2D SWE: default LSPG

• ROM technique: basic LSPG

• problem: 2D shallow water equations (SWE)

Prerequisites

• A valid build of the tutorials, see here,

• The following env variables MUST be set:

  export REPOSRC=<full-path-to-the-pressio-tutorials-source-repo>/end-to-end-roms
  export BUILDDIR=<full-path-to-where-you-built-the-tutorials>
  

To run the demo scripts below, you MUST be inside the correct directory:

cd $BUILDDIR/end-to-end-roms/2d_swe_lspg_default

Workflow File

The workflow file for this demo is shown below for exposition purposes, but it is automatically copied to the build directory, so you don’t need to do anything:

problem: 2d_swe

parameterSpace:
  names: ['coriolis', 'pulsemag', 'gravity']
  trainPoints:
    0: [-1.0, 0.125, 9.8]
    1: [ 0.0, 0.125, 9.8]
  testPoints:
    0: [-0.5, 0.125, 9.8]

fom:
  meshSize: [65, 65]
  inviscidFluxReconstruction: "Weno3"
  odeScheme: "BDF1"
  timeStepSize: 0.01
  nonlinearSolverName: NewtonRaphson
  nonlinearSolverTolerance: 1e-6
  train:
    finalTime: 5.0
    stateSamplingFreq: 10
  test:
    finalTime: 5.0
    stateSamplingFreq: 10

offlineRom:
  pod:
    stateData:
      useTrainingRuns: all

onlineRom:
  algorithm: defaultLspg
  nonlinearSolverName: GaussNewton
  nonlinearSolverTolerance: 1e-6
  podTruncation:
    energyBased: [99.999, 99.99999]

Step 1: execute FOMs

# from within $BUILDDIR/end-to-end-roms/2d_swe_lspg_default
python3 $REPOSRC/wf_foms.py --wf wf.yaml

Warning

This might take a few mins to run, be patient!

At the end, doing tree -L 1 . should produce:

.
├── CMakeFiles
├── Makefile
├── cmake_install.cmake
├── fom_mesh
├── fom_test_runid_0
├── fom_train_runid_0
├── fom_train_runid_1
├── plot.py
└── wf.yaml

Step 2: offline rom

# from within $BUILDDIR/end-to-end-roms/2d_swe_lspg_default
python3 $REPOSRC/wf_offline_rom.py --wf wf.yaml

The offline rom takes care of using the FOM training data to compute the POD modes, and creates all data into an “offline_rom” subdirectory:

./offline_rom/
├── pod_input.yaml
├── state_left_singular_vectors.bin
├── state_singular_values.txt
└── state_snapshots.bin

Step 3: lspg rom

# from within $BUILDDIR/end-to-end-roms/2d_swe_lspg_default
python3 $REPOSRC/wf_lspg.py --wf wf.yaml

At the end, you should have the following directory structure:

.
├── CMakeFiles
├── Makefile
├── cmake_install.cmake
├── default_lspg_truncation_energybased_99.99999_runid_0
├── default_lspg_truncation_energybased_99.999_runid_0
├── fom_mesh
├── fom_test_runid_0
├── fom_train_runid_0
├── fom_train_runid_1
├── offline_rom
├── plot.py
└── wf.yaml

Step 4: process results

# from within $BUILDDIR/end-to-end-roms/2d_swe_lspg_default
python3 $REPOSRC/wf_reconstruct_on_full_mesh.py
python3 plot.py