# iPINN for Broadband CARS Phase Retrieval: A Framework for Function Approximation and Inverse Modeling Problems in Nonlinear Spectroscopy

arXiv: https://arxiv.org/abs/2609.00883 · HTML: https://mlsanity.com/paper/2609.00883/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 28 references that are in the map.
- First posted on arXiv 1 Sep 2026.

## Builds on (most cited first, 6 of 6)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [SpecTNT: a Time-Frequency Transformer for Music Audio](https://mlsanity.com/paper/2110.09127/) (2021)
- [RamPINN: Recovering Raman Spectra From Coherent Anti-Stokes Spectra Using Embedded Physics](https://mlsanity.com/paper/2510.06020/) (2025)

## Abstract (arXiv)

Phase retrieval in broadband coherent anti-Stokes Raman spectroscopy (BCARS) is an ill-posed inverse problem. The Raman-like signal is encoded in the imaginary part of the resonant susceptibility, which mixes coherently with a non-resonant background (NRB) that varies across acquisitions. We introduce an inverse physics-informed neural network (iPINN) that predicts Lorentzian peak parameters from raw BCARS spectra and reconstructs the resonant susceptibility through a differentiable analytical forward model. A transformer encoder assigns spectral features to 24 learnable peak slots, and a multi-view consistency loss enforces invariance across NRB pattern, NRB strength, and noise. Unlike direct spectral regression approaches, the method retains accuracy under varying acquisition conditions. On a public benchmark, iPINN achieves the lowest error among the tested baselines (MAE 0.016 vs. next-best 0.046). On 28 zero-shot test spectra acquired across seven solvents and four focal positions, accuracy is depth-invariant in five of seven solvents. These results show that inverse parametric prediction with a differentiable physical decoder supports robust phase retrieval across measurement conditions.