Title: Physics Model-based Autoencoding for Magnetic Resonance Fingerprinting. Abstract: Magnetic Resonance Fingerprinting (MRF) is a promising paradigm to achieve fast quantitative Magnetic Resonance Imaging (QMRI). However, current MRF methods suffer from slow imaging speeds and poor generalization performance on radio frequency pulse sequences generated with varied settings. To address this challenging task, we propose a novel model-based MRF method that learns better representations by integrating a fast and differentiable MRI physics model as causal regularization. The proposed approach adopts a supervised auto-encoder framework consisting of an encoder and a decoder, where the encoder predicts the target tissue properties (anti-causal task) and the decoder reconstructs the inputs (causal task). Specifically, the encoder embeds high-dimensional MRF time sequences to a low-dimensional tissue property space, while the decoder exploits an MRI physics model to reconstruct the input signals using the estimated tissue properties and associated MRI settings. The causal regularization induced by the decoder improves the generalization performance and uniform stability of the approach, leading to the best performance on tissue property estimation, outperforming state-of-the-art competing methods.