PURPOSE: To develop a deep learning-based method for robust and rapid estimation of the fatty acid composition (FAC) in mammary adipose tissue. METHODS: A physics-based unsupervised deep learning network for estimation of fatty acid composition-network (FAC-Net) is proposed to estimate the number of double bonds and number of methylene-interrupted double bonds from multi-echo bipolar gradient-echo data, which are subsequently converted to saturated, mono-unsaturated, and poly-unsaturated fatty acids. The loss function was based on a 10 fat peak signal model. The proposed network was tested with a phantom containing eight oils with different FAC and on post-menopausal women scanned using a whole-body 3T MRI system between February 2022 and January 2024. The post-menopausal women included a control group (n = 8) with average risk for breast cancer and a cancer group (n = 7) with biopsy-proven breast cancer. RESULTS: The FAC values of eight oils in the phantom showed strong correlations between the measured and reference values (R CONCLUSION: The results in this study suggest that the proposed FAC-Net can be used to measure the FAC of mammary adipose tissue from gradient-echo MRI data of the breast.