  Chaotic time series forecasting has been far less understood despite its
tremendous potential in theory and real-world applications. Traditional
statistical/ML methods are inefficient to capture chaos in nonlinear dynamical
systems, especially when the time difference $\Delta t$ between consecutive
steps is so large that a trivial, ergodic local minimum would most likely be
reached instead. Here, we introduce a new long-short-term-memory (LSTM)-based
recurrent architecture by tensorizing the cell-state-to-state propagation
therein, keeping the long-term memory feature of LSTM while simultaneously
enhancing the learning of short-term nonlinear complexity. We stress that the
global minima of chaos can be most efficiently reached by tensorization where
all nonlinear terms, up to some polynomial order, are treated explicitly and
weighted equally. The efficiency and generality of our architecture are
systematically tested and confirmed by theoretical analysis and experimental
results. In our design, we have explicitly used two different many-body
entanglement structures---matrix product states (MPS) and the multiscale
entanglement renormalization ansatz (MERA)---as physics-inspired tensor
decomposition techniques, from which we find that MERA generally performs
better than MPS, hence conjecturing that the learnability of chaos is
determined not only by the number of free parameters but also the tensor
complexity---recognized as how entanglement entropy scales with varying
matricization of the tensor.
