Casimir effect with machine learning
This work addresses a computational bottleneck in quantum field theory for physicists, offering a novel method but is incremental as it builds on existing numerical techniques.
The authors tackled the analytically intractable problem of calculating Casimir energy for arbitrary shapes by proposing a machine-learning-based numerical approach, demonstrating that a trained neural network can quickly predict the energy for new boundaries with reasonable accuracy in a (2+1) dimensional scalar field theory.
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.