I have a prediction problem and would appreciate some guidance.

My data consists of n experimental trials where a treatment is applied at time 0, and we then measure some response over time. There are two types of predictors: dynamic predictors, which change over time like the response, and static predictors, which do not depend on time.

My goal is to predict the dynamics of the response for a new trial.

Below is an example of my data. In practice, I have more predictors and around 1000 trials to train a model.

I am wondering what kind of model I should use in this context. I have been told that long short-term memory (LSTM) neural networks could be useful, but I haven’t found any cases similar to mine. From what I have seen, the goal is usually to predict the future based on the past, which is not quite my situation.