Submitted by a1_jakesauce_ t3_z1nfma in MachineLearning
MPPDE from Brandstetter gets cited a lot. There’s also a lot of PINN, but I’m interested in supervised methods first
Comments
Top-Avocado-2564 t1_ixcrq8m wrote
PiNN aren't really supervised or unsupervised so to speak. It's a misleading way to think about PiNN architecture
Neural pde solvers can be of three flavours - operator learning, graph pde and purely function approximator ( lagaris 2007 ) approach.
SOTA in pinns is a bit useless. Nobody cares if you can do burgers equation as fast as possible. Real life systems are coupled, mixture of pde/ ode , possibly stiff, it's a smorgasbord of challenges.
Fno works great in some situations but it has limitations in handling stochastic multiscale systems - think high RANS
When it comes to PiNN ymmv
a1_jakesauce_ OP t1_ixcz153 wrote
I’m looking for competitors for FNO - any recommendations for models that would be a fair comparison?
a1_jakesauce_ OP t1_ixcz9xu wrote
I’m looking for competitors for FNO - any recommendations on models that would be a fair comparison for solving 2d time evolving NS?
Top-Avocado-2564 t1_ixd75dm wrote
Try deepOnets, but honestly without knowing specifics of your problem. It is hard to advise, PiNN is different from classic DL
a1_jakesauce_ OP t1_ixdi3b9 wrote
I want to compare FNO to other SOTA that have been published since ICLR 21 on the 2d NS task from the FNO paper - that is, predict the scalar vorticity of NS on a regular spatial temporal grid for 20-40 time steps into the future given the first 10 solutions
lewispdf t1_ixfx0kb wrote
a1_jakesauce_ OP t1_ixg4o25 wrote
This only includes FNO, Unet, and PINN
Blutjens t1_ixgb6o7 wrote
Message Passing Neural PDE by Max Welling's group is my personal highlight from this year. Relies on graph neural nets and has dank performance
a1_jakesauce_ OP t1_ixgf3y1 wrote
Yeah I mentioned that one in my description. Cool paper. Not as good as FNO, though, even if they report otherwise
FrostyFix4614 t1_ixckqxe wrote
There is a lot of "neural PDE solvers" with different features and properties. Some work only with regular spatiotemporal grid, some can be applied on arbitrary grids. Some are discrete, some are continuous. Some require a bit of data, some are very data hungry.
So, it depends on what you mean by SOTA.
Fast? FNO or any mapping-based model.
Data-efficient? Some sort of a state space model with GNN-based dynamics and node-wise encoder/decoder.
Time continuity? Something based on neural ODEs dynamics.