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Minimize a function using the results from NDSolve

Yz Wu

Posted 4 years ago

I get some results `z1` from an equation s1 = y''[x] + Sin[y[x]] y[x]; sol1 = NDSolve[{s1 == 0, y[0] == 1, y'[0] == 0}, y, {x, 0, 30}]; sy[x_] = {y[x]} /. s; z1 = Table[Take[sy[x]], {x, 5, 30, 5}] {{{-4.56095}}, {{0.999889}}, {{-4.55976}}, {{0.999555}},{{-4.55738}}, {{0.998999}}} Now a new equation `s2` contains a and b s2 = ay2''[x] + bSin[y2[x]] y2[x] The results `z2` should be solved using the same method. sol2 = NDSolve[{s2 == 0, y2[0] == 1, y2'[0] == 0}, y2, {x, 0, 30}]; sy2[x_] = {y2[x]} /. s; z2 = Table[Take[sy2[x]], {x, 5, 30, 5}] Then I want to minimize `(z1-z2).(z1-z2)` and find `a` and `b` Nminimize[(z1 - z2).(z1 - z2), {a, b}] I know my codes can't work, but I'm trying to express thought. I'm new to Mathematica. I really appreciate your help.

I get some results z1 from an equation

  s1 = y''[x] + Sin[y[x]] y[x];
    sol1 = NDSolve[{s1 == 0, y[0] == 1, y'[0] == 0}, y, {x, 0, 30}];
    sy[x_] = {y[x]} /. s;
    z1 = Table[Take[sy[x]], {x, 5, 30, 5}]
{{{-4.56095}}, {{0.999889}}, {{-4.55976}}, {{0.999555}},{{-4.55738}}, {{0.998999}}}

Now a new equation s2 contains a and b

s2 = a*y2''[x] + b*Sin[y2[x]] y2[x]

The results z2 should be solved using the same method.

sol2 = NDSolve[{s2 == 0, y2[0] == 1, y2'[0] == 0}, y2, {x, 0, 30}];
sy2[x_] = {y2[x]} /. s;
z2 = Table[Take[sy2[x]], {x, 5, 30, 5}]

Then I want to minimize (z1-z2).(z1-z2) and find a and b

Nminimize[(z1 - z2).(z1 - z2), {a, b}]

I know my codes can't work, but I'm trying to express thought. I'm new to Mathematica. I really appreciate your help.

POSTED BY: Yz Wu

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Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 4 years ago

You probably have a misconception of what `Take` does. Please have a look at the documentation.

POSTED BY: Gianluca Gorni

Yz Wu

Posted 4 years ago

Thank you. But When I try to run a complicated case, I meet another problem, z1 = Table[Take[ysol[[1]], {Nn + 1, 2 Nn}].u2n[L/2], {t, 5, 20, 5}] {0.267999, 0.483416, 0.601376, 0.661358} my function with unknowns is invysol = ParametricNDSolveValue[Thread[Join[inveqD, invicD] == 0], {invq[t]}, {t, 0, tf}, {x1, x2, x3, x4}] But when I want to make z2, an error comes, z2 = Table[Take[First[invysol], {Nn + 1, 2 Nn}].u2n[L/2], {t, 5, 20, 1}] Take::normal: Nonatomic expression expected at position 1 in Take[1,{6,10}]. Take::normal: Nonatomic expression expected at position 1 in Take[1,{6,10}]. Take::normal: Nonatomic expression expected at position 1 in Take[1,{6,10}]. General::stop: Further output of Take::normal will be suppressed during this calculation. It seems I can't use `Take` in the `ParametricNDSolveValue` function. Do you know how to solve it?

Thank you. But When I try to run a complicated case, I meet another problem,

z1 = Table[Take[ysol[[1]], {Nn + 1, 2 Nn}].u2n[L/2], {t, 5, 20, 5}]
{0.267999, 0.483416, 0.601376, 0.661358}

my function with unknowns is

invysol = ParametricNDSolveValue[Thread[Join[inveqD, invicD] == 0], {invq[t]}, {t, 0, tf}, {x1, x2, 
   x3, x4}]

But when I want to make z2, an error comes,

z2 = Table[Take[First[invysol], {Nn + 1, 2 Nn}].u2n[L/2], {t, 5, 20, 1}]
Take::normal: Nonatomic expression expected at position 1 in Take[1,{6,10}].
Take::normal: Nonatomic expression expected at position 1 in Take[1,{6,10}].
Take::normal: Nonatomic expression expected at position 1 in Take[1,{6,10}].
General::stop: Further output of Take::normal will be suppressed during this calculation.

It seems I can't use Take in the ParametricNDSolveValue function. Do you know how to solve it?

POSTED BY: Yz Wu

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 4 years ago

You can do it with `ParametricNDSolveValue`: s1 = y''[x] + Sin[y[x]] y[x]; sy = NDSolveValue[{s1 == 0, y[0] == 1, y'[0] == 0}, y, {x, 0, 30}]; z1 = Table[sy[x], {x, 5, 30, 5}]; s2 = ay2''[x] + bSin[y2[x]] y2[x]; sy2 = ParametricNDSolveValue[{s2 == 0, y2[0] == 1, y2'[0] == 0}, y2, {x, 0, 30}, {a, b}]; z2 = Table[sy2[a, b][x], {x, 5, 30, 5}]; NMinimize[(z1 - z2).(z1 - z2), {a, b}]

You can do it with ParametricNDSolveValue:

s1 = y''[x] + Sin[y[x]] y[x];
sy = NDSolveValue[{s1 == 0, y[0] == 1, y'[0] == 0}, y, {x, 0, 30}];
z1 = Table[sy[x], {x, 5, 30, 5}];
s2 = a*y2''[x] + b*Sin[y2[x]] y2[x];
sy2 = ParametricNDSolveValue[{s2 == 0, y2[0] == 1, y2'[0] == 0}, 
   y2, {x, 0, 30}, {a, b}];
z2 = Table[sy2[a, b][x], {x, 5, 30, 5}];
NMinimize[(z1 - z2).(z1 - z2), {a, b}]

POSTED BY: Gianluca Gorni

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