This paper "Optimal control of PDEs using physics informed neural networks" looks really nice:
Finally, an assessment of PINNs that includes a runtime comparison to classical adjoint methods!
4
20
152
Replies
The paper shows roughly similar performance numbers for PINNs vs the adjoint-based solver, but note that the PINN uses a V100 GPU vs. a single CPU core. The adjoint based method also uses a sub-optimal optimizer (fixed step-size gradient descent, rather than L-BFGS).
1
0
6
I'm sure there are sub-optimal things in the PINN method, too, but my guess is that if you fixed these issues, the adjoint method would be 100x faster.
1
0
9
Anyways, big kudos to the authors (Saviz Mowlavi and Saleh Nabi, who do not appear to be on Twitter) for taking a first crack at establishing some very important baselines for these new neural network methods for solving PDEs.
0
0
2
@shoyer
Cool paper, thanks for sharing! My first thought was that neural PDEs bridge these two methods, exactly satisfying the PDE but no need for manual adjoint methods - what do you think?
3
0
1
@GJ_Both
Are you referring specifically to the Julia package when you say "neural PDEs"? I'm not sure what that means from a convceptual perspective.
For writing (discrete) adjoint codes, for sure auto-diff tools like Julia/PyTorch/JAX make that much easier.
1
0
0
@shoyer
On a similar topic (including a comparisons to adjoint methods, showing that Physics-informed DeepONets are faster in this case) you may like by Sifan Wang, Mohamed Aziz Bhouri &
@ParisPerdikaris
1
1
4
@unsorsodicorda
@ParisPerdikaris
Thanks for sharing. Definitely much less surprising to see a method using a pretrained emulator be effective for PDE constrained optimization. Not sure it's entirely fair to call this approach faster, though, given that that excludes time spent training the model.
1
0
0
