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
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?