# Non-Hermitian Hamiltonian Method

Two-dimensional infrared spectroscopy has mostly supported classification or coarse parameter inference, while directly recovering the transition-dipole matrix remains a hard inverse problem. Spec2DipoleNet couples level-structure classification with dipole-matrix regression in one physics-constrained multi-task convolutional network, trained on 8000 simulated spectra generated by the non-Hermitian Hamiltonian method. On validation it reaches an RMSE of 0.085, an R-squared of 0.97 and a normalized cross-correlation of 0.98, recovering allowed transitions well while nominally forbidden transitions deviate more.

Two-dimensional infrared spectroscopy has mostly supported classification or coarse parameter inference, while directly recovering the transition-dipole matrix remains a hard inverse problem. Spec2DipoleNet couples level-structure classification with dipole-matrix regression in one physics-constrained multi-task convolutional network, trained on 8000 simulated spectra generated by the non-Hermitian Hamiltonian method. On validation it reaches an RMSE of 0.085, an R-squared of 0.97 and a normalized cross-correlation of 0.98, recovering allowed transitions well while nominally forbidden transitions deviate more.