Research Article
Comparison of Artificial Neural Network Architecture in Solving Ordinary Differential Equations
Table 1
Analytical and neural solutions with arbitrary and regression based weights (Example
1).
| Input data | Analytical | Neural results | (four nodes) | (four nodes) | (five nodes) | (five nodes) | (six nodes) | Deviation% | (six nodes) | Deviation% |
| 0 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.00 | 1.0000 | 0.00 | 0.05 | 0.9536 | 1.0015 | 0.9998 | 1.0002 | 0.9768 | 0.9886 | 3.67 | 0.9677 | 1.47 | 0.10 | 0.9137 | 0.9867 | 0.9593 | 0.9498 | 0.9203 | 0.9084 | 0.58 | 0.9159 | 0.24 | 0.15 | 0.8798 | 0.9248 | 0.8986 | 0.8906 | 0.8802 | 0.8906 | 1.22 | 0.8815 | 0.19 | 0.20 | 0.8514 | 0.9088 | 0.8869 | 0.8564 | 0.8666 | 0.8587 | 0.85 | 0.8531 | 0.19 | 0.25 | 0.8283 | 0.8749 | 0.8630 | 0.8509 | 0.8494 | 0.8309 | 0.31 | 0.8264 | 0.22 | 0.30 | 0.8104 | 0.8516 | 0.8481 | 0.8213 | 0.9289 | 0.8013 | 1.12 | 0.8114 | 0.12 | 0.35 | 0.7978 | 0.8264 | 0.8030 | 0.8186 | 0.8051 | 0.7999 | 0.26 | 0.7953 | 0.31 | 0.40 | 0.7905 | 0.8137 | 0.7910 | 0.8108 | 0.8083 | 0.7918 | 0.16 | 0.7894 | 0.13 | 0.45 | 0.7889 | 0.7951 | 0.7908 | 0.8028 | 0.7948 | 0.7828 | 0.77 | 0.7845 | 0.55 | 0.50 | 0.7931 | 0.8074 | 0.8063 | 0.8007 | 0.7960 | 0.8047 | 1.46 | 0.7957 | 0.32 | 0.55 | 0.8033 | 0.8177 | 0.8137 | 0.8276 | 0.8102 | 0.8076 | 0.53 | 0.8041 | 0.09 | 0.60 | 0.8200 | 0. 8211 | 0.8190 | 0.8362 | 0.8246 | 0.8152 | 0.58 | 0.8204 | 0.04 | 0.65 | 0.8431 | 0.8617 | 0.8578 | 0.8519 | 0.8501 | 0.8319 | 1.32 | 0.8399 | 0.37 | 0.70 | 0.8731 | 0.8896 | 0.8755 | 0.8685 | 0.8794 | 0.8592 | 1.59 | 0.8711 | 0.22 | 0.75 | 0.9101 | 0.9281 | 0.9231 | 0.9229 | 0.9139 | 0.9129 | 0.31 | 0.9151 | 0.54 | 0.80 | 0.9541 | 0.9777 | 0.9613 | 0.9897 | 0.9603 | 0.9755 | 2.24 | 0.9555 | 0.14 | 0.85 | 1.0053 | 1.0819 | 0.9930 | 0.9956 | 1. 0058 | 1.0056 | 0.03 | 0.9948 | 1.04 | 0.90 | 1.0637 | 1.0849 | 1.1020 | 1.0714 | 1.0663 | 1.0714 | 0.72 | 1.0662 | 0.23 | 0.95 | 1.1293 | 1.2011 | 1.1300 | 1.1588 | 1.1307 | 1.1281 | 0.11 | 1.1306 | 0.11 | 1.00 | 1.2022 | 1.2690 | 1.2195 | 1.2806 | 1.2139 | 1.2108 | 0.71 | 1.2058 | 0.29 |
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