Advances in machine learning have boosted the use of Earth observation data for climate change research. Yet, the interpretability of machine-learned representations remains a challenge, particularly in understanding forests' biophysical reactions to climate change. Traditional methods in remote sensing that invert radiative transfer models (RTMs) to retrieve biophysical variables from spectral data often fail to account for biases inherent in the RTM, especially for complex forests. We propose to integrate RTMs into an auto-encoder architecture, creating an end-to-end learning approach. Our method not only corrects biases in RTMs but also outperforms traditional techniques for variable retrieval like neural network regression. Furthermore, our framework has potential generally for inverting biased physical models.