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Solution Bundle #3
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Yes. The other files in the ThreeBodyProblem folder use this method as well, but also include curriculum learning |
Okay, also can you tell me if I use spring mass system where there are double derivatives, according to your naming system, would it be like. should it be the value I get if I pass xOut through the network? |
For second derivatives, you would require another function, d2TrialSolution, that uses the analytic expression for the second derivative of trialSolution. It would look something like this: def d2TrialSolution(varOut, dVarOut, d2VarOut, t):
In the train function you would be required to evaluate d2xOut in the same was dxOut was calculated: Problems 5, 7 and 8 have more examples of doing this for second derivatives, as well as calculating mixed partial derivatives using autograd. Hope this helps! |
@Isaac-Somerville Is this and prob7 and prob8 in LagarisProblems folder are using solution bundle? |
No but the methodology is the same regarding calculating derivatives of the
trial solution
…On Mon, 4 Mar 2024, 21:46 tanmay2798, ***@***.***> wrote:
https://github.com/Isaac-Somerville/Neural-Networks-for-Solving-Differential-Equations/blob/main/LagarisProblems/prob5.py
Is this and prob7 and prob8 in LagarisProblems folder are using solution
bundle?
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Okay, and should it be d2TrialSoln = ((1 - torch.exp(-t)) * d2VarOut) + (torch.exp(-t) * (2 * dVarOut - varOut)) |
Yes that's right |
@Isaac-Somerville |
The solution bundle method is used in this file - https://github.com/Isaac-Somerville/Neural-Networks-for-Solving-Differential-Equations/blob/main/ThreeBodyProblem/threeBodyOriginalMethod.py ?
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