Module dlkoopman.config

Configuration options

Classes

class Config (precision='float', use_cuda=True, torch_compile_backend='aot_eager', normalize_Xdata=True, use_exact_eigenvectors=True, sigma_threshold=1e-25)

Configuration options.

Parameters

• precision (str, optional) - Numerical precision of tensors. Must be one of "half" / "float" / "double".

  • Note that setting precision = "double" may make predictions slightly more accurate, however, may also lead to inefficient GPU runtimes.

• use_cuda (bool, optional) - If True, tensor computations will take place on CuDA GPUs if available.

• torch_compile_backend (str / None, optional) - The backend to use for torch.compile(), which is a feature added in torch major version 2 to potentially speed up computation.

  • If you are using torch 1.x or you set torch_compile_backend = None, torch.compile() will not be invoked on the DLKoopman neural nets.
  • If you are using torch 2.x, full lists of possible backends can be obtained by running torch._dynamo.list_backends() and torch._dynamo.list_backends(None). See the torch.compile() documentation for more details.

• normalize_Xdata (bool, optional) - If True, all input states (training, validation, test) are divided by the maximum absolute value in the training data.

  • Note that normalizing data is a generally good technique for deep learning, and is normally done for each feature $f$ in the input data as $$X_f = \frac{X_f-\text{offset}_f}{\text{scale}_f}$$ (where offset and scale are mean and standard deviation for Gaussian normalization, or minimum value and range for Minmax normalization.)
    However, this messes up the spectral techniques such as singular value and eigen value decomposition required in Koopman theory. Hence, setting normalize_Xdata=True will just use a single scale value for normalizing the whole data to get $$X = \frac{X}{\text{scale}}$$ which results in the singular and eigen vectors remaining the same.
  • Caution: Setting normalize_Xdata=False may end the run by leading to imaginary parts of tensors reaching values where the loss function depends on the phase (in torch >= 1.11, this leads to "RuntimeError: linalg_eig_backward: The eigenvectors in the complex case are specified up to multiplication by e^{i phi}. The specified loss function depends on this quantity, so it is ill-defined"). The only benefit to setting normalize_Xdata=False is that if the run successfully completes, the final error metrics such as ANAE are slightly more accurate since they are reported on the un-normalized data values.

• use_exact_eigenvectors (bool, optional) - If True, the exact eigenvectors of the Koopman matrix are used in StatePred, if False, the projected eigenvectors are used.

  • For a discussion on exact and projected eigenvectors, see Tu et al or Chapter 1 of Kutz et al. The basic idea is that using exact eigenvectors is more accurate, but their computation may become less numerically stable than that of projected eigenvectors.

• sigma_threshold (float, optional) - When computing the SVD in StatePred, singular values lower than this will be reported, since they can be a possible cause of unstable gradients.

Attributes

• RTYPE (torch.dtype) - Data type of real tensors. Is automatically set to torch.<precision> (e.g. torch.float if precision="float").

• CTYPE (torch.dtype) - Data type of complex tensors. Is automatically set to torch.c<precision> (e.g. torch.cfloat if precision="float").

• DEVICE (torch.device) - Device where tensors reside. Is automatically set to "cpu" if use_cuda=False or CuDA is not available, otherwise "cuda".