RamPINN: Recovering Raman Spectra From Coherent Anti-Stokes Spectra Using Embedded Physics

Transferring the recent advancements in deep learning into scientific disciplines is hindered by the lack of the required large-scale datasets for training. We argue that in these knowledge-rich domains, the established body of scientific theory provides reliable inductive biases in the form of governing physical laws. We address the ill-posed inverse problem of recovering Raman spectra from noisy Coherent Anti-Stokes Raman Scattering (CARS) measurements, as the true Raman signal here is suppressed by a dominating non-resonant background. We propose RamPINN, a model that learns to recover Raman spectra from given CARS spectra. Our core methodological contribution is a physics-informed neural network that utilizes a dual-decoder architecture to disentangle resonant and non-resonant signals. This is done by enforcing the Kramers-Kronig causality relations via a differentiable Hilbert transform loss on the resonant and a smoothness prior on the non-resonant part of the signal. Trained entirely on synthetic data, RamPINN demonstrates strong zero-shot generalization to real-world experimental data, explicitly closing this gap and significantly outperforming existing baselines. Furthermore, we show that training with these physics-based losses alone, without access to any ground-truth Raman spectra, still yields competitive results. This work highlights a broader concept: formal scientific rules can act as a potent inductive bias, enabling robust, self-supervised learning in data-limited scientific domains.