Discovering nonlinear resonances through physics-informed machine learning

For an ensemble of nonlinear systems that model for instance molecules or photonic systems we propose a method that finds efficiently the configuration that has prescribed transfer properties. Specifically, we use physics-informed machine-learning (PIML) techniques to find the optimal parameters for the efficient transfer of an electron (or photon) to a targeted state in a non-linear dimer. We create a machine learning model containing two variables, $\chi_D$ and $\chi_A$, representing the non-linear terms in the donor and acceptor target system states. We then define a loss function as $1.0 - P_j$, where $P_j$ is the probability, the electron being in the targeted state, $j$. By minimizing the loss function, we maximize the transition probability to the targeted state. The method recovers known results in the Targeted Energy Transfer (TET) model and it is then applied to a more complex system with an additional intermediate state. In this trimer configuration the PIML approach discovers optimal resonant paths from the donor to acceptor units. 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.