Discovering dynamical symmetry breaking and resonances in nonlinear systems through AI.

For an ensemble of nonlinear systems described through the discrete non-linear Schrödinger equation that model, for instance, molecules or photonic systems, we propose a method that finds efficiently the configuration that has prescribed transfer properties. We use physics-informed (PI) machine learning (PIML) to find the parameters for the targeted energy transfer (TET) [1] of an electron (or photon) to a state and the parameters for the self-trapping (ST) [2] transition in a nonlinear dimer. We create a model containing two variables, χ_D and χ_A, representing the nonlinear terms in the donor and acceptor system states. We then introduce a data-free PI loss function as 1.0 - Pj, for the TET and as 0.5 - Pj, for the ST transition, where Pj is the probability, the electron being in the targeted state, j. By minimizing the loss function, the method recovers known results in the TET model, and recaptures the original dynamic ST transition and its dependence on initial conditions. The model is also applied to a trimer configuration, containing a linear intermediate unit, discovering new resonant paths. The proposed PIML method is general and may be used in the chemical design of molecular complexes or engineering design of quantum or photonic systems.