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Neoadjuvant chemotherapy (NAC) is standard for locally advanced breast cancer, with pathologic complete response (pCR) strongly predicting improved survival. However, only 30–40% of patients achieve pCR, while the rest undergo toxicity and delayed surgery without benefit. Current prediction methods rely on tumor volume at isolated time points or simple pre- and post-treatment comparisons, ignoring continuous tumor dynamics during therapy. Sparse and irregular MRI sampling further limits accurate modeling. We introduce a Neural Ordinary Differential Equation (Neural ODE) framework to model continuous tumor growth from sparse serial MRI during NAC. The model learns a time-continuous function describing tumor evolution and predicts individual response trajectories and final pCR status. The framework includes (1) MRI-based tumor segmentation, (2) construction of sparse longitudinal tumor volume series, (3) Neural ODE modeling of continuous dynamics via a neural network–parameterized derivative function, and (4) classification of the final latent state for pCR prediction. An optional module enables trajectory visualization and interpretability. This approach captures hidden continuous tumor behavior between scans, handles irregular sampling without imputation, and enables earlier response prediction. It is also computationally efficient using adjoint-based training and may reveal distinct growth patterns between responders and non-responders. Neural ODE-based modeling offers a more informative framework for predicting NAC response by capturing continuous tumor dynamics, with potential to improve pCR prediction over conventional volume-based methods.