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Hi, ChebyKAN is indeed simple, elegant and powerful, I believe it can do more.
So I implemented it on solving some models with dynamical systems, economic models to be precise, where the dynamical …
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There is apparent demand for using Bessel functions in complex-values PDEs, however, is there a C or C++ implementation available somewhere? Quasi-standard C libraries have `j0`, `j1`, `jn`, `y0`,
`…
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The intro of "A Gallery of finite element solvers" mentions advection-diffusion-reaction equations as a final example, I was wondering whether this might be added anytime soon?
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While on the Implicit RK rampage, I plan to pick up methods specific for hyperbolic PDEs.
http://www.sciencedirect.com/science/article/pii/S0168927407001651
http://people.maths.ox.ac.uk/macdonald/…
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In equation 17 of the paper the depth differences are scaled by the normal vector z component. The paper reads:
> Here, the depth differences are scaled by nz to measure the difference along the no…
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Larger PDE solves may benefit from a reverse mode AD and also helps with adding support for neural networks as surrogates or part of training the PDEs themselves, therefore I was wondering what it wou…
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The Navier-Stokes equations, which describe the motion of fluid substances such as liquids and gases, are fundamental to the field of fluid dynamics. However, several challenging problems related to t…
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Hi again :)
I'd like to bring up a topic that's been keeping me busy lately in the field of Physics-Informed Neural Networks (PINNS). During research I've come across a number of papers that discus…
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[Here's an interesting discussion](https://youtu.be/6U3YCfPDylk).
The researchers manually generate a PDE system from their ABM. The system is large, so they get a massive speed up for a decent app…
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Hi authors,
The paper _Solving high-dimensional parabolic PDEs using the tensor train format_ is really insightful and I have learned a lot from it. Thanks a lot for sharing your codes. However, th…