynamical systems using bifurcation theory is key to understanding systems from biological clocks and neurons to physical phase transitions. Data generated from such systems can feature complex transients, an unknown number of attractors, and stochasticity. Characterization of these often-complicated behaviors remains challenging. Making an analogy to bifurcation analysis, which specifies that useful dynamical features are often invariant to coordinate transforms, we leverage contrastive learning to devise a generic tool to discover dynamical classes from stochastic trajectory data. By providing a model-free trajectory analysis tool, this method automatically recovers the dynamical phase diagram of known models and provides a "map" of dynamical behaviors for a large ensemble of dynamical systems. The method thus provides a way to characterize and compare dynamical trajectories without governing equations or prior knowledge of target behavior. We additionally show that the same strategy can be used to characterize the stochastic motion of bacteria, establishing that this approach can be used as a standalone analysis tool or as a component of a broader data-driven analysis framework for dynamical data. Show Chinese abstract

Abstract: 使用分岔理论对动力系统进行定性研究，是理解从生物钟和神经元到物理相变的系统的关键。 此类系统生成的数据可能具有复杂的瞬态、未知数量的吸引子和随机性。 对这些常常复杂的的行为进行表征仍然具有挑战性。 通过与分岔分析类比，分岔分析指出有用的动力学特征通常对坐标变换是不变的，我们利用对比学习设计了一个通用工具，以从随机轨迹数据中发现动力学类别。 通过提供一个无模型的轨迹分析工具，该方法可以自动恢复已知模型的动力学相图，并为大量动力学系统提供动力学行为的“地图”。 因此，该方法提供了一种在没有控制方程或目标行为先验知识的情况下表征和比较动力学轨迹的方法。 我们还表明，同样的策略可以用来表征细菌的随机运动，证明该方法可以作为独立的分析工具，或者作为动力学数据分析更广泛的数据驱动分析框架的一部分。