jdtoscano94
commented
1 year ago Hello, Xgxg1314,
Thank you so much for your kind words. I am glad you found them useful.
With deepONets, you approximate the evaluated operator (i.e., numbers). The output of your operator say (i.e., $G(f(x))=h(x)$ ) is a function. Since $h(x)$ is a function, when you evaluate it at $x=y$, you get a set of numbers, say $h(y)=z$. Those numbers $z$ are the ones you approximate with your DeepOnet. So they are kinda "numerical approximators."
Regarding your specific problem, I am not sure if you could solve it with a Physics-Informed DeepONet (i.e., it would be tricky to include the integral in the loss function related to your PDE). But, you should be able to solve it with a traditional DeepONet. You may need some input-output functions $f(x)-h(x)$ to compute your loss and train your operator. Please review: https://github.com/jdtoscano94/Learning-Python-Physics-Informed-Machine-Learning-PINNs-DeepONets/blob/main/DeepONets/7_Antiderivative.ipynb
I am not sure if that answers your question. If not, please let me know. Also, I would suggest you review this research group: https://www.brown.edu/research/projects/crunch/home
They are the pioneers of DeepONets and have many studies in that field. So maybe, they have faced a similar problem as yours in the past.
Thank you so much for your comment and for watching my videos.
I hope you have a nice day.
xgxg1314
A great repository!Thank you very much for your open source, i also really like your videos about this on your Youtube! It is so awesome！
I have a question about deeponet.
$$ \frac{d y}{d x}+y(x)=\int_0^x e^{t-x} y(t) d t $$
i want to use DeepOnet to solve this integro-differential equations, but i have no idea how to implement it. The main problem is that i don't want to approximate integral op- erators numerically, i just hope to make it with DeepOnet
Is it possible to solve it using DeepOnet only?
Best Regrads!