how to use the nndmd in other nonlinear dynamic system

[fdu-goya]

In addition, for other complex nonlinear systems, using the NNDMD in the code library for Koopman learning does not seem to work well. Could you provide more examples of other nonlinear cases?

[fdu-goya]

Because the results from using nndmd on other nonlinear dynamical systems are particularly poor, and nndmd is mainly based on LBFGS optimization, which is a second-order algorithm, its computational speed is particularly slow when the model requires a large number of epochs to run.

[fdu-goya]

When I applied the NNDMD to the Duffing oscillator system, I adjusted the depth of the neural network, the number of neurons, activation functions, and optimizers multiple times but still did not achieve a good approximation of the Koopman operator. I would like to know how to construct a better neural network for this NNDMD to obtain a better approximation of the Koopman operator for the Duffing oscillator. I would greatly appreciate it if you could provide more examples of nonlinear dynamical systems.

[fdu-goya]

dlk_regressor = pk.regression.NNDMD(mode="Dissipative",dt=unforcing_sys.dt, look_forward=look_forward,
config_encoder=dict(input_size=2,
hidden_sizes=[64]*3,
output_size=10,
activations="elu"),
config_decoder=dict(input_size=10, hidden_sizes=[],
output_size=2, activations="linear"),
batch_size=512, lbfgs=False,
normalize=True, normalize_mode='equal',
normalize_std_factor=1.0,
trainer_kwargs=dict(max_epochs=2000,accelerator="gpu", devices=1))

hello,These are the parameters I set for the Duffing oscillator, and the training loss obtained is as follows. The results are not very good, and I am unable to learn the correct Koopman operator.loss is below :the result is not good
Epoch 1999: 100%|██████████| 6/6 [00:01<00:00, 3.39it/s, v_num=309, loss=0.0253, rec_loss=0.000504, rnn_loss=0.0248]