Röhm André, Gauthier Daniel J, Fischer Ingo
Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain.
Department of Physics, The Ohio State University, 191 West Woodruff Ave., Columbus, Ohio 43210, USA.
Chaos. 2021 Oct;31(10):103127. doi: 10.1063/5.0065813.
Reservoir computers are powerful tools for chaotic time series prediction. They can be trained to approximate phase space flows and can thus both predict future values to a high accuracy and reconstruct the general properties of a chaotic attractor without requiring a model. In this work, we show that the ability to learn the dynamics of a complex system can be extended to systems with multiple co-existing attractors, here a four-dimensional extension of the well-known Lorenz chaotic system. We demonstrate that a reservoir computer can infer entirely unexplored parts of the phase space; a properly trained reservoir computer can predict the existence of attractors that were never approached during training and, therefore, are labeled as unseen. We provide examples where attractor inference is achieved after training solely on a single noisy trajectory.
储层计算机是用于混沌时间序列预测的强大工具。它们可以通过训练来近似相空间流，因此既能高精度地预测未来值，又能在无需模型的情况下重建混沌吸引子的一般特性。在这项工作中，我们表明学习复杂系统动力学的能力可以扩展到具有多个共存吸引子的系统，这里是著名的洛伦兹混沌系统的四维扩展。我们证明，储层计算机可以推断相空间中完全未探索的部分；经过适当训练的储层计算机可以预测在训练期间从未接近过的吸引子的存在，因此这些吸引子被标记为未见。我们提供了一些示例，其中仅在单个噪声轨迹上进行训练后就实现了吸引子推断。
