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

Sai Karthikeya Vemuri, Adithya Ashok Chalain Valapil, Tim Büchner, Joachim Denzler

TL;DR

RamPINN tackles the ill-posed problem of recovering Raman spectra from CARS measurements by disentangling resonant Raman signals from the non-resonant background using physics-informed losses. It uses a dual-decoder 1D U‑Net architecture and enforces Kramers-Kronig causality via a differentiable Hilbert-transform loss, together with a smoothness prior on NRB. Trained solely on synthetic data, RamPINN achieves strong zero-shot generalization to six real molecules and outperforms purely data-driven baselines, with a self-supervised variant remaining competitive. This work demonstrates that embedding established physical laws into neural networks provides a principled, robust inductive bias for data-limited scientific inverse problems, with broad implications for spectroscopic reconstruction and beyond.

Abstract

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.

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

TL;DR

RamPINN tackles the ill-posed problem of recovering Raman spectra from CARS measurements by disentangling resonant Raman signals from the non-resonant background using physics-informed losses. It uses a dual-decoder 1D U‑Net architecture and enforces Kramers-Kronig causality via a differentiable Hilbert-transform loss, together with a smoothness prior on NRB. Trained solely on synthetic data, RamPINN achieves strong zero-shot generalization to six real molecules and outperforms purely data-driven baselines, with a self-supervised variant remaining competitive. This work demonstrates that embedding established physical laws into neural networks provides a principled, robust inductive bias for data-limited scientific inverse problems, with broad implications for spectroscopic reconstruction and beyond.

Abstract

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.

Paper Structure

This paper contains 63 sections, 1 theorem, 28 equations, 15 figures, 12 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. RELATED WORK
  3. Physics-informed Learning
  4. Deep Learning for Spectroscopy
  5. THEORY
  6. Physics-Informed Learning
  7. CARS-to-Raman Spectra Mapping
  8. RamPINN - METHODOLOGY
  9. Model Architecture
  10. Optimization
  11. Kramers-Kronig Regularization.
  12. NRB Regularization.
  13. Optimization Term.
  14. Implementation
  15. EXPERIMENTS AND RESULTS
  16. ...and 48 more sections

Key Result

Proposition 1

Let $x$ be the measured CARS spectrum, which consists of both a real-valued non-resonant background $\chi^{(3)}_{\text{NRB}}$ and a complex-valued resonant term $\chi^{(3)}_{\text{res}}$. That is, Assume that $\chi^{(3)}_{\text{NRB}}$ is a smooth, real-valued function and that $\chi^{(3)}_{\text{res}}$ is causal and analytic in the upper-half complex frequency plane. Then, if a neural network pre

Figures (15)

  • Figure 1: RamPINN Architecture. Our architecture builds upon recent advancements wang2021vectorvalensise2020specnetvaswani2017attentionronneberger2015unet, with a key modification: a dual-branch decoder for reconstructing Raman and non-resonant background (NRB) signals. We incorporate physical constraints via losses $\mathcal{L}_{\mathrm{KK}}$ and $\mathcal{L}_\mathrm{smooth}$ on the predicted signals. Note that the encoder and decoder have identical dimensions (outlined in \ref{['sec:rampinn-model-architecture']}), but are depicted here with different scales for clarity.
  • Figure 2: Qualitative Comparison of Raman Signal Extraction. We visualize the Raman reconstruction of RamPINN, BiLSTM, and CNN-GRU on three synthetic samples (\ref{['fig:top-3-1']}-\ref{['fig:top-3-3']}). RamPINN outperforms the other methods, both qualitatively and quantitatively, as shown by the error values and lines (best viewed digitally). We provide additional plots in \ref{['ap:reconstruction-plots']}.
  • Figure 3: Zero-shot Raman Spectra Extraction -- Toluene. Looking at input CARS, ground truth Raman, and reconstructions from baseline methods (VECTOR, BiLSTM, CNN-GRU), our RamPINN approach provides a more accurate zero-shot Raman spectra recovery, achieving the lowest MSE and highest PSNR.
  • Figure 4: Ablation Study Quantifying the Effects of Individual Loss Terms on Test MSE. We observe that scaling our physics-based Kramers-Kronig regularization term, $\mathcal{L}_{\mathrm{KK}}$, steadily decreases the test MSE with increasing influence. We also see similar effects with increasing the amount of training data ($\mathcal{L}_{\mathrm{Data}}$) and the smoothness constraint imposed on NRB ($\mathcal{L}_{\mathrm{smooth}}$).
  • Figure 5: Additional qualitative comparison of Raman reconstruction.
  • ...and 10 more figures

Theorems & Definitions (1)

  • Proposition 1: Kramers--Kronig Consistency from Residual Decomposition