On the probability of finding nonphysical solutions through shadowing

JOURNAL OF COMPUTATIONAL PHYSICS

卷:440

Article

Chandramoorthy, Nisha^1,2  Wang, Qiqi^1,3 

[1] MIT, Ctr Computat Sci & Engn, 77 Massachusetts Ave, Cambridge, MA 02139 USA

[2] Dept Mech Engn, Cambridge, MA USA

[3] Dept Aeronaut & Astronaut, Cambridge, MA USA

关键词: Chaotic dynamics;    Numerical simulations;    Scientific computing;    Shadowing sensitivity analysis;   

DOI  :  10.1016/j.jcp.2021.110389

来源: Elsevier

【 摘 要 】

This paper proves that shadowing solutions can be almost surely nonphysical. This finding invalidates the argument that small perturbations in a chaotic system can only have a small impact on its statistical behavior. This theoretical finding has implications for many applications in which chaotic dynamics plays an important role. It suggests, for example, that we can control the climate through subtle perturbations. It also suggests that numerical simulations of chaotic dynamics, such as turbulent flows and global atmosphere and ocean circulation, may fail to predict the true long-term or statistical behavior. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free