# Integral Transforms in a Physics-Informed (Quantum) Neural Network setting: Applications & Use-Cases

arXiv: https://arxiv.org/abs/2206.14184 · HTML: https://mlsanity.com/paper/2206.14184/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 37 references that are in the map.
- First posted on arXiv 28 Jun 2022.

## Builds on (most cited first, 2 of 2)

- [Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series](https://mlsanity.com/paper/2108.03190/) (2021)
- [Quantum Model-Discovery](https://mlsanity.com/paper/2111.06376/) (2021)

## Built on by (most cited first, 1 of 1)

- [Physics informed Neural Networks applied to the description of wave-particle resonance in kinetic simulations of fusion plasmas](https://mlsanity.com/paper/2308.12312/) (2023)

## Abstract (arXiv)

In many computational problems in engineering and science, function or model differentiation is essential, but also integration is needed. An important class of computational problems include so-called integro-differential equations which include both integrals and derivatives of a function. In another example, stochastic differential equations can be written in terms of a partial differential equation of a probability density function of the stochastic variable. To learn characteristics of the stochastic variable based on the density function, specific integral transforms, namely moments, of the density function need to be calculated. Recently, the machine learning paradigm of Physics-Informed Neural Networks emerged with increasing popularity as a method to solve differential equations by leveraging automatic differentiation. In this work, we propose to augment the paradigm of Physics-Informed Neural Networks with automatic integration in order to compute complex integral transforms on trained solutions, and to solve integro-differential equations where integrals are computed on-the-fly during training. Furthermore, we showcase the techniques in various application settings, numerically simulating quantum computer-based neural networks as well as classical neural networks.