Lec.3: ODEs Damped Oscillator Exact Solution [Physics Informed Machine Learning]

#simulation #pinns #engineering #nvidia #machinelearning #technology
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Physics Informed Neural Networks (PINNs)
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[@azeemishaq8240]

Great sir

[@Dr.Mohammad_Samara]

Thank you for your support

[@Dr.Mohammad_Samara]

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[@BIKRAMDAS-mk1tj]

Sir, I have a question. I am basically applying PINNs in mathematical biology. Sir, if a differential equation already has exact solution then what is the necessity to use PINNs? And if there doesn't exist an exact solution for a differential equations, then in most of the literatures they are generating numerical data using traditional numerical methods and then applying those data for the training of our neural network. Then what is the advantages of PINNs in those cases sir? I truly believe that PINNs is a useful method for the differential equations in which numerical methods fail or in the cases of complex solution like Schrodinger equation. Sir, I have a lots of doubt and I think I may get those answers from you. Is there any platform except youtube so that I can contact with you for your valuable suggestions?

[@Dr.Mohammad_Samara]

Hi I will try to answer it seems a long question:
- we usually use exact solutions to see how far our PINNs method from the exact solution which is the reference point of your solver accuracy after that we can apply PINNs for problems that doesn't have exact solution.
- PINNs is a method to solve a system of equations (pdes or odes) it doesn't need any data generated by numerical methods.
- There are methods that needs data such as the deep neural operator such method do need a lot of data to work.
- please seebthe video "Is PINNs useful" it can show you what can it be uses for.
Later we will cover deep neural operator and inverse PINNs for ODEs these methods have more practical use cases than PINNs.

[@BIKRAMDAS-mk1tj]

Sir, I am research scholar. I want to apply PINNs and inverse PINNs in a Hepatitis B infection model for predicting the disease. It is a ode system. But sir, for my model I don't have the real life data available because it is an immunological model. That is why I had to generate the data using the parameter values. But it is very confusing to me. I am solving a system using PINNs whose solution is already generated by me. If a differential equation don't have exact solution and if no real life data is not available for that special differential equation then we have to generate the data nah? Then in those cases what is the importance of our method, sir?

[@BIKRAMDAS-mk1tj]

And you have replied sir, PINNs is a method to solve a system of differential equation. It does not require any data generated from numerical method. But, sir if our system of differential equation don't have exact solution and for it if experimental data is also not available how can we get the observed data which will be used to train our model?

[@BIKRAMDAS-mk1tj]

​@@Dr.Mohammad_Samara
Sir please answer

[@Dr.Mohammad_Samara]

Sorry I sometimes don't get a notification if I didn't reply please post it in a new comment it will notify me quickly... Anyway regarding your issue:
- for your confusion please take it slow and step by step.
- first PINNs solves the system of equations by minimizing the loss generated by that system so we don't need any data the equations will be used for that.
- if we need to make our model more suitable for real life results we can train the network with PINNs methods first and then use our real life data later but you need to change the loss equations to match your data that is for example simply calculator the MSE for the data batches.
- usually if you want to make a general model you will need to use PINNs with the network of deep neural operator, that somethimes refered to it as physics informed deep neural operator , it is a little different that deep neural operator in which you calculate the loss via the system of equations you have.
Hope this is made it more clear

[@Dr.Mohammad_Samara]

Hope you can enjoy our courses in our Podia platform:
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