  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 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 introduce a data-free physics-informed 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 occupation
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 desired 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.
