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@@ -39,4 +39,5 @@ The following table summarizes these findings:
As a summary, both methods are definitely interesting, and leave a lot of room for improvement with more complicated extensions and algorithmic modifications that change and improve on the various negative aspects we have discussed for both sides.
However, as of this writing, the physics-informed (PI) approach has clear limitations when it comes to performance and campatibility with existing numerical methods. Thus, when knowledge of the problem at hand is available, which typically is the case when we choose a suitable PDE model to constrain the learning process, employing a differentiable physics (DP) solver can significantly improve the training process as well as the quality of the obtained solution. Next, we will target a more setting, i.e., fluids with Navier Stokes, to illustrate this behavior.
However, as of this writing, the physics-informed (PI) approach has clear limitations when it comes to performance and campatibility with existing numerical methods. Thus, when knowledge of the problem at hand is available, which typically is the case when we choose a suitable PDE model to constrain the learning process, employing a differentiable physics (DP) solver can significantly improve the training process as well as the quality of the obtained solution. Next, we will target more complex settings, i.e., fluids with Navier Stokes, to illustrate this in more detail.