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I have a very simple non-linear model:

lm(Y ~ poly(X, degree = 2), data=data)

The results I obtained are:

model output from R

My question is, to test the validity of the model, is testing for autocorrelation, heteroscedasticity and normal distribution of residuals relevant for non-linear models?

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You do not have a nonlinear model, you have a linear model with a polynomial predictor. So yes, this model is nonlinear in the predictor x, but it is linear in the unknown model parameters, and that is what is meant with a linear model.

So your model assumes that, around the parabolic expectation, there is a normal-distributed error term with zero expectation and constant variance.

So to your question:

My question is, to test the validity of the model, is testing for autocorrelation, heteroscedasticity and normal distribution of residuals relevant for non-linear models?

Yes, yes, and yeas, all of those are potentially relevant for your linear model. And, if you had a nonlinear model with additive normal errors, those would still be relevant.

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