I would like to know if it was possible to train a neural network on daily new data. Let me explain this more in detail. Let's say you have daily data from 2010 to 2019. You train your NN on all of it, but, from now on, every day in 2019 you get new data. Is it possible to "append" the training of the NN or do we need to retrain an entire NN with the data from $2010$ to $2019+n$ with $n$ the day for every new day?
I don't know if it is relevant but my work is on binary classification.
Yes, this is possible. Continuously extending your training data is known as incremental learning.
You might also want to take a look at transfer learning, in which you reuse a trained model for a different purpose. This is very useful if you have a smaller dataset.
In your particular case, you could train a NN once using your data from 2010 to 2019 and use it as a base model. Every time you get new data, you can use transfer learning to slightly re-train this model. Based on parameters such as the number of epochs and the learning rate, you can determine how much of an impact this new data will have.
