Inferring nonlinear parabolic field equations from modulus data

TL;DR

This paper introduces a method to determine the evolution equations of complex scalar fields from modulus data across multiple planes, enabling the inference of nonlinear parabolic PDEs in various physical systems.

Contribution

It presents a novel formalism for inferring nonlinear parabolic equations from modulus measurements, applicable to diverse (2+1)-D systems including those with symmetry breaking.

Findings

Successfully recovered nonlinear interactions from simulated data.

Demonstrated broad applicability to systems like nonlinear optics and quantum fluids.

Validated the method on systems exhibiting spontaneous symmetry breaking.

Abstract

We give a means for measuring the equation of evolution of a complex scalar field that is known to obey an otherwise unspecified (2+1)-dimensional dissipative nonlinear parabolic differential equation, given field moduli over three closely-spaced planes. The formalism is tested by recovering nonlinear interactions and the associated equation of motion from simulated data for a range of (2+1)-dimensional nonlinear systems, including those which exhibit spontaneous symmetry breaking. The technique is of broad applicability, being able to infer a wide class of partial differential equations, which govern systems ranging from nonlinear optics to quantum fluids.