First-order-principles-based constructive network topologies: An application to robot inverse dynamics

Modeling physical systems with neural networks (NN) requires expert architects to determine the best number of nodes, layers and activation functions. For complex systems, such as articulated robots, reported results are limited in accuracy and generalization capabilities. In this work, we introduce the concept FOPnet. It is based on first-order principles and system knowledge to determine topologies of parametrized operator networks that accurately model input-output mappings of physical systems. These topologies consist of meaningful building elements and connections as well as a reduced number of parameters that describe the variables' interdependencies. In this way, learning speed is boosted and the model's accuracy, precision and generalization power improved. We apply the methodology to a 7 degrees-of-freedom LWR4 manipulator and discuss the estimation and generalization capabilities of the network. Results are compared to conventional Feed Forward NN as well as a state-of-the-art Deep Recurrent NN. For the considered complex robot dynamics FOPnet was able to achieve a seven orders of magnitude smaller generalization RMSE.