DeepOnet for the Linear Wave Equation

[ShaikhaTheGreen]

Hello @lululxvi and all other contributors,

thank you for the great work and continuous support! I have a couple of questions about DeepOnet:

1. Is there an example for using DeepXDE's DeepOnet implementation for a PDE. This will greatly help in implementing my problem of the wave equation.

2. Is it necessary to use classical methods for obtaining a solution for training process of DeepOnet?

3. Can we consider DeepOnet a way to use PINN for extrapolating prediction? If we have the solution of the wave equation for t[0,5] and we feed that to DeepOnet, can DeepOnet infer an operator for predicting the solution for t[5,10]?

The equation I'm referring to is the linear wave equation with a time-dependent source function:

f(x,t):= u_tt-cu_xx-s(x,t) where, s(x,t) = sin(2pi*f *t)

Looking forward for your reply!

[lululxvi]

Please see

• https://github.com/lululxvi/deeponet
• https://github.com/lu-group/deeponet-fno

Yes, you need a dataset for training DeepONet.

This can be done by the newly added feature of physics-informed DeepONet (PINN + DeepONet), but I haven't added an example online yet.