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1. Context

I'm studying Health-Monitoring techniques, and I practice on the C-MAPSS dataset. The goal is to predict the Remaining Useful Life (RUL) of an engine given sensor measurements series. There's a wide litterature about the C-MAPSS dataset, including both classical (non-DL) ML techniques and DL-based approaches. A few years ago, LSTM-based networks showed promising results (see Long Short-Term Memory Network for Remaining Useful Life estimation, Zheng et al, 2017), and I'm trying to reproduce these results.

The C-MAPSS dataset contains a low amount of data. The FD001 subset has for instance only 100 run-to-failure series. When I pre process it to get fixed-length time series, I can get up to ~20 000 framed series. In the article mentioned above using LSTM, they use two hidden LSTM layers with 64 units each, and two fully-connected layers with 8 neurons each (~55 000 parameters).

2. Problem

LSTMs induce a great number of parameter, so overfitting may be encountered when training such a network. I can use L1 or L2 regularization, dropouts, the net will still be largely oversized regarding to the dataset. Keeping the same architecture, I can't reach the scores and RMSE in the paper in the validation set, and overfitting is always here.

However, one thing that works is reducing the number of units of the LSTM layers. Expectedly, with only 24 units instead of 64 per layer, the net has much less parameters (~9000), and it presents no overfitting. The scores and RMSE are a bit worse than the one in the paper, but it's the best I can get so far. Although these results are fine for me, I'm curious about how it was possible for the authors of the paper to avoid overfitting on their LSTM(64,64) net.

3. Question

LSTM are great, but they induce a lot of parameters that hinder a correct learning on small dataset : I wonder if there is any method to tackle this specific issue. Would you have any advice on how to avoid overfitting with a LSTM-based net on a small dataset ?

4. Infos

I provide here below more infos about my net and results :

Network architecture

model = keras.models.Sequential([
    keras.layers.LSTM(24, return_sequences=True, kernel_regularizer=keras.regularizers.l1(0.01),
                      input_shape=input_shape),
    keras.layers.Dropout(0.2),
    keras.layers.LSTM(24, return_sequences=False, kernel_regularizer=keras.regularizers.l1(0.01)),
    keras.layers.Dropout(0.2),
    keras.layers.Dense(8, activation='relu', kernel_regularizer=keras.regularizers.l2()),
    keras.layers.Dropout(0.2),
    keras.layers.Dense(8, activation='relu', kernel_regularizer=keras.regularizers.l2(), bias_regularizer=keras.regularizers.l2()),
    keras.layers.Dense(1, activation='relu')
])

Scores (Validation set)

  • Paper: Score = 16.14 ; RMSE = 338
  • My LSTM(64, 64): Score = 26.47; RMSE = 3585 (overfits)
  • My LSTM(24, 24): Score = 16.82; RMSE = 515
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