Table 5 Best equation obtained by PySR using (1-R), where x0, x1, and x2 represent lnΔK, (1-R), and ln(1-ΔKth/ΔK), respectively
From: Crack Growth Rate Model Derived from Domain Knowledge-Guided Symbolic Regression
Complexity | Loss | SCORE | Equation |
|---|---|---|---|
1 | 11.95728320 | 0 | \(- 16.64\) |
3 | 6.85792887 | 0.506034 | \(x_{0} - 18.65\) |
4 | 5.12093165 | 1.015250 | \(- \ln (\left| {x_{2} } \right|) - 17.52\) |
5 | 1.62683224 | 5.138852 | \({{ - 0.79} \mathord{\left/ {\vphantom {{ - 0.79} {x_{2} }}} \right. \kern-0pt} {x_{2} }} - 20.06\) |
6 | 0.38504615 | 7.903765 | \(- 2.78{ \times }\ln (\left| {x_{2} } \right|) - 19.08\) |
8 | 0.26074687 | 1.355014 | \(- 3.66{ \times }\ln (\left| {x_{2} } \right|) - x_{2} - 20.76\) |
9 | 0.20797211 | 1.920022 | \(3.97{ \times }x_{0} - 2.99{ \times }x_{1} - 21.83\) |
10 | 0.18593335 | 1.063166 | \(- 3.33{ \times }\ln (\left| {x_{2} } \right|) - 0.62{ \times }x_{2} - 20.12\) |
11 | 0.16588967 | 1.196780 | \(\ln (\left| {x_{2} } \right|){ \times ((} - 0.31{ \times }\ln (\left| {x_{2} } \right|)) + 2.38) - 19.44\) |
12 | 0.14459242 | 1.579150 | \(1.65{ \times }\left( {x_{0} - \ln (\left| {x_{2} } \right|)} \right) + 1.12{ \times }x_{1} - 20.32\) |
13 | 0.13260567 | 1.081161 | \(3.65{ \times }x_{0} - 2.72{ \times }x_{1} + 0.30{ \times }x_{2} - 21.17\) |
14 | 0.11579778 | 1.828878 | \(2.55{ \times }x_{0} - {{(1.79{ \times }x_{1} + \ln (\left| {x_{2} } \right|))} \mathord{\left/ {\vphantom {{(1.79{ \times }x_{1} + \ln (\left| {x_{2} } \right|))} {0.97}}} \right. \kern-0pt} {0.97}} - 20.95\) |
16 | 0.11292975 | 0.187817 | \(2.55{ \times }x_{0} - (\ln (\left| {x_{2} } \right|) + x_{1} { \times }(1.79 - 0.05{ \times }x_{2} )) - 20.95\) |
18 | 0.11002615 | 0.221151 | \(2.64{ \times }x_{0} - {{{{0.04} \mathord{\left/ {\vphantom {{0.04} {x_{0} }}} \right. \kern-0pt} {x_{0} }}} \mathord{\left/ {\vphantom {{{{0.04} \mathord{\left/ {\vphantom {{0.04} {x_{0} }}} \right. \kern-0pt} {x_{0} }}} {x_{1} }}} \right. \kern-0pt} {x_{1} }} + 1.84{ \times }x_{1} - \ln (\left| {x_{2} } \right|) + 0.44 - 21.17\) |
20 | 0.11002614 | 0.000001 | \(2.64{ \times (}x_{0} - 0.07) - {{{{0.04} \mathord{\left/ {\vphantom {{0.04} {x_{0} }}} \right. \kern-0pt} {x_{0} }}} \mathord{\left/ {\vphantom {{{{0.04} \mathord{\left/ {\vphantom {{0.04} {x_{0} }}} \right. \kern-0pt} {x_{0} }}} {x_{1} }}} \right. \kern-0pt} {x_{1} }} + 1.84{ \times }x_{1} - \ln (\left| {x_{2} } \right|) + 0.44 - 20.99\) |