A machine learning framework based on physical information: a little problem!

Questions
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1

I found that the physical information neural network I made did not have a good prediction effect outside the training domain. How can I solve the problem

This document I reproduced：
[1] Han S , Stelz L , Stoecker H ,et al.Approaching epidemiological dynamics of COVID-19 with physics-informed neural networks[J].Journal of the Franklin Institute, 2024, 361(6).DOI:10.1016/j.jfranklin.2024.106671.

Approaching epidemiological dynamics of COVID-19 with__physics-informed neural networks.pdf (1.2 MB)

2

I found that the physical information neural network I made did not have a good prediction effect outside the training domain. How can I solve the problem?

3

Thanks for this really excellent example. Minor correction in your code. The (“Time”->1) at the bottom of the "pde’ net should be changed to (“Time” → “Scalar”) because of the input data:

Take[data,5]
{0. -> {970., 20., 0.}, 0.1 -> {969.572, 20.1854, 0.18824}, 
 0.2 -> {969.14, 20.372, 0.377969}, 
 0.3 -> {968.704, 20.5599, 0.569198}, 
 0.4 -> {968.266, 20.7491, 0.76194}}

Could you please explain why #[[1]] is used for “Sres”, “Ires” and “Rres”?

"cate1" -> CatenateLayer[],
"Sres" -> FunctionLayer[Function[{#[[1]] + \[Beta]*#[[2]]*#[[3]]/N1}]],
"cate2" -> CatenateLayer[],
"Ires" -> 
 FunctionLayer[
  Function[{#[[1]] - \[Beta]*#[[2]]*#[[3]]/N1 + \[Gamma]*#[[3]]}]],
"cate3" -> CatenateLayer[],
"Rres" -> FunctionLayer[Function[{#[[1]] - \[Gamma]* #[[2]]}]],

I thought #[[1]],#[[2]], and #[[3]] should be used instead?

"cate1" -> CatenateLayer[],
"Sres" -> FunctionLayer[Function[{#[[1]] + \[Beta]*#[[2]]*#[[3]]/N1}]],
"cate2" -> CatenateLayer[],
"Ires" -> 
 FunctionLayer[
  Function[{#[[2]] - \[Beta]*#[[2]]*#[[3]]/N1 + \[Gamma]*#[[3]]}]],
"cate3" -> CatenateLayer[],
"Rres" -> FunctionLayer[Function[{#[[3]] - \[Gamma]* #[[2]]}]],
4

Thanks! I modified this according to your suggestions，Sres, Ires, Rres are the loss of physical information，I think this example is more complicated and may not be easy to understand

5

This is the true result:

11.jpg
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