Casimir effect with machine learning

TL;DR

This paper introduces a machine learning approach to efficiently estimate Casimir energies for objects of arbitrary shapes, overcoming analytical challenges in quantum field theory calculations.

Contribution

The authors develop a neural network-based method to predict Casimir energies from boundary shapes, demonstrating its effectiveness in a (2+1)D scalar field model.

Findings

Neural network accurately predicts Casimir energy for new shapes.

Method significantly reduces computational time compared to traditional techniques.

Effective for arbitrary boundary geometries in scalar field theory.

Abstract

Vacuum fluctuations of quantum fields between physical objects depend on the shapes, positions, and internal composition of the latter. For objects of arbitrary shapes, even made from idealized materials, the calculation of the associated zero-point (Casimir) energy is an analytically intractable challenge. We propose a new numerical approach to this problem based on machine-learning techniques and illustrate the effectiveness of the method in a (2+1) dimensional scalar field theory. The Casimir energy is first calculated numerically using a Monte-Carlo algorithm for a set of the Dirichlet boundaries of various shapes. Then, a neural network is trained to compute this energy given the Dirichlet domain, treating the latter as black-and-white pixelated images. We show that after the learning phase, the neural network is able to quickly predict the Casimir energy for new boundaries of general shapes with reasonable accuracy.