Comments (15)
KirillZubov
commented on August 23, 2024
@asdasdqwdqwfsdf do you mean PINNs ?
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asdasdqwdqwfsdf
commented on August 23, 2024
@KirillZubov I would like to use PINNs for solving high order problems.
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ChrisRackauckas
commented on August 23, 2024
@KirillZubov I think you're confused because you implemented it already. But, you forgot to add it to the docs, so this is mostly a docs issue for just creating an example with higher order derivatives. It's the same as before: @derivative D'''~x, but yes we should probably have an example. I'd suggest K-S.
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asdasdqwdqwfsdf
commented on August 23, 2024
@ChrisRackauckas thanks!
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KirillZubov
commented on August 23, 2024
@ChrisRackauckas ok, it will be done. Also then it is worth adding at docs an example with systems of PDE and an example with Neumann boundary conditions
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asdasdqwdqwfsdf
commented on August 23, 2024
@KirillZubov thanks for your support!
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asdasdqwdqwfsdf
commented on August 23, 2024
@KirillZubov from the new example "3rd order derivative", the difference between numerical one and analytical one is large, why?
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KirillZubov
commented on August 23, 2024
@asdasdqwdqwfsdf Currently, the high-order numerical derivative is poorly stable in the learning process. It should work better when we improve the learning strategy and support automatic differentiation.
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asdasdqwdqwfsdf
commented on August 23, 2024
@KirillZubov thanks for your reply!
what is limit for the highest order derivative, 10th order derivative, 100th order derivative or 10000th order derivative?
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KirillZubov
commented on August 23, 2024
@asdasdqwdqwfsdf currently 4th already is a challenge.
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asdasdqwdqwfsdf
commented on August 23, 2024
@KirillZubov can we have a stable solution for Biharmonic equation (2D/3D) using "NeuralPDE.jl"?
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KirillZubov
commented on August 23, 2024
@asdasdqwdqwfsdf I guess, yes, but I haven't tested this equation.
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KirillZubov
commented on August 23, 2024
hi, @asdasdqwdqwfsdf probably, it will be interesting for you to look at this example with 4th order derivative. https://neuralpde.sciml.ai/dev/examples/pinns_example/#Example-7-:-Kuramoto%E2%80%93Sivashinsky-equation-1
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asdasdqwdqwfsdf
commented on August 23, 2024
@asdasdqwdqwfsdf I guess, yes, but I haven't tested this equation.
hi, I have tested this equation (#218).
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ChrisRackauckas
commented on August 23, 2024
There's a doc example working with this.
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Related Issues (20)
- Parameter Estimation in NNODE
- Parameter Estimation formulation in PINNs HOT 5
- Documentation for BayesianPINN and ahmc_bayesian_pinn_pde
- Encountering Precompilation Error Messages When Adding NeuralPDE Package in Julia HOT 3
- Distance functions as a description of complex geometries HOT 1
- Bump CUDA Compat HOT 1
- How can I solve complex-valued ordinary differential equations (ODEs) using neural networks, given limitations with complex data types in libraries like Lux? HOT 7
- Can't get the @named pde_system to work with a ode system HOT 4
- Add support for equations with complex numbers HOT 20
- Neural Adapter Documentation Example Not Working HOT 6
- DGM Tutorial fails HOT 2
- KeyError when solving Parameter Identification problem using NeuralPDE.jl HOT 9
- Linear parabolic example throws an error on new julia install HOT 2
- NeuralPDE slows when using old weights and biases on a new but related ode HOT 3
- NeuralPDE with LuxAMDGPU, Optimize.solve throws error
- GPU Compatibility Issue: Compilation Error with Complex-Valued Data in LuxCUDA Broadcasting Kernel HOT 8
- Tutorial: imposing constraint on PINN solution of Fokker Planck fails HOT 5
- The trial solutions to additional_loss function are different depending on parameters
- API PINO PDE HOT 5
- How to solve SDEs with NeuralPDE?
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