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NVIDIA / modulus-sym

Framework providing pythonic APIs, algorithms and utilities to be used with Modulus core to physics inform model training as well as higher level abstraction for domain experts
https://developer.nvidia.com/modulus
Apache License 2.0
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🐛[BUG]: Validator L2 Relative Error Loss #96

Open BoomChawit opened 9 months ago

BoomChawit commented 9 months ago

Version

v1.3.0

On which installation method(s) does this occur?

No response

Describe the issue

I would like to report an issue in modulus/sym/domain/validator/validator.py.

As in lines 39 - 42, the L2 relative error is written as

$$ e{L^2} = \sqrt{\frac{ \frac{1}{N} \sum{i} \left( u_{truei} - u{pred_i} \right)^2} {\frac{1}{N-\delta N} \sumi \left(u{truei} - \overline{u}{true}\right)^2}} $$

new_var["l2_relative_error_" + str(key)] = torch.sqrt(
                torch.mean(torch.square(true_var[key] - pred_var[key]))
                / torch.var(true_var[key])
            )

However, I understand that the L2 relative error is defined as

$$ e{L^2} = \sqrt{ \frac{ \sum{i} \left( u_{truei}-u{pred_i} \right)^2} {\sumi \left(u{true_i}\right)^2} } $$

new_var["l2_relative_error_" + str(key)] = torch.sqrt(
                torch.sum(torch.square(true_var[key] - pred_var[key]))
                /  torch.sum(torch.square(true_var[key]))
            )

Regarding the validation loss, I would like to bring up this concern. If I misunderstand the concept of the function, please correct my understanding. Thank you very much for your consideration.

Minimum reproducible example

No response

Relevant log output

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Environment details

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Other/Misc.

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