Multi-fidelity deep neural network

An implementation of the multi-fidelity deep neural network architecture proposed in "A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems".

Files:

• mdfl.py: Implementation of a single- and multi-fidelity architectures.
• multifidelity_benchmark.ipynb: some of the benchmark problems presented in the paper (linear and non-linear correlations), I forgot to add the plot legends but you can see that the predictions are good :)

Notes:

• It is written in PyTorch.

• I didn't include the MPINN part.

• The cost function is slightly modified, leaving a separate regularization for each network:

  $\mathcal{L} = MSE_{y_{L}} + MSE_{y_{H}} + \lambda_{L} \Sigma{\theta_L^2} + \lambda_{H1} \Sigma{\theta_{H1}^2} + \lambda_{H2} \Sigma{\theta_{H2}^2}$

• In addition to 'Tanh' I also included 'ReLU'.

• I tried to extend it to Bayesian network (see the notebook) but it is too expensive.