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An inversion problem for optical spectrum data via physics-guided machine learning

Hwiwoo Park, Jun H. Park, Jungseek Hwang

TL;DR

The paper tackles the ill-posed problem of extracting the pairing glue spectrum $I^2\chi(\Omega,T)$ from optical spectra using the generalized kernel, framing it as a Fredholm integral of the first kind. It introduces the regularized recurrent inference machine (rRIM), a physics-guided solver that embeds the forward model into both training and inference via a learned update based on the preconditioned Landweber gradient, effectively performing an iterative Tikhonov regularization. Across synthetic data experiments, the rRIM requires far less training data than fully data-driven baselines and demonstrates superior noise robustness and out-of-distribution generalization, with reconstructions of Bi-2212 spectra comparable to MEM. The work provides a practical, interpretable approach for challenging inverse problems in spectroscopy and suggests a path toward broader applications of physics-guided iterative solvers.

Abstract

We propose the regularized recurrent inference machine (rRIM), a novel machine-learning approach to solve the challenging problem of deriving the pairing glue function from measured optical spectra. The rRIM incorporates physical principles into both training and inference and affords noise robustness, flexibility with out-of-distribution data, and reduced data requirements. It effectively obtains reliable pairing glue functions from experimental optical spectra and yields promising solutions for similar inverse problems of the Fredholm integral equation of the first kind.

An inversion problem for optical spectrum data via physics-guided machine learning

TL;DR

The paper tackles the ill-posed problem of extracting the pairing glue spectrum from optical spectra using the generalized kernel, framing it as a Fredholm integral of the first kind. It introduces the regularized recurrent inference machine (rRIM), a physics-guided solver that embeds the forward model into both training and inference via a learned update based on the preconditioned Landweber gradient, effectively performing an iterative Tikhonov regularization. Across synthetic data experiments, the rRIM requires far less training data than fully data-driven baselines and demonstrates superior noise robustness and out-of-distribution generalization, with reconstructions of Bi-2212 spectra comparable to MEM. The work provides a practical, interpretable approach for challenging inverse problems in spectroscopy and suggests a path toward broader applications of physics-guided iterative solvers.

Abstract

We propose the regularized recurrent inference machine (rRIM), a novel machine-learning approach to solve the challenging problem of deriving the pairing glue function from measured optical spectra. The rRIM incorporates physical principles into both training and inference and affords noise robustness, flexibility with out-of-distribution data, and reduced data requirements. It effectively obtains reliable pairing glue functions from experimental optical spectra and yields promising solutions for similar inverse problems of the Fredholm integral equation of the first kind.
Paper Structure (4 sections, 15 equations, 4 figures)

This paper contains 4 sections, 15 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Results and discussions
  4. Conclusions

Figures (4)

  • Figure 1: (Color online) Schematic model of rRIM. Shown in blue is only used for training. Further details concerning the update network is provided in the Supplemental Material (adopted and modified from Putzky2017).
  • Figure 2: (Color online) Comparison of average test losses for rRIM, FCN, and CNN (a) for different training set sizes $N$ and (b) for different noise levels for $N$ = 1000. (c) Inference steps of rRIM for noiseless data for a selection of initial and final predictions (dotted lines) alongside with the true values of $x$ (solid line) and (d) their corresponding $y$ values, which are scaled down by 300.
  • Figure 3: (Color online) Comparison of prediction capabilities of rRIM, FCN, and CNN; for noisy test data samples: (a), (b), and (c); for OOD data samples: (d), (e), and (f).
  • Figure 4: (Color online) (a) Inference results of rRIM (dashed) with those of MEM (dotted) for experimental data. (b) Experimentally measured data (solid) with rRIM (dashed) and MEM (dotted) reconstruction. Samples (OD60, D82, and OPT96) are differentiated using the same color code in both figures.