I have a number of ODEs (58) with 16 parameters and 9 variables. I want to solve the ODEs to obtain the analytical relationship between the parameters and variables. It is obviously that the ODEs cannot be solved using regular analytical methods. It is also not easily solved by simulations since too many parameter sets should be included, and the follow-up fitting should not be easy. May I solve the ODEs using deep learning methods? Could anyone offer the relevant packages or logics or algorithms? Many many thanks!
Dear Miaoxiao Wang
These articles might help, have a look:
1. https://towardsdatascience.com/using-neural-networks-to-solve-ordinary-differential-equations-a7806de99cdd
2. https://towardsdatascience.com/how-to-solve-an-ode-with-a-neural-network-917d11918932
3. https://www.analyticsvidhya.com/blog/2021/09/ordinary-differential-equations-made-easy-with-deep-learning/
Kind Regards
Qamar Ul Islam
You can reqd this articles:
https://www.sciencedirect.com/science/article/pii/S2666827021000293
https://ieeexplore.ieee.org/abstract/document/712178?casa_token=dniUIE06FNUAAAAA:cbjoPzcYgE41qCfu4XwGshUXlpFfOCMJpN4pywoZVQvUyIMvEahau9YpOIQNEY9Poh68Lac
The best way is to use MATLAB for ODE/PDE via its numerical analysis. See for example https://au.mathworks.com/help/matlab/math/partial-differential-equations.html
MATLAB Tool Box for ODE/PDE: https://au.mathworks.com/products/pde.html
https://au.mathworks.com/help/matlab/math/solve-system-of-pdes.html
Thanks for all the suggestions! These papers are helpful. I also found a useful paper that are specific the biological system: https://www.nature.com/articles/s41467-019-12342-y
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