Two-dimensional infrared spectra get an inverse solver: a multi-task network recovers transition-dipole matrices at 0.085 RMSE

Two-dimensional infrared spectra can now yield the transition-dipole matrix directly rather than only a classifier label. Transition-dipole matrix elements characterize molecular structure and light-matter interaction, and are rarely measured directly; they are inferred from linear and nonlinear observables such as absorption and emission intensities, radiative lifetimes and coherent coupling signals. Earlier machine-learning work on spectroscopy focused mainly on classification and coarse parameter inference, leaving direct inference of physically meaningful quantities from 2D IR spectra a challenging inverse problem that demands high predictive accuracy. On the validation set the model reaches a root-mean-square error of 0.085, an R-squared of 0.97 and a normalized cross-correlation of 0.98 for the transition-dipole matrix, alongside high accuracy for the number of singly excited states and for the presence of doubly excited states.

The network handles level-structure decisions and dipole-matrix regression together, with a physical mask restricting which matrix elements are predicted. A convolutional backbone encodes one 2D IR spectrum, a gated fusion module and spatial attention refine the features, and three heads output the number of singly excited states, the presence of doubly excited states and the transition-dipole matrix. The regression head predicts only the off-diagonal elements in the upper triangle of the symmetric dipole matrix, excluding ground-to-doubly-excited, singly-to-singly and doubly-to-doubly transitions, so prior physical knowledge reduces parameter redundancy. Training data were generated with the non-Hermitian Hamiltonian method: 8000 simulated 2D IR spectra spanning systems with 3 to 10 energy levels, split 80% training and 20% validation with stratification by sub-dataset, over 160 epochs.

Errors stratify by transition type instead of falling uniformly. In the ten-level system, ground-to-singly-excited transitions show the lowest relative errors and allowed singly-to-doubly-excited transitions stay relatively low, while nominally forbidden or weakly allowed transitions show clearly larger relative errors. Weakly allowed transition dipole elements are small and produce weak spectral features, and they appear in the denominator of the relative error, so a small absolute deviation becomes a large relative error; overlapping peaks from near-degenerate transition frequencies further limit disentanglement. In simpler level structures, ground-to-singly-excited relative errors are about an order of magnitude lower than in the ten-level case, yet the simplest configurations show higher relative errors, indicating that spectral identifiability itself sets a limit.

The demonstrated scope is limited to simulated 2D IR spectra at fixed molecular orientation and a single waiting time of zero, for systems with 3 to 10 energy levels generated by the non-Hermitian Hamiltonian method in the short-population-time regime. The target quantity is the projected dipole amplitude along a chosen polarization axis in the laboratory frame, suited to evaluating inverse problems that take simulated spectra as input.

The non-Hermitian Hamiltonian method may deviate for long population times and steady-state behavior, mainly affecting the absolute signal scale. The dataset excludes orientational averaging, and the signs of Cartesian projections cannot be uniquely determined from the polarization configurations considered. Whether rotationally invariant quantities can be uniquely recovered in isotropic ensembles remains to be established.