DR_RNN in Tensorflow

Tensorflow implementation of DR-RNN: A deep residual recurrent neural network for model reduction.

convergence for DR_RNN_2 with Adam optimizer and learning rate = 0.1. We half lr every 500 iterations.

To execute the code, simply run:

$ python DR_RNN.py

To monitor the training process, run:

$ tensorboard --logdir=./saved_logs

Result

Reproduced result of Fig.2 from the paper

Results for increasing time steps in DR-RNN

Extrapolation in time, from 10s to 20s.

iter:744 train_cost: 1.49850947651e-07 test_cost: 0.00102584168781 extrapolation of y1

Sensitivity analysis. Partial derivative of predicted y w.r.t. x.

This result is obtained from DR_RNN_2, at iter:1300, when train_cost=1.52661107222e-06 and test_cost=0.00327986711636

Parameter estimation. When parameter is unknown but fixed:

When parameter is an unknown distribution:

Todo

• extrapolation in time
• larger time step
• parameter estimation
• scalability with y
• include mapping from x to y
• compute sensitivity w.r.t x for control purpose
• adding external loading and see if it is predictable given observation in y
• partial observed
• Direct Acyclic Graph and Bayesian