Scattering with Neural Operators
This work addresses computational challenges in fundamental physics, specifically for quantum mechanics simulations, though it is incremental as it applies existing neural operator methods to new physics problems.
The paper tackles the problem of simulating quantum scattering processes by using neural operators to approximate maps between function spaces, achieving orders of magnitude efficiency gains over traditional solvers in inference.
Recent advances in machine learning establish the ability of certain neural-network architectures called neural operators to approximate maps between function spaces. Motivated by a prospect of employing them in fundamental physics, we examine applications to scattering processes in quantum mechanics. We use an iterated variant of Fourier neural operators to learn the physics of Schrödinger operators, which map from the space of initial wave functions and potentials to the final wave functions. These deep operator learning ideas are put to test in two concrete problems: a neural operator predicting the time evolution of a wave packet scattering off a central potential in $1+1$ dimensions, and the double-slit experiment in $2+1$ dimensions. At inference, neural operators can become orders of magnitude more efficient compared to traditional finite-difference solvers.