Hamiltonian Operator Inference
shanemcq18 opened this issue · comments
New feature: Hamiltonian Operator Inference from the paper Hamiltonian operator inference: Physics-preserving learning of reduced-order models for canonical Hamiltonian systems by Harsh Sharma (@harsh5332392), Zhu Wang, and Boris Kramer (@bokramer). The goal is to use Operator Inference for a canonical Hamiltonian system to learn a ROM that
- is a canonical Hamiltonian system;
- retains the physical interpretation of the state variables and preserves the coupling structure; and
- respects the symmetric property of structure-preserving space discretizations.
@harsh5332392 will take the lead on this. To begin, the main steps will be creating a SymplecticBasis
class (cotangent lift algorithm) and a HamiltonianModel
class that does the constrained optimization in fit()
and symplectic integration in predict()
.
Suggested implementation steps:
Basis
- Create a new file,
/src/opinf/basis/_symplectic.py
- Write a
SymplecticBasis
class that inherits fromopinf.basis.LinearBasis
and implementfit()
. Or, you might be able to do this quickly by inheriting from thePODBasisMulti
class, which represents a block diagonal POD (one POD for each variable). - Import the new class in
/src/opinf/basis/__init__.py
. - Write and run tests for the new classes in a new file
/tests/basis/test_symplectic.py
. - Compile the docs (
make docs
) and check that the automatically generated documentation page looks good. - If possible, write a short section about this class in
docs/source/guides/reduction.md
. We should probably turn this into a notebook that shows the different kinds of basis functions you get from POD and the symplectic approach.
Model Class
- Create a new file,
/src/opinf/models/multi/_hamiltonian.py
. - Write a
HamiltonianModel
class in the new file.- The
fit()
method should take in the data matrices, do the constrained optimizations, and initialize the operators of the ROM. - Implement the
predict()
method with a symplectic integrator.
- The
- Write and run tests for the new class in a new file
/tests/models/multi/test_hamiltonian.py
- Compile the docs and check that the automatically generated documentation page looks good.
- Write a tutorial as a new Jupyter Notebook,
docs/source/tutorials/hamiltonian.ipynb
with the linear wave equation example.