  Data-driven methods are widely used to develop physical models, but there
still exist limitations that affect their performance, generalizability and
robustness. By combining gene expression programming (GEP) with artificial
neural network (ANN), we propose a novel method for symbolic regression called
the gene expression programming neural network (GEPNN). In this method,
candidate expressions generated by evolutionary algorithms are transformed
between the GEP and ANN structures during training iterations, and efficient
and robust convergence to accurate models is achieved by combining the GEP's
global searching and the ANN's gradient optimization capabilities. In addition,
sparsity-enhancing strategies have been introduced to GEPNN to improve the
interpretability of the trained models. The GEPNN method has been tested for
finding different physical laws, showing improved convergence to models with
precise coefficients. Furthermore, for large-eddy simulation of turbulence, the
subgrid-scale stress model trained by GEPNN significantly improves the
prediction of turbulence statistics and flow structures over traditional
models, showing advantages compared to the existing GEP and ANN methods in both
a priori and a posteriori tests.
