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vikumwijekoon97 t1_j9fho30 wrote

Reply to comment by Optimal-Asshole in [D] On papers forcing the use of GANs where it is not relevant by AlmightySnoo

I was looking into similar things in my undergrad thesis. My math wasn't great so I couldn't comprehend much. Are there actual NN methods that can PDEs without depending on the initial conditions? I was looking into soft body physics simulation using gpus.

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Optimal-Asshole t1_j9fktzg wrote

> Are there actual NN methods that can PDEs without depending on the initial conditions?

The initial condition needs to be known (but we can actually have some noisy initial condition, like measurements corrupted by noise [1]), but NN based models can efficiently solve some parametric PDEs faster than traditional solvers. [2]

There is also a lot of work in training NNs on data generated from traditional methods, and this can be combined jointly with the above method to solve a whole class of problems at once. [3]

Solving a whole parametric family of PDEs (i.e. a parameterized family of initial conditions) and handling complicated geometries will be the next avenue of this specific field IMO. Actually it is being actively worked on.

[1] https://arxiv.org/abs/2205.07331

[2] https://arxiv.org/abs/2110.13361

[3] https://arxiv.org/abs/2111.03794

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