I looking for a books and examples of code of mechanistic/neural network models especially for time-series forecasting. The best option is if this is implemented on Tensorflow/Keras. How to integrate mechanistic part, how to implement BIBO stability, how to train such model? At this stage any links to books, articles, blogs with tutorials, code examples would be helpful.
Dear Vladimir Golubev
There are many hybrid neural networks specially in Python like CNN-LSTM, CNN-GRU or CNN-BiLSTM and CNN-BiGRU or even hybrid versions of XGBoost . you can search in GitHub website to find some hybrid codes to inspire from them and learn to build your model to forecast time series. But for bounded input-bounded output (BIBO) stability application in control theory and signal processing I have not seen scripts or codes specially with the aim of time series prediction, but you can search with different keywords may be some more details could be found .
Good luck.
Simple ways to combine neural networks (NN) with other methods would be:
1. Use functions as inputs.
2. Add constrains in form of loss function.
3. Replace actimation function to match your data behaviour.
4. Other ways mostly described by Mr. Hossein Safar Yousefifard in previous comment.
Best way to do it is based on data what you will use. E. g., in case of clear seasonal data sometimes it can be better to remove seanonal part with models like SARIMA and after that use NN on top. NN can learn it from scrach but if we already know the behaviour of data I see no point to make it harder for model. Sure, some cases might require to keep entire information for context but data transformations can help ML models in multiple cases and reduce number of neurons in NN case.
As for BIBO, you can read about PINNS, it is NN with physics-based equations in loss function.
Dear Vladimir, to create a hybrid mechanistic/neural network model focused on time series forecasting in Python, particularly using TensorFlow or Keras, it's essential to integrate knowledge from both the field of deep learning and system mechanics. In my experience working with time series for predicting failures in induction motors, I've found that treating sensory data as numerical values and their proper normalization is crucial. An effective strategy is to work with sample mean values to reinforce the input variables in neural models. Additionally, defining control variables and maximizing the amount of information feeding into the model can be very beneficial.
Regarding model construction, direct classification techniques such as Artificial Neural Networks (ANN), Support Vector Machines (SVM), decision trees, among others, can be applied. Proper organization of databases is fundamental for the success of these models. An interesting technique I used was the representation of time series data in images, which allows for the use of image-based models.
As for choosing between Keras and PyTorch, this depends on your programming skills and preferences. Personally, I prefer using PyTorch as it allows for a deeper immersion into networks and a more profound analysis of learning from a programming perspective.
For a deeper understanding, I would recommend consulting a publication I made on time series, available at https://doi.org/10.3390/s23198196.
Best regards
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