Nicoletti Giorgio, Maritan Amos, Busiello Daniel Maria
Department of Physics and Astronomy "G. Galilei," University of Padova, Padova, Italy.
Institute of Physics, École Polytechnique Fédérale de Lausanne-EPFL, 1015 Lausanne, Switzerland.
Phys Rev E. 2022 Jul;106(1-1):014118. doi: 10.1103/PhysRevE.106.014118.
Low-dimensional representations of underdamped systems often provide useful insights and analytical tractability. Here, we build such representations via information projections, obtaining an optimal model that captures the most information on observed spatial trajectories. We show that, in paradigmatic systems, the minimization of the information loss drives the appearance of a discontinuous transition in the optimal model parameters. Our results raise serious warnings for general inference approaches, and they unravel fundamental properties of effective dynamical representations impacting several fields, from biophysics to dimensionality reduction.
欠阻尼系统的低维表示通常能提供有用的见解和分析易处理性。在此，我们通过信息投影构建这样的表示，得到一个能捕捉观测空间轨迹上最多信息的最优模型。我们表明，在典型系统中，信息损失的最小化推动了最优模型参数中不连续转变的出现。我们的结果对一般推理方法提出了严重警告，并且揭示了影响从生物物理学到降维等多个领域的有效动力学表示的基本性质。
