Knowledge Based Neural Networks

Demonstration code for a Knowledge Based Neural Network (KBaNN), a bi-fidelity machine learning architecture

Knowledge Based Neural Networks are a bi-fidelity machine learning architecture that allow the outputs of a coarse scale model, , to be augmented by the predictions of a neural network. Having been trained using a dataset comprising outputs of a high-fidelity model, Fe(x), the KBaNN corrects the outputs of the coarse model to emulate the output of . The architecture is based on the KBaNN proposed in Wang et al (1997) but adapted for bi-fidelity modelling. The formalism has also been modified to produce an additive rather than multiplicative correction to . It also now incorporates regularisation.

The KBaNN formulation attempots to leverage the flexibility and scalability of neural networks, while addressing the criticism that they are data-driven black boxes by incorporating the coarse model.

The attached code demonstrates the KBaNN architecture for the Forrester problem. The main file is "forrester_test_main".

Please do provide us with feedback on the code, we are happy to engage to improve it!

Mathematical details may be found in Pepper, Gaymann, Montomoli, and Sharma, "Local bi-fidelity field approximation with Knowledge Based Neural Networks for Computational Fluid Dynamics" (2021). DoI: https://www.nature.com/articles/s41598-021-93280-y#additional-information