This video explains physics-informed sampling procedure for reduced order models. Then the numerical demonstration of greedy algorithm is shown for the reduced order model of Poisson equations.

A list of libROM tutorials:

1. Poisson equation & its finite element discretization ( [ Ссылка ] )
2. Projection-based reduced order model for Poisson equation ( [ Ссылка ] )
3. Physics-informed sampling method for reduced order models ( [ Ссылка ] )
4. Local reduced order models and interpolation-based parameterization ( [ Ссылка ] )
5. Projection-based reduced order model for nonlinear system ( [ Ссылка ] )
6. A complete derivation of dynamic mode decomposition ( [ Ссылка ] )

More detailed description of physics-informed greedy algorithm is described in the journal paper, "Gradient-based constrained optimization using a database of linear reduced-order models" ( [ Ссылка ] ).

The webpage for libROM is available at [ Ссылка ]

The physics-informed greedy example can be run with libROM as the following three lines of commands:

1. build_database phase in greedy fashion:
./poisson_local_rom_greedy -build_database -greedy-param-min 0.5 -greedy-param-max 3 -greedy-param-size 15 -greedysubsize 4 -greedyconvsize 6 -greedyrelerrortol 0.01

2. generate target FOM solution:
./poisson_local_rom_greedy -fom -f X.XX (create a new solution to compare with. Set X.XX to your desired frequency.)

3. predict target FOM solution with the trained parametric ROM:
./poisson_local_rom_greedy -use_database -online -f X.XX (use the database to compute at f X.XX while comparing to the true offline solution at f X.XX)

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