Casimir effect with machine learning

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.

7 pages, 4 figures; minor changes, published version

References in corpus (41)

• Machine learning and the physical sciences
• Machine learning phases of matter
• Precision Measurement of the Casimir Force from 0.1 to 0.9 microns
• A high-bias, low-variance introduction to Machine Learning for physicists
• Measurement of the Casimir force between parallel metallic surfaces
• Learning phase transitions by confusion
• Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders
• Casimir forces between arbitrary compact objects
• Machine learning quantum phases of matter beyond the fermion sign problem
• Template-stripped gold surfaces with 0.4 nm rms roughness suitable for force measurements. Application to the Casimir force in the 20-100 nm range
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• Quantum Loop Topography for Machine Learning
• Machine Learning Topological Invariants with Neural Networks
• The Casimir effect within scattering theory
• Machine Learning Phases of Strongly Correlated Fermions
• Measurement of the Casimir force between a gold sphere and silicon surface with nanoscale trench arrays
• Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems
• Identifying Quantum Phase Transitions using Artificial Neural Networks on Experimental Data
• Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem
• Casimir Effect on the Worldline
• HMC algorithm with multiple time scale integration and mass preconditioning
• Constructing neural stationary states for open quantum many-body systems
• The Dirichlet Casimir Problem
• Worldline algorithms for Casimir configurations
• Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory
• Machine learning out-of-equilibrium phases of matter
• Casimir Energies in Light of Quantum Field Theory
• Optimized Verlet-like algorithms for molecular dynamics simulations
• Efficient Computation of Casimir Interactions between Arbitrary 3D Objects
• Regressive and generative neural networks for scalar field theory
• Discriminative Cooperative Networks for Detecting Phase Transitions
• Extrapolating quantum observables with machine learning: Inferring multiple phase transitions from properties of a single phase
• Casimir effect in Yang-Mills theory
• Status and Future Perspectives for Lattice Gauge Theory Calculations to the Exascale and Beyond
• Nonperturbative Casimir effect and monopoles: compact Abelian gauge theory in two spatial dimensions
• The Casimir effect and deconfinement phase transition
• Casimir effect on the lattice: U(1) gauge theory in two spatial dimensions
• Casimir energy calculations within the formalism of the noncompact lattice QED
• Fluctuation-induced interactions between dielectrics in general geometries
• Monte-Carlo calculation of the lateral Casimir forces between rectangular gratings within the formalism of lattice quantum field theory
• Image-processing the topological charge density in the CP(N-1) model

Cited by in corpus (4)

• Lattice-fermionic Casimir effect and topological insulators
• Decoding Quantum Field Theory with Machine Learning
• Effective model for pure Yang-Mills theory on ${\mathbb{T}}^2\times {\mathbb{R}}^2$ with Polyakov loops
• Casimir energy for $N$ constant conductivity $\delta$-plates with a neural network perception