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README.md

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@@ -61,36 +61,37 @@ behavior in a vector;</li>
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## Tutorials
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The nonlinear ROM methodology has been tested on 10 different benchmarks, including:
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* scalar/vector and linear/nonlinear equations (*01_poisson.py*)
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* advection-dominated regime (*02_advection.py*)
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* physical and geometrical parametrizations (*03_graetz.py*)
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* bifurcating phenomena (*04_navier_stokes_vx.py*, *05_navier_stokes_vy.py*, *06_navier_stokes_p.py*)
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* time-dependent models (*07_diffusion.py*, *08_poiseuille.py*)
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* a 3D elastic problem (*09_elasticity.py*)
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* high-dimensional parametric applications (*10_stokes.py*)
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To run a benchmark, navigate to the tutorial folder and run the corresponding *file.py*. If available, a GUI will open with preset values for the hyperparameter configuration of the network. Once the window is closed, the code starts the training phase, unless a trained model with the same configuration already exists.
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The nonlinear ROM methodology has been tested on 14 different benchmarks, including:
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* scalar/vector and linear/nonlinear equations (*01_poisson.ipynb*)
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* advection-dominated regime (*02_advection.ipynb*)
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* physical and geometrical parametrizations (*03_graetz.ipynb*)
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* bifurcating phenomena (*04_navier_stokes_vx.ipynb*, *05_navier_stokes_vy.ipynb*, *06_navier_stokes_p.ipynb*)
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* time-dependent models (*07_diffusion.ipynb*, *08_poiseuille.ipynb*)
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* a 3D elastic problem (*09_elasticity.ipynb*)
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* high-dimensional parametric applications (*10_stokes.ipynb*)
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* complex time-dependent problems (*11_holed_advection.ipynb*, *12_lid_driven_cavity.ipynb*, *13_moving_hole_advection.ipynb*)
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To run a benchmark, navigate to the tutorial folder and run the corresponding *file.ipynb*. If available, a GUI will open with preset values for the hyperparameter configuration of the network. Once the window is closed, the code starts the training phase, unless a trained model with the same configuration already exists.
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<p align="center">
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<img src="docs/images/gui.png" width="90%" height="70%"/></p>
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After the GCA-ROM is evaluated, many plots are automatically generated, ranging from training losses, latent evolution, relative errors, solution and error fields
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After the GCA-ROM is evaluated, many plots are automatically generated, ranging from training losses, latent evolution, relative errors, solution and error fields, and gif of the dynamics.
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Below are some snaphots of the approximated solutions for the available becnhamrks:
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<p align="center">
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<img src="tutorials/poisson/_standard/U_poisson_lmap10.0_btt15_seed10_lv4_hc3_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_63_standard.png" width="35.7%" height="70%"/>
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<img src="tutorials/advection/_standard/U_advection_lmap10.0_btt15_seed10_lv4_hc2_nd100_ffn200_skip1_lr0.001_sc4_rate30/field_solution_46_standard.png" width="31%" height="70%"/>
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<img src="tutorials/elasticity/_standard/U_elasticity_lmap10.0_btt15_seed10_lv4_hc3_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_79_standard.png" width="32%" height="70%"/>
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<img src="tutorials/graetz/_standard/U_graetz_lmap10.0_btt25_seed10_lv4_hc2_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_175_standard.png" width="60.1%" height="70%"/>
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<img src="tutorials/graetz/_standard/U_graetz_lmap10.0_btt25_seed10_lv4_hc2_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_4_standard.png" width="38.3%" height="70%"/>
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<img src="tutorials/poiseuille/_standard/U_poiseuille_lmap10.0_btt15_seed10_lv4_hc3_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_910_standard.png" width="62%" height="70%"/>
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<img src="tutorials/diffusion/_standard/U_diffusion_lmap10.0_btt15_seed10_lv4_hc3_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_27_standard.png" width="36.5%" height="70%"/>
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<img src="tutorials/stokes_u/_standard/U_stokes_u_lmap10.0_btt25_seed10_lv4_hc2_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_7_standard.png" width="34%" height="70%"/>
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<img src="tutorials/stokes_u/_standard/U_stokes_u_lmap10.0_btt25_seed10_lv4_hc2_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_525_standard.png" width="32%" height="70%"/>
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<img src="tutorials/stokes_u/_standard/U_stokes_u_lmap10.0_btt25_seed10_lv4_hc2_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_326_standard.png" width="32%" height="70%"/>
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<img src="tutorials/navier_stokes/_standard/VX_navier_stokes_lmap1.0_btt25_seed10_lv4_hc3_nd100_ffn200_skip1_lr0.001_sc4_rate10/field_solution_57_standard.png" width="49%" height="70%"/>
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<img src="tutorials/navier_stokes/_standard/VY_navier_stokes_lmap1.0_btt25_seed10_lv4_hc3_nd100_ffn200_skip1_lr0.001_sc4_rate10/field_solution_150_standard.png" width="49%" height="70%"/>
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<img src="tutorials/poisson/_standard/U_poisson_lmap10.0_btt15_seed10_lv4_hc3_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_63_standard_U.png" width="35.7%" height="70%"/>
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<img src="tutorials/advection/_standard/U_advection_lmap10.0_btt15_seed10_lv4_hc2_nd100_ffn200_skip1_lr0.001_sc4_rate30/field_solution_46_standard_U.png" width="31%" height="70%"/>
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<img src="tutorials/elasticity/_standard/U_elasticity_lmap10.0_btt15_seed10_lv4_hc3_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_79_standard_U.png" width="32%" height="70%"/>
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<img src="tutorials/graetz/_standard/U_graetz_lmap10.0_btt25_seed10_lv4_hc2_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_175_standard_U.png" width="60.1%" height="70%"/>
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<img src="tutorials/graetz/_standard/U_graetz_lmap10.0_btt25_seed10_lv4_hc2_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_4_standard_U.png" width="38.3%" height="70%"/>
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<img src="tutorials/poiseuille/_standard/U_poiseuille_lmap10.0_btt15_seed10_lv4_hc3_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_388_standard_U.png" width="62%" height="70%"/>
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<img src="tutorials/diffusion/_standard/U_diffusion_lmap10.0_btt15_seed10_lv4_hc3_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_27_standard_U.png" width="34.85%" height="70%"/>
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<img src="tutorials/stokes_u/_standard/U_stokes_u_lmap10.0_btt25_seed10_lv4_hc2_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_7_standard_U.png" width="32%" height="70%"/>
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<img src="tutorials/stokes_u/_standard/U_stokes_u_lmap10.0_btt25_seed10_lv4_hc2_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_266_standard_U.png" width="32.5%" height="70%"/>
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<img src="tutorials/stokes_u/_standard/U_stokes_u_lmap10.0_btt25_seed10_lv4_hc2_nd50_ffn200_skip1_lr0.001_sc4_rate30/field_solution_326_standard_U.png" width="30%" height="70%"/>
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<img src="tutorials/navier_stokes/_standard/VX_navier_stokes_lmap1.0_btt25_seed10_lv4_hc3_nd100_ffn200_skip1_lr0.001_sc4_rate10/field_solution_57_standard_U.png" width="49%" height="70%"/>
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<img src="tutorials/navier_stokes/_standard/VY_navier_stokes_lmap1.0_btt25_seed10_lv4_hc3_nd100_ffn200_skip1_lr0.001_sc4_rate10/field_solution_150_standard_U.png" width="49%" height="70%"/>
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</p>
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