How is PACF analysis output related to LSTM? I was going through a recent paper “A Novel Hybrid Data-Driven Model for Daily Land Surface Temperature ForecastingUsing Long Short-Term Memory Neural Network Based on Ensemble Empirical ModeDecomposition” found here.

The EEMD-LSTM scheme mentioned is indeed a very well designed model for predicting land surface temperature with more accuracy. I was reading and trying to implement the given steps (as mentioned in the publication) working with similar climatological time series data. I got the different IMFs and the residual.

For the next step, which is to feed all the IMFs and Residual to LSTM, as in Section 3.5 (Forecasting IMFs), the paper mentions that to fix input of the LSTM, a PACF (Partial Auto Correlation Function) analysis has to be done and the number of lags beyond 95% Confidence Interval(CI) is the number of inputs to LSTM.

I understand you are getting the PACF order for the decomposed results (for example: 4,6,5,5,6,6,1,1,1,1,1 for the max pooling station as shown in Fig 7 of the publication where 4 is the number of lags for original data series, 6 is the number of lags for IMF1 series,...., 1 is the number of lags for IMF9 series, and 1 is the number of lags for Residual series).

My question is: how exactly is this PACF order related to input of LSTM (does it determine the number of past data points to look back)?

It would be great if someone could provide some explanation on this.

Thanks.
When used for time series, LSTM (or any Neural Network approach) fall under the category of auto-regressive models. The most general formulation of an auto-regressive model is: 

$Y_t = f(Y_{t-1}, Y_{t-2},...,Y_{t-n})$ with n the number of past lags to include in your model. 

When using a neural network for univariate time series modeling, n will determine the number of input neurons to use (It could be n, or could be n+k, with k additional causal features). 

The PACF will help you determine n. 

The key here is that neural networks are a generalization of AR(p) models.