Learning Analytical Solutions
摘要
In this chapter we try to merge machine learning with the nonlinear dynamics problems discussed in the previous chapter. The application of simple machine learning ideas to recover exact DNLS equation results is a significant test for the applicability of the methods. We focus on the nonlinear dimer problem that is completely known analytically and apply machine learning with the aim to recover the self-trapping transition. We show that both for the simple localized initial condition and for the more general solution of the dimer the machine learning method works very efficiently. Furthermore it also produces the transition line of the nondegenerate dimer. The fact that we can obtain known analytical results through machine learning opens up the possibility of further engagement of artificial intelligence in complex nonlinear systems.