Sun Dec 15 10:28:41 2024 paraheat_gaussian_parameter(): python version: 3.10.12 numpy version: 1.26.4 tensorflow version: 2.16.1 keras version: 3.1.1 Neural network to solve a multivariate regression problem. Estimate the parameter vc used in a Gaussian diffusivity given vs, 50 samples of the resulting heat distribution Data of many records of vc and vs is available. The data is read from an external file. Read data from vc500.txt Data contains 500 records with 55 features. Training data uses 475 records with 50 features and 1 targets. Test data uses 25 records with 50 features and 1 targets. train_data[0,0:10]: [ 9.6265467 13.613504 27.642524 23.320682 25.420298 20.927116 12.464001 6.2774213 23.433233 24.045476 ] train_targets[0]: 2.8977486 test_data[0,0:10]: [ 9.629448 13.617584 27.651117 23.327865 25.428162 20.933537 12.46775 6.2793045 23.440456 24.052893 ] test_targets[0]: 2.8966315 Using 200 nodes per layer Model: "sequential" ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ dense (Dense) │ (None, 200) │ 10,200 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_1 (Dense) │ (None, 200) │ 40,200 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_2 (Dense) │ (None, 200) │ 40,200 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_3 (Dense) │ (None, 200) │ 40,200 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_4 (Dense) │ (None, 200) │ 40,200 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_5 (Dense) │ (None, 200) │ 40,200 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_6 (Dense) │ (None, 200) │ 40,200 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_7 (Dense) │ (None, 1) │ 201 │ └─────────────────────────────────┴────────────────────────┴───────────────┘ Total params: 251,601 (982.82 KB) Trainable params: 251,601 (982.82 KB) Non-trainable params: 0 (0.00 B) Training: Epoch 1/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 16s 2s/step - loss: 10.8120 - mean_squared_error: 10.8120 12/12 ━━━━━━━━━━━━━━━━━━━━ 2s 14ms/step - loss: 18.1468 - mean_squared_error: 18.1585 - val_loss: 5.1980 - val_mean_squared_error: 5.2061 Epoch 2/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 6.2361 - mean_squared_error: 6.2361 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 5.1379 - mean_squared_error: 5.1385 - val_loss: 5.2254 - val_mean_squared_error: 5.2333 Epoch 3/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 17ms/step - loss: 4.2785 - mean_squared_error: 4.2785 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 4.8890 - mean_squared_error: 4.8871 - val_loss: 5.6145 - val_mean_squared_error: 5.6223 Epoch 4/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 4.6645 - mean_squared_error: 4.6645 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 4.7932 - mean_squared_error: 4.7939 - val_loss: 4.6694 - val_mean_squared_error: 4.6768 Epoch 5/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 5.1810 - mean_squared_error: 5.1810 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 4.5374 - mean_squared_error: 4.5352 - val_loss: 4.5963 - val_mean_squared_error: 4.6035 Epoch 6/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 4.4420 - mean_squared_error: 4.4420 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 4.2825 - mean_squared_error: 4.2830 - val_loss: 3.9889 - val_mean_squared_error: 3.9956 Epoch 7/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 17ms/step - loss: 4.1800 - mean_squared_error: 4.1800 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 4.1018 - mean_squared_error: 4.1036 - val_loss: 3.6650 - val_mean_squared_error: 3.6713 Epoch 8/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 3.9311 - mean_squared_error: 3.9311 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 3.7052 - mean_squared_error: 3.7062 - val_loss: 3.3604 - val_mean_squared_error: 3.3663 Epoch 9/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 3.5366 - mean_squared_error: 3.5366 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 3.5864 - mean_squared_error: 3.5871 - val_loss: 3.2837 - val_mean_squared_error: 3.2891 Epoch 10/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 3.3433 - mean_squared_error: 3.3433 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 3.4748 - mean_squared_error: 3.4757 - val_loss: 2.7711 - val_mean_squared_error: 2.7763 Epoch 11/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 2.6562 - mean_squared_error: 2.6562 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 2.7392 - mean_squared_error: 2.7403 - val_loss: 2.2847 - val_mean_squared_error: 2.2892 Epoch 12/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 1.7389 - mean_squared_error: 1.7389 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 1.9824 - mean_squared_error: 1.9837 - val_loss: 1.3755 - val_mean_squared_error: 1.3787 Epoch 13/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 1.7611 - mean_squared_error: 1.7611 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 1.3471 - mean_squared_error: 1.3460 - val_loss: 2.0855 - val_mean_squared_error: 2.0882 Epoch 14/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 2.1221 - mean_squared_error: 2.1221 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 1.4200 - mean_squared_error: 1.4211 - val_loss: 0.5121 - val_mean_squared_error: 0.5139 Epoch 15/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 0.6002 - mean_squared_error: 0.6002 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.4832 - mean_squared_error: 0.4835 - val_loss: 0.3030 - val_mean_squared_error: 0.3041 Epoch 16/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 15ms/step - loss: 0.1660 - mean_squared_error: 0.1660 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.2889 - mean_squared_error: 0.2891 - val_loss: 0.1916 - val_mean_squared_error: 0.1920 Epoch 17/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 15ms/step - loss: 0.1975 - mean_squared_error: 0.1975 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.2089 - mean_squared_error: 0.2091 - val_loss: 0.1870 - val_mean_squared_error: 0.1876 Epoch 18/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 0.3010 - mean_squared_error: 0.3010 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1777 - mean_squared_error: 0.1777 - val_loss: 0.0630 - val_mean_squared_error: 0.0631 Epoch 19/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 0.0502 - mean_squared_error: 0.0502 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1152 - mean_squared_error: 0.1153 - val_loss: 0.4857 - val_mean_squared_error: 0.4854 Epoch 20/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 0.5267 - mean_squared_error: 0.5267 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.2985 - mean_squared_error: 0.2987 - val_loss: 0.0712 - val_mean_squared_error: 0.0715 Epoch 21/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 0.0690 - mean_squared_error: 0.0690 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0816 - mean_squared_error: 0.0816 - val_loss: 0.0940 - val_mean_squared_error: 0.0944 Epoch 22/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 0.0831 - mean_squared_error: 0.0831 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1143 - mean_squared_error: 0.1141 - val_loss: 0.1603 - val_mean_squared_error: 0.1607 Epoch 23/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 0.1273 - mean_squared_error: 0.1273 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1016 - mean_squared_error: 0.1016 - val_loss: 0.1559 - val_mean_squared_error: 0.1563 Epoch 24/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 0.1650 - mean_squared_error: 0.1650 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.1135 - mean_squared_error: 0.1136 - val_loss: 0.0504 - val_mean_squared_error: 0.0506 Epoch 25/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 0.0290 - mean_squared_error: 0.0290 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0379 - mean_squared_error: 0.0379 - val_loss: 0.0270 - val_mean_squared_error: 0.0270 Epoch 26/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 0.0320 - mean_squared_error: 0.0320 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0385 - mean_squared_error: 0.0385 - val_loss: 0.0367 - val_mean_squared_error: 0.0366 Epoch 27/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 0.0405 - mean_squared_error: 0.0405 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0439 - mean_squared_error: 0.0438 - val_loss: 0.0260 - val_mean_squared_error: 0.0260 Epoch 28/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 0.0277 - mean_squared_error: 0.0277 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0342 - mean_squared_error: 0.0342 - val_loss: 0.0217 - val_mean_squared_error: 0.0218 Epoch 29/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 0.0283 - mean_squared_error: 0.0283 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0210 - mean_squared_error: 0.0210 - val_loss: 0.0221 - val_mean_squared_error: 0.0222 Epoch 30/30  1/12 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - loss: 0.0198 - mean_squared_error: 0.0198 12/12 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - loss: 0.0213 - mean_squared_error: 0.0214 - val_loss: 0.0142 - val_mean_squared_error: 0.0142 Testing: Case True Estimate 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 56ms/step 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 56ms/step 0: 2.8966 2.9774 1: 3.5714 3.7383 2: 1.3504 1.4001 3: 4.4512 4.4175 4: 3.5437 3.7120 5: 2.2862 2.2473 6: 1.8434 1.8247 7: 1.4530 1.4906 8: 1.7830 1.7685 9: 3.6567 3.8167 10: 4.0334 4.1278 11: 2.9695 3.0735 12: 3.4010 3.5710 13: 2.1963 2.1641 14: 3.5508 3.7189 15: 0.9818 0.9815 16: 2.4629 2.4066 17: 2.0502 2.0243 18: 2.7961 2.8476 19: 4.4257 4.4013 20: 3.6132 3.7771 21: 4.8695 4.6610 22: 4.8942 4.6729 23: 4.9986 4.7060 24: 1.0783 1.1087 Graphics saved as "paraheat_gaussian_parameter.png" paraheat_gaussian_parameter(): Normal end of execution. Sun Dec 15 10:28:50 2024