I am trying to use the Modulus library to solve a set of partial differential equations, specifically, a set of heat diffusion equations with varying heat source terms. This requires DeepONet, and the methods in the manual all rely on prepared training data, but I hope to introduce physical information as constraints (predicted temperature results are brought into the equation to calculate the loss) without using training data, because I need to obtain training data through the finite element method, which is time-consuming. So, is there an example of this method that is completely physically driven? Or has anyone else tried this? Can you give me some guidance, thank you!
If you know the governing PDE, you may define it and use it as a constraint.