Parameterization for grown ups

Hello:

I want to add another twist to the parametrized solution shown in “Parameterized Simulations and Design Optimization: 3D heat sink”

What if you have not just 6 dimensions that are a possible parameter, but a whole function?

Simple example: f(x)_xx + k(x)*f(x) = 0,

but there are many possible functions k(x) and you want the network to learn the output f(x) under many k(x), so in the future you have a new k(x) as an input and want the network to get the most likely answer f(x).

Any ideas? Thx in advance.

Hello, One approach to solving something like this is to use “Neural Operators” like our example here Darcy Flow with Physics-Informed Fourier Neural Operator — Modulus 22.03 Release documentation. In this case our k(x) is is the permeability and we are solving for the darcy flow. You can physics inform this using several methods as shown. Another approach is to parameterize your k(x) function. For example, you could take the first couple of terms of the Taylor series and solve for them.