Hamiltonian Learning using Machine Learning Models Trained with Continuous Measurements

We present a machine learning approach for Hamiltonian parameter estimation in quantum systems using weak measurement data. Our model combines an LSTM-based encoder with a physics-informed decoder, incorporating a trainable correction term for unmodeled dynamics. Evaluated in both supervised and unsupervised settings, the method demonstrates high accuracy and robustness against noise. This approach offers a scalable solution for quantum system identification, outperforming traditional methods in parameter estimation tasks.