<p>There are multiple options, and you need to experiment which one will be optimal for your case.</p>

<p>Option 1: You can treat your static features as fixed temporal data. So, you make a temporal dimension for each of your static features and let LSTM handle the rest.</p>

<p>For example your transformed data will look like this:</p>

<pre><code>                water rate   pump speed   total produced water   depth_wall
2000-01-01         10            4                 1120             100
2000-01-02         20            8                 1140             100
2000-01-03         10            4                 1150             100
2000-01-04         10            3                 1160             100
2000-01-05         10            4                 1170             100
</code></pre>

<p>Option 2: Designing multi-head networks.</p>

<pre><code>TIME_SERIES_INPUT ------&gt; LSTM -------\
                                       *---&gt; MERGE / Concatenate ---&gt; [more layers]
STATIC_INPUTS --&gt; [FC layer/ conv] ---/
</code></pre>

<p>Here is a paper explaining a combining strategy: <a href="https://arxiv.org/pdf/1712.08160.pdf" rel="nofollow noreferrer">https://arxiv.org/pdf/1712.08160.pdf</a></p>

<p>Here is another paper utilizing option 2: <a href="https://www.researchgate.net/publication/337159046_Classification_of_ECG_signals_by_dot_Residual_LSTM_Network_with_data_augmentation_for_anomaly_detection" rel="nofollow noreferrer">https://www.researchgate.net/publication/337159046_Classification_of_ECG_signals_by_dot_Residual_LSTM_Network_with_data_augmentation_for_anomaly_detection</a></p>

<p>Source code for paper 2: <a href="https://github.com/zabir-nabil/dot-res-lstm" rel="nofollow noreferrer">https://github.com/zabir-nabil/dot-res-lstm</a></p>
How to combine static features with time series in forecasting
<p>I tried to find a similar question and its answers but was not successful in doing so. That's why I'm asking a question that might be asked before:</p>

<p>I'm working on a problem that outputs the cumulative water production of several water wells. The features I have are both time series (water rate and pump speed as functions of time) and static (depth of the wells, latitude and longitude of the well, thickness of the water bearing zone, etc.)</p>

<p>My input data can be shown as below for well#1.</p>

<p>dynamic data:</p>

<pre><code>                water rate   pump speed   total produced water
2000-01-01         10            4                 1120
2000-01-02         20            8                 1140
2000-01-03         10            4                 1150
2000-01-04         10            3                 1160
2000-01-05         10            4                 1170
</code></pre>

<p>static data:</p>

<pre><code>depth of the well_1 = 100
latitude and longitude of the well_1 = x1, y1
thickness of the water bearing zone of well_1 = 3
</code></pre>

<p>My question is how a RNN model (LSTM, GRU, ...) can be built that can take both dynamic and static features?</p>