Neural Chains and Discrete Dynamical Systems

than the unique tridiagonal form in matrix space, which explains why the PINN search typically lands on the random ensemble. The price is a much larger number of parameters, causing lack of physical transparency (explainability) as well as large training costs with no counterpart in the FD procedure. However, our results refer to one-dimensional dynamic problems, hence they don’t rule out the possibility that PINNs and ML in general, may offer better strategies for high-dimensional problems.