Some initial/brainstorming ideas on specifying and scoping the problem

One possible avenue is to examine the heat equation (later, any convection-diffusion-reaction PDE..). I feel the method is ideally suited to inverse problems, e.g. computing unknown thermal conductivity, initial condition, boundary conditions. This is a competitor to traditional (numerical) regularization approaches and will hopefully eliminate well-known stability issues due to the ill-posed nature of the problem.

An excellent article IMO (

**paging Mr. @ISayMoo**) is

https://pdfs.semanticscholar.org/4fc5/c ... 72a128.pdf
It is at the very least a good

*baseline example *and no confusion is possible, hopefully.

There’ something in that paper for everyone as many steps can be implemented in different ways. Personally, I like Appendix A as it draws the analogy between the Method of Lines (MOL) and the Hopfield continuous-time neural network (flashback Kirchoff network..). It means that you can potentially use ODE solvers to solve them.

I would like try Differential Evolution (DE), maybe someone with like to try a gradient-based method.

I suggest using this approach but instead of finding the unknown BC based on temperature samples we estimate the thermal conductivity parameter based on temperature samples.

**Once an unambiguous spec is drawn up and we are reading from the same page, we can start with a detailed design.**
Q: do we use supervised or unsupervised learning? Is NN better than traditional approaches?

Any more on board besides Paul and myself?

Feedback welcome!