├── A multi-frequency ├── Hard Constraint │ ├── 1.mat │ └── Hard Constraints MFF.py ├── MFF │ ├── 1.mat │ └── MFF.py ├── MMPINN-INN │ ├── 1.mat │ └── MMPINN-INN.py └── MMPINN-MFF │ ├── 1.mat │ └── MMPINN-MFF.py ├── A problem with dramatic variations in different subdomains ├── MMPINN-DNN-GRS │ ├── MMPINN-DNN-GRS.ipynb │ ├── log1.txt │ ├── log2.txt │ ├── log3.txt │ ├── plotting.py │ └── uu.mat ├── MMPINN-DNN │ ├── MMPINN-DNN.ipynb │ ├── log1.txt │ ├── log2.txt │ ├── log3.txt │ ├── plotting.py │ └── uu.mat ├── PINN(1000k Adam) │ ├── PINN(1000K Adam).py │ ├── log1.txt │ ├── log2.txt │ ├── log3.txt │ └── uu.mat └── PINN │ ├── PINN.ipynb │ ├── log1.txt │ ├── log2.txt │ ├── log3.txt │ ├── plotting.py │ └── uu.mat ├── A typical multi-scale problem ├── MFF+hard constraint │ ├── 1.mat │ ├── Compute_Jacobian.py │ ├── MFF+hard constraint.ipynb │ └── models_tf.py ├── MFF │ ├── 1.mat │ ├── Compute_Jacobian.py │ ├── MFF.ipynb │ └── models_tf.py ├── MMPINN │ ├── Ref │ │ ├── 1.mat │ │ ├── Compute_Jacobian.py │ │ ├── MMPINN-MFF.ipynb │ │ └── models_tf.py │ └── others │ │ ├── 1.mat │ │ ├── Compute_Jacobian.py │ │ ├── MMPINN-MFF.ipynb │ │ └── models_tf.py ├── PINN(1000k Adam) │ ├── 1.mat │ ├── 1000k PINN.ipynb │ ├── Compute_Jacobian.py │ └── models_tf.py └── PINN │ ├── 1.mat │ ├── Compute_Jacobian.py │ ├── PINN.ipynb │ └── models_tf.py ├── Helmholtz equation ├── Hard Constraint │ ├── Hard Constraints PINN.ipynb │ └── plotting.py ├── LRA with IFNN │ ├── Helmholtz2D_model_tf.py │ └── LRA with IFNN.ipynb ├── MFF │ ├── 1.mat │ ├── MFF.ipynb │ └── plotting.py ├── MMPINN-INN │ ├── MMPINN-INN.ipynb │ └── plotting.py ├── MMPINN-MFF │ ├── MMPINN-MFF.ipynb │ └── plotting.py └── SAPINN │ ├── 1.mat │ ├── SAPINN.ipynb │ ├── eager_lbfgs.py │ ├── helmholtz-NTK.py │ └── plotting.py ├── Klein–Gordon equation ├── a10 │ ├── LRA with IFNN │ │ ├── Klein_Gordon_model_tf.py │ │ ├── LRA with IFNN.ipynb │ │ └── plotting.py │ ├── MMPINN-INN │ │ ├── Klein_Gordon_model_tf.py │ │ └── MMPINN-INN-kg.ipynb │ ├── MMPINN-MFF │ │ ├── Klein_Gordon_model_tf.py │ │ ├── MMPINN-MFF.ipynb │ │ └── plotting.py │ └── PINN │ │ ├── Klein_Gordon_model_tf.py │ │ └── PINN.ipynb └── a5 │ ├── LRA with IFNN │ ├── Klein_Gordon_model_tf.py │ └── LEA with IFNN.ipynb │ ├── MMPINN-INN │ ├── Klein_Gordon_model_tf.py │ └── MMPINN-INN.ipynb │ ├── MMPINN-MFF │ ├── Klein_Gordon_model_tf.py │ └── MMPINN-MFF.ipynb │ └── PINN │ ├── Klein_Gordon_model_tf.py │ └── PINN.ipynb ├── README.md └── heat conduction problem ├── 0.11 └── MMPINN │ ├── 0.11MMPINN.py │ ├── log1.txt │ ├── log2.txt │ ├── log3.txt │ ├── log5.txt │ ├── log6.txt │ └── log7.txt ├── 0.15 ├── Hard Constraint │ ├── 0.3hard constraint.ipynb │ ├── 3.mat │ ├── S │ ├── log1.txt │ ├── log2.txt │ ├── log3.txt │ ├── log5.txt │ ├── log6.txt │ ├── log7.txt │ └── plotting.py ├── MMPINN │ ├── 0.15MMPINN.ipynb │ └── plotting.py ├── PINN (1000K Adam) │ ├── 0.15PINN(1000k Adam).py │ ├── 1.mat │ ├── 2.mat │ ├── 3.mat │ ├── log1.txt │ ├── log2.txt │ ├── 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