ODE Inverse problem : Wrong inferred value of parameter , though small loss

[ZSTanone]

Hi @lululxvi,

Thank you for your wonderful framework and documentation!

And I have used deepxde to make some simple inverse problems in odes which have 6~8 eqs.

But I meet some problems in doing a more complex invers ode model. The majority of my step are followed your SBINN paper. First I did Structural Identifiability of all parameters. define my parameters I did little scaling in ode Set my model And I also did some scaling in output_transform to ensure the output of NN in the proper magnitude

In training NN ，I set the loss_weight to make sure each loss items in same magnitude in step 0

After training about 80k the loss is pretty small ，but the inference was wrong The right value should be 0.7 , 0.16, 0.63 , 5.5 respectively

However the PINN can work well when I estimate 1 or 2 parameters

I really hope you can give me suggestion about my problems. Much appreciate！！！！！

[lululxvi]

How about adding more state observations?

[elliot-hicks]

@ZSTanone I was looking at this and noticed this relationship across the targets and outputs. This might happen if your problem is defined up to an arbitrary scale (this hypothesis breaks down on the last variable, but 3/4 to 0.0001 is pretty sus):

[ZSTanone]

@elliot-hicks Thank you for such a careful observation, I have some doubts about ‘your problem is defined up to an arbitrary scale’ does that mean I need to restrict the parameter search range？or I have to reduce the number of parameters to be identified？