The adjoint computation of an unsteady nonlinear primal function requires the full primal trajectory in reverse temporal order. Storing this can exceed the available memory. In that case, Checkpointing can be used to store the state only at carefully selected points in time. From there, the forward computation can be restarted to recompute lost sections of the trajectory when they are needed during the adjoint computation. This is always a tradeoff between memory and runtime. The classic and provably optimal way to do this for a known number of time steps is Revolve1, and there are other algorithms for optimal online checkpointing if the number of steps is unknown a priori, or for multistage checkpointing if there are multiple layers of storage, e.g. memory and hard drive.
The pyrevolve library contains two parts: crevolve, which is a thin Python wrapper around a previously published C++ implementation2, and pyrevolve itself, which sits on top of crevolve and manages data and computation management for the user.
The C++ files in this package are slightly modified to play more nicely with Python, but the original is available from the link below. In addition, there is a C wrapper around the C++ library, to simplify the interface with Python. This C wrapper is taken from libadjoint3.
The crevolve wrapper requires cython, and the compilation of the C++ files require that a C++ compiler is installed. To install pyrevolve, clone the repo and call
python setup.py build_ext --inplace
There are two wrappers: a classic wrapper that follows the behaviour of Revolve as described in the papers, and leaves the data mangement, the actual copying of data, and the calling of operators to the user. An example of how to use it can be executed by calling
python examples/use_classic.py
The other, modernised wrapper, takes care of all this. The user creates a
Revolver object, and passes a forward operator, reverse operator, and
checkpoint operator to it. The Revolver provides two important methods:
apply_forward, and apply_reverse. A call to apply_forward executes the
forward computation, while creating the necessary checkpoints for the reverse
computation. After this, a user may also call the apply_reverse method to
compute the adjoints.
For this to work, the user is responsible that the operators have an apply()
method that takes arguments t_start and t_end, and that the checkpoint
object has a property size to report the size of one checkpoint, and methods
load(ptr) and save(ptr) that deep-copy all time-dependent live data into
a location given in ptr.
An example of this can be found here:
python examples/use_modernised.py
Footnotes
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Algorithm 799: Revolve: An Implementation of Checkpointing for the Reverse or Adjoint Mode of Computational Differentiation ↩
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Revolve.cpp: http://www2.math.uni-paderborn.de/index.php?id=12067&L=1 ↩
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libadjoint: https://bitbucket.org/dolfin-adjoint/libadjoint ↩