  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.
