this post was submitted on 08 Jul 2024
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In my experience, papers which propose numerical solutions cover in great detail the methodology (which relates to some underlying physical phenomena), and also explain boundary conditions to their solutions. In ML/DL papers, they tend to go over the network architecture in great detail as the network construction is the methodology. But the problem I think is that there’s a disconnect going from raw data to features to outputs. I think physics informed ML models are trying to close this gap somewhat.
As I was reading your comment I was thinking Physics Informed NN’s and then you went there. Nice. I agree.
I’ve built some models that had a solution constrained loss functions—featureA must be between these values, etc. Not quite the same as defining boundary conditions for ODE/PDE solutions but in a way gets to a similar space. Also, ODE/PDE solutions tend to find local minima and short of changing the initial conditions there aren’t very many good ways of overcoming that. Deep learning approaches offer more stochasticity so converge to global solutions more readily (at the risk of overfitting).
The convergence of these fields is exciting to watch.
Yeah, thats a fair point and another appealing reason for DL based methods