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lululxvi
Confidence interval of unknown parameters in inverse problem
@lululxvi Thanks for your great work! I have solved my inverse problem by DeepXDE. DeepXDE can predict the value of unknown parameters. Here's my question: Is it possible for DeepXDE to show the confidence interval of unknown parameters? Thanks for you help!
One of my friend is doing the same thing with GPR. But it is very hard to implement this in PINNs without the reconstruction loss. I also trying to do the same for ill-posed problems. Had some initial success with some gradient based loss in the Laplace equation, but things do not work well in 2D and 3D.
I am actively working in my PhD to extend the Bayesian PINNs which can be used to achieve the same, but it doesn't seem to work with multiple confidence intervals.
We have made some progress with some gPINN like loss involving probability, which we will publish once we achieve good results on 2D and 3D problem. We are not looking into 1D problems.
One of my friend is doing the same thing with GPR. But it is very hard to implement this in PINNs without the reconstruction loss. I also trying to do the same for ill-posed problems. Had some initial success with some gradient based loss in the Laplace equation, but things do not work well in 2D and 3D.
I am actively working in my PhD to extend the Bayesian PINNs which can be used to achieve the same, but it doesn't seem to work with multiple confidence intervals.
We have made some progress with some gPINN like loss involving probability, which we will publish once we achieve good results on 2D and 3D problem. We are not looking into 1D problems.
Recently, I have seen a library called neuraluq published by ZongrenZou. Can this package be used to solve the problem you are talking about?
Hi This is the author of Bayesian PINNs as well as the collaborator of neuraluq. I didn't quite understand "multiple confidence intervals". Could you talk a little bit more about the details? Also, neuraluq supports various UQ methods to quantify uncertainties in PINNs and DeepONets. You can also leave comments there and we can discuss more about it.
