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I have a function

F[x_] := x^3/(e^x -1)

I generate many data points i = 1,2,3,4, ...

Data := Table[ (x_i, F[x_i]), {i,1,10}]

Can I use machine learning to recover F[x] from this data? I mean I want an analytical expression, not some numerical function.

FindFormula does not seem to work.

FindFormula[{{0.01`, 0.00009950083333194553`}, {0.51`, 
0.19938787858268528`}, {1.01`, 0.5902270857639341`}, {1.51`, 
0.9762443466200139`}, {2.01`, 1.256413783143141`}, {2.51`, 
1.3987924662389322`}, {3.01`, 1.4139231366437974`}, {3.51`, 
1.3326921266779141`}, {4.01`, 1.1908573908149254`}, {4.51`, 
1.0201511993361019`}, {5.01`, 0.844509746648546`}, {5.51`, 
0.6795993704877206`}, {6.01`, 0.5340484840896383`}, {6.51`, 
0.41127547121761243`}, {7.01`, 0.31127339153687206`}, {7.51`, 
0.232063120869884`}, {8.01`, 0.17074304099618653`}, {8.51`, 
0.12417384640247439`}, {9.01`, 0.08937872541975592`}, {9.51`, 
0.06374310481612774`}}, x]

gives an answer 0.64198 (one number!) instead of the function x^3/(e^x -1)

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  • 3
    $\begingroup$ What about FindFormula? $\endgroup$ – Kuba May 2 at 11:38
  • $\begingroup$ FindFormula does not work. FindFormula[Data,x] gives an answer as a single real number ! .... which is 0.64198 ... Bug maybe? $\endgroup$ – Quasar Supernova May 2 at 11:44
  • 3
    $\begingroup$ Make sure your Data is correct. 1) e is not E, 2) what do you think Table[x_i, {i, 10}] does? $\endgroup$ – Kuba May 2 at 11:46

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