Using PINNs with Dynamic Initial Conditions in Time-Dependent PDEs

[101AlexMartin]

Hi, thank you for the great library!

I'm using DeepXDE to solve chemical reaction dynamics using a TimePDE, with time and power as inputs and species concentrations as outputs. My goal is to use the trained model within a dynamic simulator, where the initial conditions (i.e., species concentrations) change at every timestep — meaning the final state of timestep n becomes the initial state of timestep n+1.

For example, the model might be trained using an initial concentration of 1000. However, during simulation, this initial concentration will vary over time, as the reaction is not reset at each timestep. With standard ANNs, I’ve handled this by including the initial concentration as one of the input features.

One option could be to store the full history of inputs (i.e. for all the previous timesteps) to the reactor and compute the current timestep from that, but this approach has obvious memory limitations.

Is there a way to use a PINN model in this type of application, where the initial conditions are dynamic and evolve over time? How can I incorporate these changing initial concentrations into the PINN framework?

Thanks in advance for your help!