I don't know a lot about Partial Differential Equations (PDEs) but I think they are used to find solutions to complex interaction problems. So my first question does solving a PDE enable us to obtain the forward dynamics model of physics that describes such complex interactions, at least in theory? If so, can one then use the obtained forward dynamics model and change its parameters to generate a new fluid simulation scenes?
The reason that I'm asking this is because I have some videos of various liquids interacting with one another and my goal is to find a solution that governs such interactions. The way I'm currently thinking about it is that I first need to somehow obtain a PDE from this video. Then I plug this PDE into a numerical PDE solver. Assuming that the PDE solver is general and accurate enough it should give me the correct governing equation (i.e. forward dynamics model). However, I'm not sure if my intuition on how I can find that governing equation/method is correct in the first place. In other words, I'm not sure if the steps I explained (video -> PDE -> PDE Solver -> forward dynamics model) are correct.
If obtaining a PDE is the first step, how can I obtain a PDE from fluid simulation videos? In other words, what are the general steps that one should take in order to get the corresponding PDE? Also, given that I am working with some videos, how would the corresponding PDE look like? For instance, would the PDE be a huge matrix/tensor with dimensions corresponding to changes of each element in my scene w.r.t each other over time t?
For the example above, you may also assume that I have access to the underlying causal mechanism that generated that video as well. In other words, I can tell the physics simulator how much of liquid 1, 2, ..., N should be poured into the tank at time t, what their viscosity is and so on.