Improve differential operators (#528)
* Improve grad logic and fix issues * Add operators' fast versions * Fix bug in laplacian + new tests + restructuring Co-authored-by: Dario Coscia <dariocos99@gmail.com> * fix advection bug --------- Co-authored-by: Dario Coscia <dariocos99@gmail.com>
This commit is contained in:
Giovanni Canali
committed by
FilippoOlivo
FilippoOlivo
parent
938bdeb421
commit
fa6fda0bd5
564
pina/operator.py
564
pina/operator.py
@@ -10,10 +10,309 @@ Each differential operator takes the following inputs:
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- A tensor with respect to which the operator is computed.
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- The names of the output variables for which the operator is evaluated.
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- The names of the variables with respect to which the operator is computed.
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Each differential operator has its fast version, which performs no internal
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checks on input and output tensors. For these methods, the user is always
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required to specify both ``components`` and ``d`` as lists of strings.
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"""
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import torch
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from pina.label_tensor import LabelTensor
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from .label_tensor import LabelTensor
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def _check_values(output_, input_, components, d):
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"""
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Perform checks on arguments of differential operators.
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:param LabelTensor output_: The output tensor on which the operator is
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computed.
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:param LabelTensor input_: The input tensor with respect to which the
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operator is computed.
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:param components: The names of the output variables for which to compute
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the operator. It must be a subset of the output labels.
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If ``None``, all output variables are considered. Default is ``None``.
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:type components: str | list[str]
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:param d: The names of the input variables with respect to which the
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operator is computed. It must be a subset of the input labels.
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If ``None``, all input variables are considered. Default is ``None``.
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:type d: str | list[str]
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:raises TypeError: If the input tensor is not a LabelTensor.
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:raises TypeError: If the output tensor is not a LabelTensor.
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:raises RuntimeError: If derivative labels are missing from the ``input_``.
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:raises RuntimeError: If component labels are missing from the ``output_``.
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:return: The components and d lists.
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:rtype: tuple[list[str], list[str]]
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"""
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# Check if the input is a LabelTensor
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if not isinstance(input_, LabelTensor):
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raise TypeError("Input must be a LabelTensor.")
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# Check if the output is a LabelTensor
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if not isinstance(output_, LabelTensor):
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raise TypeError("Output must be a LabelTensor.")
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# If no labels are provided, use all labels
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d = d or input_.labels
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components = components or output_.labels
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# Convert to list if not already
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d = d if isinstance(d, list) else [d]
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components = components if isinstance(components, list) else [components]
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# Check if all labels are present in the input tensor
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if not all(di in input_.labels for di in d):
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raise RuntimeError("Derivative labels missing from input tensor.")
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# Check if all labels are present in the output tensor
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if not all(c in output_.labels for c in components):
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raise RuntimeError("Component label missing from output tensor.")
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return components, d
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def _scalar_grad(output_, input_, d):
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"""
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Compute the gradient of a scalar-valued ``output_``.
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:param LabelTensor output_: The output tensor on which the gradient is
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computed. It must be a column tensor.
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:param LabelTensor input_: The input tensor with respect to which the
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gradient is computed.
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:param list[str] d: The names of the input variables with respect to
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which the gradient is computed. It must be a subset of the input
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labels. If ``None``, all input variables are considered.
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:return: The computed gradient tensor.
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:rtype: LabelTensor
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"""
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grad_out = torch.autograd.grad(
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outputs=output_,
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inputs=input_,
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grad_outputs=torch.ones_like(output_),
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create_graph=True,
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retain_graph=True,
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allow_unused=True,
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)[0]
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return grad_out[..., [input_.labels.index(i) for i in d]]
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def _scalar_laplacian(output_, input_, d):
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"""
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Compute the laplacian of a scalar-valued ``output_``.
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:param LabelTensor output_: The output tensor on which the laplacian is
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computed. It must be a column tensor.
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:param LabelTensor input_: The input tensor with respect to which the
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laplacian is computed.
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:param list[str] d: The names of the input variables with respect to
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which the laplacian is computed. It must be a subset of the input
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labels. If ``None``, all input variables are considered.
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:return: The computed laplacian tensor.
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:rtype: LabelTensor
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"""
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first_grad = fast_grad(
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output_=output_, input_=input_, components=output_.labels, d=d
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)
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second_grad = fast_grad(
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output_=first_grad, input_=input_, components=first_grad.labels, d=d
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)
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labels_to_extract = [f"d{c}d{d_}" for c, d_ in zip(first_grad.labels, d)]
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return torch.sum(
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second_grad.extract(labels_to_extract), dim=-1, keepdim=True
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)
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def fast_grad(output_, input_, components, d):
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"""
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Compute the gradient of the ``output_`` with respect to the ``input``.
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Unlike ``grad``, this function performs no internal checks on input and
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output tensors. The user is required to specify both ``components`` and
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``d`` as lists of strings. It is designed to enhance computation speed.
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This operator supports both vector-valued and scalar-valued functions with
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one or multiple input coordinates.
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:param LabelTensor output_: The output tensor on which the gradient is
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computed.
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:param LabelTensor input_: The input tensor with respect to which the
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gradient is computed.
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:param list[str] components: The names of the output variables for which to
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compute the gradient. It must be a subset of the output labels.
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:param list[str] d: The names of the input variables with respect to which
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the gradient is computed. It must be a subset of the input labels.
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:return: The computed gradient tensor.
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:rtype: LabelTensor
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"""
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# Scalar gradient
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if output_.shape[-1] == 1:
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return LabelTensor(
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_scalar_grad(output_=output_, input_=input_, d=d),
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labels=[f"d{output_.labels[0]}d{i}" for i in d],
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)
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# Vector gradient
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grads = torch.cat(
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[
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_scalar_grad(output_=output_.extract(c), input_=input_, d=d)
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for c in components
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],
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dim=-1,
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)
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return LabelTensor(
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grads, labels=[f"d{c}d{i}" for c in components for i in d]
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)
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def fast_div(output_, input_, components, d):
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"""
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Compute the divergence of the ``output_`` with respect to ``input``.
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Unlike ``div``, this function performs no internal checks on input and
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output tensors. The user is required to specify both ``components`` and
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``d`` as lists of strings. It is designed to enhance computation speed.
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This operator supports vector-valued functions with multiple input
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coordinates.
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:param LabelTensor output_: The output tensor on which the divergence is
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computed.
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:param LabelTensor input_: The input tensor with respect to which the
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divergence is computed.
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:param list[str] components: The names of the output variables for which to
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compute the divergence. It must be a subset of the output labels.
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:param list[str] d: The names of the input variables with respect to which
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the divergence is computed. It must be a subset of the input labels.
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:rtype: LabelTensor
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"""
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grad_out = fast_grad(
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output_=output_, input_=input_, components=components, d=d
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)
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tensors_to_sum = [
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grad_out.extract(f"d{c}d{d_}") for c, d_ in zip(components, d)
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]
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return LabelTensor.summation(tensors_to_sum)
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def fast_laplacian(output_, input_, components, d, method="std"):
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"""
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Compute the laplacian of the ``output_`` with respect to ``input``.
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Unlike ``laplacian``, this function performs no internal checks on input and
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output tensors. The user is required to specify both ``components`` and
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``d`` as lists of strings. It is designed to enhance computation speed.
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This operator supports both vector-valued and scalar-valued functions with
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one or multiple input coordinates.
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:param LabelTensor output_: The output tensor on which the laplacian is
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computed.
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:param LabelTensor input_: The input tensor with respect to which the
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laplacian is computed.
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:param list[str] components: The names of the output variables for which to
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compute the laplacian. It must be a subset of the output labels.
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:param list[str] d: The names of the input variables with respect to which
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the laplacian is computed. It must be a subset of the input labels.
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:param str method: The method used to compute the Laplacian. Available
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methods are ``std`` and ``divgrad``. The ``std`` method computes the
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trace of the Hessian matrix, while the ``divgrad`` method computes the
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divergence of the gradient. Default is ``std``.
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:return: The computed laplacian tensor.
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:rtype: LabelTensor
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"""
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# Scalar laplacian
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if output_.shape[-1] == 1:
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return LabelTensor(
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_scalar_laplacian(output_=output_, input_=input_, d=d),
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labels=[f"dd{c}" for c in components],
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)
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# Initialize the result tensor and its labels
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labels = [f"dd{c}" for c in components]
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result = torch.empty(
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input_.shape[0], len(components), device=output_.device
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)
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# Vector laplacian
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if method == "std":
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result = torch.cat(
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[
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_scalar_laplacian(
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output_=output_.extract(c), input_=input_, d=d
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)
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for c in components
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],
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dim=-1,
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)
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elif method == "divgrad":
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grads = fast_grad(
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output_=output_, input_=input_, components=components, d=d
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)
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result = torch.cat(
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[
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fast_div(
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output_=grads,
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input_=input_,
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components=[f"d{c}d{i}" for i in d],
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d=d,
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)
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for c in components
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],
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dim=-1,
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)
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else:
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raise ValueError(
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"Invalid method. Available methods are ``std`` and ``divgrad``."
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)
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return LabelTensor(result, labels=labels)
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def fast_advection(output_, input_, velocity_field, components, d):
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"""
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Perform the advection operation on the ``output_`` with respect to the
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``input``. This operator support vector-valued functions with multiple input
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coordinates.
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Unlike ``advection``, this function performs no internal checks on input and
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output tensors. The user is required to specify both ``components`` and
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``d`` as lists of strings. It is designed to enhance computation speed.
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:param LabelTensor output_: The output tensor on which the advection is
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computed.
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:param LabelTensor input_: the input tensor with respect to which advection
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is computed.
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:param str velocity_field: The name of the output variable used as velocity
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field. It must be chosen among the output labels.
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:param list[str] components: The names of the output variables for which to
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compute the advection. It must be a subset of the output labels.
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:param list[str] d: The names of the input variables with respect to which
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the advection is computed. It must be a subset of the input labels.
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:return: The computed advection tensor.
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:rtype: torch.Tensor
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"""
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# Add a dimension to the velocity field for following operations
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velocity = output_.extract(velocity_field).unsqueeze(-1)
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# Remove the velocity field from the components
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filter_components = [c for c in components if c != velocity_field]
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# Compute the gradient
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grads = fast_grad(
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output_=output_, input_=input_, components=filter_components, d=d
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)
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# Reshape into [..., len(filter_components), len(d)]
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tmp = grads.reshape(*output_.shape[:-1], len(filter_components), len(d))
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# Transpose to [..., len(d), len(filter_components)]
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tmp = tmp.transpose(-1, -2)
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return (tmp * velocity).sum(dim=tmp.tensor.ndim - 2)
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def grad(output_, input_, components=None, d=None):
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@@ -27,95 +326,25 @@ def grad(output_, input_, components=None, d=None):
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computed.
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:param LabelTensor input_: The input tensor with respect to which the
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gradient is computed.
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:param components: The names of the output variables for which to
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compute the gradient. It must be a subset of the output labels.
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:param components: The names of the output variables for which to compute
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the gradient. It must be a subset of the output labels.
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If ``None``, all output variables are considered. Default is ``None``.
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:type components: str | list[str]
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:param d: The names of the input variables with respect to which
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the gradient is computed. It must be a subset of the input labels.
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:param d: The names of the input variables with respect to which the
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gradient is computed. It must be a subset of the input labels.
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If ``None``, all input variables are considered. Default is ``None``.
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:type d: str | list[str]
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:raises TypeError: If the input tensor is not a LabelTensor.
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:raises RuntimeError: If the output is a scalar field and the components
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are not equal to the output labels.
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:raises NotImplementedError: If the output is neither a vector field nor a
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scalar field.
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:raises TypeError: If the output tensor is not a LabelTensor.
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:raises RuntimeError: If derivative labels are missing from the ``input_``.
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:raises RuntimeError: If component labels are missing from the ``output_``.
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:return: The computed gradient tensor.
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:rtype: LabelTensor
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"""
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def grad_scalar_output(output_, input_, d):
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"""
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Compute the gradient of a scalar-valued ``output_``.
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:param LabelTensor output_: The output tensor on which the gradient is
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computed. It must be a column tensor.
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:param LabelTensor input_: The input tensor with respect to which the
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gradient is computed.
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:param d: The names of the input variables with respect to
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which the gradient is computed. It must be a subset of the input
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labels. If ``None``, all input variables are considered.
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:type d: str | list[str]
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:raises RuntimeError: If a vectorial function is passed.
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:raises RuntimeError: If missing derivative labels.
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:return: The computed gradient tensor.
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:rtype: LabelTensor
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"""
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if len(output_.labels) != 1:
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raise RuntimeError("only scalar function can be differentiated")
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if not all(di in input_.labels for di in d):
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raise RuntimeError("derivative labels missing from input tensor")
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output_fieldname = output_.labels[0]
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gradients = torch.autograd.grad(
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output_,
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input_,
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grad_outputs=torch.ones(
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output_.size(), dtype=output_.dtype, device=output_.device
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),
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create_graph=True,
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retain_graph=True,
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allow_unused=True,
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)[0]
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gradients.labels = input_.stored_labels
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gradients = gradients[..., [input_.labels.index(i) for i in d]]
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gradients.labels = [f"d{output_fieldname}d{i}" for i in d]
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return gradients
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if not isinstance(input_, LabelTensor):
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raise TypeError
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if d is None:
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d = input_.labels
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if components is None:
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components = output_.labels
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if not isinstance(components, list):
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components = [components]
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if not isinstance(d, list):
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d = [d]
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if output_.shape[1] == 1: # scalar output ################################
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if components != output_.labels:
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raise RuntimeError
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gradients = grad_scalar_output(output_, input_, d)
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elif (
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output_.shape[output_.ndim - 1] >= 2
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): # vector output ##############################
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tensor_to_cat = []
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for i, c in enumerate(components):
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c_output = output_.extract([c])
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tensor_to_cat.append(grad_scalar_output(c_output, input_, d))
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gradients = LabelTensor.cat(tensor_to_cat, dim=output_.tensor.ndim - 1)
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else:
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raise NotImplementedError
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return gradients
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components, d = _check_values(
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output_=output_, input_=input_, components=components, d=d
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)
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return fast_grad(output_=output_, input_=input_, components=components, d=d)
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def div(output_, input_, components=None, d=None):
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@@ -129,51 +358,31 @@ def div(output_, input_, components=None, d=None):
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computed.
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:param LabelTensor input_: The input tensor with respect to which the
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divergence is computed.
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:param components: The names of the output variables for which to
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compute the divergence. It must be a subset of the output labels.
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:param components: The names of the output variables for which to compute
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the divergence. It must be a subset of the output labels.
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If ``None``, all output variables are considered. Default is ``None``.
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:type components: str | list[str]
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:param d: The names of the input variables with respect to which
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the divergence is computed. It must be a subset of the input labels.
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:param d: The names of the input variables with respect to which the
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divergence is computed. It must be a subset of the input labels.
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If ``None``, all input variables are considered. Default is ``None``.
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:type d: str | list[str]
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:type components: str | list[str]
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:raises TypeError: If the input tensor is not a LabelTensor.
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:raises ValueError: If the output is a scalar field.
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:raises ValueError: If the number of components is not equal to the number
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of input variables.
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:raises TypeError: If the output tensor is not a LabelTensor.
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:raises ValueError: If the length of ``components`` and ``d`` do not match.
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:return: The computed divergence tensor.
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:rtype: LabelTensor
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"""
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if not isinstance(input_, LabelTensor):
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raise TypeError
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if d is None:
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d = input_.labels
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if components is None:
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components = output_.labels
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if not isinstance(components, list):
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components = [components]
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if not isinstance(d, list):
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d = [d]
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if output_.shape[1] < 2 or len(components) < 2:
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raise ValueError("div supported only for vector fields")
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components, d = _check_values(
|
||||
output_=output_, input_=input_, components=components, d=d
|
||||
)
|
||||
|
||||
# Components and d must be of the same length
|
||||
if len(components) != len(d):
|
||||
raise ValueError
|
||||
raise ValueError(
|
||||
"Divergence requires components and d to be of the same length."
|
||||
)
|
||||
|
||||
grad_output = grad(output_, input_, components, d)
|
||||
labels = [None] * len(components)
|
||||
tensors_to_sum = []
|
||||
for i, (c, d_) in enumerate(zip(components, d)):
|
||||
c_fields = f"d{c}d{d_}"
|
||||
tensors_to_sum.append(grad_output.extract(c_fields))
|
||||
labels[i] = c_fields
|
||||
div_result = LabelTensor.summation(tensors_to_sum)
|
||||
return div_result
|
||||
return fast_div(output_=output_, input_=input_, components=components, d=d)
|
||||
|
||||
|
||||
def laplacian(output_, input_, components=None, d=None, method="std"):
|
||||
@@ -195,71 +404,22 @@ def laplacian(output_, input_, components=None, d=None, method="std"):
|
||||
the laplacian is computed. It must be a subset of the input labels.
|
||||
If ``None``, all input variables are considered. Default is ``None``.
|
||||
:type d: str | list[str]
|
||||
:param str method: The method used to compute the Laplacian. Default is
|
||||
``std``.
|
||||
:raises NotImplementedError: If ``std=divgrad``.
|
||||
:param str method: The method used to compute the Laplacian. Available
|
||||
methods are ``std`` and ``divgrad``. The ``std`` method computes the
|
||||
trace of the Hessian matrix, while the ``divgrad`` method computes the
|
||||
divergence of the gradient. Default is ``std``.
|
||||
:raises TypeError: If the input tensor is not a LabelTensor.
|
||||
:raises TypeError: If the output tensor is not a LabelTensor.
|
||||
:raises ValueError: If the passed method is neither ``std`` nor ``divgrad``.
|
||||
:return: The computed laplacian tensor.
|
||||
:rtype: LabelTensor
|
||||
"""
|
||||
|
||||
def scalar_laplace(output_, input_, components, d):
|
||||
"""
|
||||
Compute the laplacian of a scalar-valued ``output_``.
|
||||
|
||||
:param LabelTensor output_: The output tensor on which the laplacian is
|
||||
computed. It must be a column tensor.
|
||||
:param LabelTensor input_: The input tensor with respect to which the
|
||||
laplacian is computed.
|
||||
:param components: The names of the output variables for which
|
||||
to compute the laplacian. It must be a subset of the output labels.
|
||||
If ``None``, all output variables are considered.
|
||||
:type components: str | list[str]
|
||||
:param d: The names of the input variables with respect to
|
||||
which the laplacian is computed. It must be a subset of the input
|
||||
labels. If ``None``, all input variables are considered.
|
||||
:type d: str | list[str]
|
||||
:return: The computed laplacian tensor.
|
||||
:rtype: LabelTensor
|
||||
"""
|
||||
|
||||
grad_output = grad(output_, input_, components=components, d=d)
|
||||
result = torch.zeros(output_.shape[0], 1, device=output_.device)
|
||||
|
||||
for i, label in enumerate(grad_output.labels):
|
||||
gg = grad(grad_output, input_, d=d, components=[label])
|
||||
result[:, 0] += super(torch.Tensor, gg.T).__getitem__(i)
|
||||
|
||||
return result
|
||||
|
||||
if d is None:
|
||||
d = input_.labels
|
||||
|
||||
if components is None:
|
||||
components = output_.labels
|
||||
|
||||
if not isinstance(components, list):
|
||||
components = [components]
|
||||
|
||||
if not isinstance(d, list):
|
||||
d = [d]
|
||||
|
||||
if method == "divgrad":
|
||||
raise NotImplementedError("divgrad not implemented as method")
|
||||
|
||||
if method == "std":
|
||||
|
||||
result = torch.empty(
|
||||
input_.shape[0], len(components), device=output_.device
|
||||
)
|
||||
labels = [None] * len(components)
|
||||
for idx, c in enumerate(components):
|
||||
result[:, idx] = scalar_laplace(output_, input_, [c], d).flatten()
|
||||
labels[idx] = f"dd{c}"
|
||||
|
||||
result = result.as_subclass(LabelTensor)
|
||||
result.labels = labels
|
||||
|
||||
return result
|
||||
components, d = _check_values(
|
||||
output_=output_, input_=input_, components=components, d=d
|
||||
)
|
||||
return fast_laplacian(
|
||||
output_=output_, input_=input_, components=components, d=d
|
||||
)
|
||||
|
||||
|
||||
def advection(output_, input_, velocity_field, components=None, d=None):
|
||||
@@ -274,34 +434,34 @@ def advection(output_, input_, velocity_field, components=None, d=None):
|
||||
is computed.
|
||||
:param str velocity_field: The name of the output variable used as velocity
|
||||
field. It must be chosen among the output labels.
|
||||
:param components: The names of the output variables for which
|
||||
to compute the advection. It must be a subset of the output labels.
|
||||
:param components: The names of the output variables for which to compute
|
||||
the advection. It must be a subset of the output labels.
|
||||
If ``None``, all output variables are considered. Default is ``None``.
|
||||
:type components: str | list[str]
|
||||
:param d: The names of the input variables with respect to which
|
||||
the advection is computed. It must be a subset of the input labels.
|
||||
:param d: The names of the input variables with respect to which the
|
||||
advection is computed. It must be a subset of the input labels.
|
||||
If ``None``, all input variables are considered. Default is ``None``.
|
||||
:type d: str | list[str]
|
||||
:raises TypeError: If the input tensor is not a LabelTensor.
|
||||
:raises TypeError: If the output tensor is not a LabelTensor.
|
||||
:raises RuntimeError: If the velocity field is not in the output labels.
|
||||
:return: The computed advection tensor.
|
||||
:rtype: LabelTensor
|
||||
:rtype: torch.Tensor
|
||||
"""
|
||||
if d is None:
|
||||
d = input_.labels
|
||||
|
||||
if components is None:
|
||||
components = output_.labels
|
||||
|
||||
if not isinstance(components, list):
|
||||
components = [components]
|
||||
|
||||
if not isinstance(d, list):
|
||||
d = [d]
|
||||
|
||||
tmp = (
|
||||
grad(output_, input_, components, d)
|
||||
.reshape(-1, len(components), len(d))
|
||||
.transpose(0, 1)
|
||||
components, d = _check_values(
|
||||
output_=output_, input_=input_, components=components, d=d
|
||||
)
|
||||
|
||||
tmp *= output_.extract(velocity_field)
|
||||
return tmp.sum(dim=2).T
|
||||
# Check if velocity field is present in the output labels
|
||||
if velocity_field not in output_.labels:
|
||||
raise RuntimeError(
|
||||
f"Velocity {velocity_field} is not present in the output labels."
|
||||
)
|
||||
|
||||
return fast_advection(
|
||||
output_=output_,
|
||||
input_=input_,
|
||||
velocity_field=velocity_field,
|
||||
components=components,
|
||||
d=d,
|
||||
)
|
||||
|
||||
Reference in New Issue
Block a user