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.

Coherent Anti-Stokes Raman Spectroscopy (CARS) provides non-invasive, label-free chemical analysis at high spatial resolution, making it a powerful tool for biomedical and material imaging. However, their effectiveness is hindered by a dominant and unpredictable non-resonant background (NRB) that distorts meaningful spectral features. Existing NRB removal methods often require additional measurements or computationally intensive post-processing. In this work, we present a physics-informed framework that leverages the broadband, low-rank structure of the NRB using Dynamic Mode Decomposition (DMD) for unsupervised separation of resonant Raman modes from non-resonant contributions in the spectral domain. We further introduce DA-DMD - a Deep Learning-Assisted DMD approach, that uses an attention mechanism to adaptively weight DMD modes and a CNN with skip connection to enhance Raman signal reconstruction. Trained entirely on synthetic data, DA-DMD eliminates the need for experimental labels or calibration. We validate our methods on synthetic and real CARS measurements, demonstrating superior background suppression, fidelity preservation, and generalization compared to existing approaches. DA-DMD offers fast inference and improves robustness, positioning it as a practical tool for scalable chemical imaging in complex environments.