The Log-Periodic Power Law Singularity (LPPLS) model offers a general framework for capturing dynamics and predicting transition points in diverse natural and social systems. In this work, we present two calibration techniques for the LPPLS model using deep learning. First, we introduce the Mono-LPPLS-NN (M-LNN) model; for any given empirical time series, a unique M-LNN model is trained and shown to outperform state-of-the-art techniques in estimating the nonlinear parameters $(t_c, m, \omega)$ of the LPPLS model as evidenced by the comprehensive distribution of parameter errors. Second, we extend the M-LNN model to a more general model architecture, the Poly-LPPLS-NN (P-LNN), which is able to quickly estimate the nonlinear parameters of the LPPLS model for any given time-series of a fixed length, including previously unseen time-series during training. The Poly class of models train on many synthetic LPPLS time-series augmented with various noise structures in a supervised manner. Given enough training examples, the P-LNN models also outperform state-of-the-art techniques for estimating the parameters of the LPPLS model as evidenced by the comprehensive distribution of parameter errors. Additionally, this class of models is shown to substantially reduce the time to obtain parameter estimates. Finally, we present applications to the diagnostic and prediction of two financial bubble peaks (followed by their crash) and of a famous rockslide. These contributions provide a bridge between deep learning and the study of the prediction of transition times in complex time series.

翻译：对数周期幂律奇异性（LPPLS）模型为捕捉各类自然与社会系统的动态行为并预测其转折点提供了通用框架。本文提出两种基于深度学习的LPPLS模型校准技术。首先，我们引入单型LPPLS神经网络（M-LNN）模型：针对任意给定的经验时间序列，训练一个专属的M-LNN模型，通过参数误差的综合分布证明，其在估计LPPLS模型非线性参数（t_c, m, ω）方面优于现有最优技术。其次，我们将M-LNN模型扩展至更具通用性的架构——多元LPPLS神经网络（P-LNN），该模型能快速估计任意固定长度时间序列（包括训练中未见过的时间序列）的LPPLS模型非线性参数。多元类模型通过监督学习在大量含多种噪声结构的合成LPPLS时间序列上进行训练。参数误差综合分布表明，在训练样本充足时，P-LNN模型在估计LPPLS模型参数方面同样超越现有最优技术。此外，该类模型可大幅缩短参数估计时间。最后，我们展示了其在诊断与预测两次金融泡沫峰值（伴随随后的崩盘）及一次著名岩崩事件中的应用。这些研究成果为深度学习与复杂时间序列转折点预测研究之间搭建了桥梁。