Unsupervised spectra information extraction using physics-informed neural networks in the presence of non-linearities and multi-agent problems.

Spectroscopy covers a huge range of applications in various fields of science, such as physics, biology, chemistry, engineering, and medicine. In some spectroscopic applications, the data analysis of spectra plays a leading role in the determination of the technique's performance in terms of sensitivity, specificity, and reliability. For this reason, solutions based on machine and deep learning algorithms have been deeply explored as possible alternatives to standard methodologies. Recently, an innovative neural network architecture and training approach have been developed to solve problems where standard supervised deep learning algorithms cannot be used, by exploiting a physics-informed neural network. This new method allows for information extraction from spectra without a supervised approach, i.e. without the need to have controlled experiments where both the spectra and the desired pieces of information to be extracted are known, opening the possibility to solve a huge number of problems where a controlled set (what it is known as training set in machine and deep learning) is present. However, in the previous work, the method has been presented only for simple and linear cases, limiting the range of applications of this new method. In this work, the previous physics-informed deep learning methodology is generalised to tackle both non-linear and multi-agent cases. The methodology, once it has been formally introduced, will be tested on synthetic cases and compared with standard supervised algorithms.