ZCS support for PINNs about deepxde HOT 4 CLOSED

Hi.

Building ZCS into DeepXDE is an ongoing process. We just merged the code itself, while examples and docs are to be added recently.

Changing from an existing script to ZCS is straightforward. Please refer to https://github.com/stfc-sciml/DeepXDE-ZCS/tree/main, but be aware that the class names are changed.

Or, if you can post your training script here (or send to me privately), I can change it to ZCS for you at this moment. Please note that your original script should be using deepxde.data.PDEOperatorCartesianProd instead of deepxde.data.PDEOperator.

from deepxde.

Thanks.

The scripts you gave above are not using DeepONets. Please note that ZCS is not designed for PINNs but for operators (such as DeepONet).

Please make sure your script uses deepxde.data.PDEOperatorCartesianProd for data, and dde.nn.DeepONetCartesianProd for net. For example, https://github.com/lululxvi/deepxde/blob/master/examples/operator/diff_rec_aligned_pideeponet.py.

Once you have one such script ready, I can change a few line for ZCS support to speed it up.

With ZCS, high-dimensional and high-order derivates are made much easier, e.g,:

grad_zcs = dde.zcs.LazyGrad(x, y)
grad_zcs.compute((1, 1, 1, 1))

will compute $\partial{x_1}\partial{x_2}\partial{x_3}\partial{x_4}$.

grad_zcs.compute((2, 2, 2, 2))

will compute $\partial^2{x_1}\partial^2{x_2}\partial^2{x_3}\partial^2{x_4}$.

from deepxde.

Hi, thank you for your quick reply.

I am considering trying ZCS for PINNs involving high-order derivatives. My main case is outlined in the following link:

https://github.com/pescap/TensorPINNs/blob/main/Poisson/tensoruq.py

In this case, one has:

 \partial_{x_1}^2 \cdots \partial_{x_k}^2 \Sigma(x_1, \cdots, x_k) = C(x_1,\cdots,x_k)

I was recursively applying dde.grad.hessian -> Exponential with k.

Another interesting case, as mentioned in your work, is gradient-enhanced PINNs, for example:

https://github.com/lu-group/gpinn/blob/09dd5903c326389f041341ed8cfe4984b24278cd/src/poisson_1d.py#L52

from deepxde.

Hi, thank you. I had misunderstood that ZSF could be extended to PINNs as a special simple case (M=1). This led me to believe that I could apply it to PINNs by editing the PDE class.

from deepxde.