Open alexiscltrn opened 7 months ago
Yeah we just don't support this yet. It can be done by representing this on a square manually, i.e. it's just a 2D rectangular grid with periodic BCs on the left and right. This is something we want to get to soon though.
Hello SciML team !
I have been using NeuralPDE for a few months as part of my thesis. The challenge I am facing is the need to solve both inverse and direct PDE problems in various complex geometries. Following the approach outlined in this paper, I am currently utilizing distance functions to hardcode boundary conditions in PINNs and to sample collocation points exclusively within the valid domain of my physical model.
Concretely, I utilize
symbolic_discretize
to formulate data-free loss functions and manually merge a sampling strategy to exclude collocation points outside the geometry. Unfortunately, this manual process restricts the utilization of extra features in NeuralPDE, such as adaptive loss for training.My feature request is to seamlessly integrate this methodology within NeuralPDE, allowing for a more streamlined workflow and full utilization of the tool's advanced features. I'm looking forward to receiving insights on the best approach for implementing this integration.
Here is a MWE of my current workaround:
Problem : Poiseuille flow in an annular section
PDE: $u(x,y)$ satisfies: $$\frac{\partial^2u(x,y)}{\partial x^2} + \frac{\partial^2u(x,y)}{\partial y^2} = -\frac{G}{\mu}$$
Geometry: In an annular pipe with inner radius $R_1$ and outer radius $R_2$, defining the cross-section.
Boundary Conditions: In polar coordinates $(r,\theta)$: $$u(R_1, \theta) = u(R_2, \theta) = 0$$ Here, the geometry is quite simple, and the problem could have been solved using a polar formulation. However, the workflow is designed to accommodate more complex cross-sectional shapes.
Additional Parameters: