Mini batch training of collocation points?

[mattragoza]

My question is how to do minibatch training with deepxde using point set boundary conditions?

I noticed in issue #320 that it is possible to use PDEResidualResampler to sample new PDE training points on each epoch. However, this is not sufficient for my use case. I am solving an inverse problem where the boundary conditions are defined by a large multidimensional displacement image (hundreds of thousands of vector-valued data points). I provide these to deepxde as a PointSetBC which works just fine for smaller problems, but I run out of memory when scaling up to the full problem.

I need a way to train using minibatches that resample not just the PDE residual points, but the boundary condition collocation points as well. Is this possible currently or do I need to implement a new trainer?

[lululxvi]

For any PDE, the number inside the domain for PDE loss is always orders of magnitude larger than the number of points in the boundary, right? If the problem has a lot of BC points, then the PDE points should be even more. So the PDE point is always dominant. You can simply do a downsampling for the BC points, unless I misunderstand your problem.

On the other hand, you can also check PointCloud

[mattragoza]

Maybe describing my problem in more detail will help. I am trying to solve the following inverse Helmholtz problem:

$\mu \nabla^2 u = -\rho \omega^2 u$

Where $u: R^3 \to C^3 $ represents 3D steady-state displacements and $\mu: R^3 \to C $ represents a 3D map of stiffness. I have a set of observed displacement values in the form of a very large multidimensional image, and I would like to solve the PDE in order to reconstruct $\mu$. The displacement values are measured on a regular grid that spans the entire domain of interest, so I would prefer to just use these data points rather than sampling additional points in the domain for which the displacement values are not known.

I would like to use all of the observed displacement values for training the model instead of downsampling the image. Ideally, I would be able to do this by training the model on batches of image coordinates/displacement value pairs. I am currently providing these data pairs to the model using a PointSetBC, but I don't know how to resample or subsample these BC points to implement batch training.

[lululxvi]

PointSetBC can be used together with PDEResidualResampler to sample mini-batch of PDE residual points, in the same way as other standard geometry. But for the points of data loss, DeepXDE currently doesn't support mini-batch. You have to modify the code. But based on my experience, a down-sampling of u could be enough.

[mattragoza]

Thanks for your response. I was able to solve this by creating a subclass of PointSetBC that handles the resampling of the data points internally. Each call to bc.collocation_points() gets and returns the next batch of training points, then subsequent calls to bc.error() computes the boundary condition loss wrt the current batch.

[lululxvi]

Great! If you would like, feel free to submit a PR.