Neural Integral Operators for Inverse problems in Spectroscopy (2505.03677v2)

Abstract: Deep learning has shown high performance on spectroscopic inverse problems when sufficient data is available. However, it is often the case that data in spectroscopy is scarce, and this usually causes severe overfitting problems with deep learning methods. Traditional machine learning methods are viable when datasets are smaller, but the accuracy and applicability of these methods is generally more limited. We introduce a deep learning method for classification of molecular spectra based on learning integral operators via integral equations of the first kind, which results in an algorithm that is less affected by overfitting issues on small datasets, compared to other deep learning models. The problem formulation of the deep learning approach is based on inverse problems, which have traditionally found important applications in spectroscopy. We perform experiments on real world data to showcase our algorithm. It is seen that the model outperforms traditional machine learning approaches such as decision tree and support vector machine, and for small datasets it outperforms other deep learning models. Therefore, our methodology leverages the power of deep learning, still maintaining the performance when the available data is very limited, which is one of the main issues that deep learning faces in spectroscopy, where datasets are often times of small size.

Neural Integral Operators for Inverse Problems in Spectroscopy

The paper "Neural Integral Operators for Inverse Problems in Spectroscopy" presents a sophisticated approach to addressing inverse problems in spectroscopy utilizing deep learning architectures. The framework proposed by the authors leverages neural integral operators, specifically designed to curtail overfitting issues prevalent when working with sparse spectral datasets in spectroscopy. This paper contributes a profound exploration of learning integral operators from a novel perspective, positioning integral equations of the first kind at the heart of solving these enduring problems.

Overview and Key Contributions

Inverse problems are paramount in many scientific domains, with operators like integral equations playing a crucial role in their resolution. In spectroscopy, these issues manifest prominently in tasks such as structural determination and sample analysis based on spectral data. Traditional methods often stumble when datasets are limited, leading to constrained accuracy and applicability. The authors address these limitations by introducing a deep learning-based methodology framing inverse problems via learned integral operators. They focus primarily on the kernel functions of integral equations, which are parameterized through neural networks, thus enabling the learning process within the domains applicable to spectroscopy.

The authors employ a deep neural network setup comprising a convolutional layer architecture and feed-forward networks, carefully optimized using contemporary gradient descent algorithms. The neural integral operator developed during training inherently absorbs the characteristics of small datasets, sustaining performance through intricate Monte Carlo integration strategies. This approach serves not only to mitigate overfitting but effectively enhances system stability, aligning robustly against established machine learning techniques such as support vector machines (SVMs) and decision trees (DTs).

Experimental Insights

Experiments were conducted across multiple spectroscopic datasets, varying in complexity and size. The datasets include IR spectra from fruit purees, meat samples, and textiles, all having been preprocessed through Fourier transform normalization techniques. The results indicate that the neural integral operator framework maintains superior performance, notably on datasets where traditional deep learning models (such as CNNs and FFNNs) exhibit substantial accuracy degradation due to overfitting. The neural integral operator paradigm consistently reported high accuracies, outperforming conventional machine learning methods. Particularly with smaller datasets, the integral operator model demonstrated significant robustness, achieving accuracy levels above those of other models in similar conditions.

Implications and Future Directions

The implications of this research are profound, both from practical perspectives in spectroscopy and theoretical advancements in deep learning frameworks. By validating the efficacy of integral equations of the first kind through neural operators, this research advances an alternative methodology that potentially reorganizes how inverse problems can be structured and solved within spectroscopy. The robustness exhibited across varied datasets suggests potential application in other domains where inverse problems are paramount, such as medical imaging and material science.

Moving forward, the exploration of neural integral operators, especially in synergizing computational cost and efficiency during training and evaluation, bears notable potential. As machine learning continues to intertwine with physical sciences, further research may explore dynamic adaptation strategies or hybrid models incorporating direct multivariate analyses. As more datasets become available, the extension of this framework to accommodate larger, more complex spectral challenges remains an intriguing prospect, broadening the scope of deep learning applications in scientific data analysis.

Overall, "Neural Integral Operators for Inverse Problems in Spectroscopy" provides a compelling contribution to the field, enriching the toolkit available to researchers faced with the challenges embedded in spectroscopic analysis and beyond.