Lattice fermion formulation via Physics-Informed Neural Networks: Ginsparg-Wilson relation and Overlap fermions
TLDR
This paper introduces a PINN-based framework to construct lattice fermions, accurately reproducing overlap operators and discovering new Ginsparg-Wilson relations.
Key contributions
- Proposes a PINN framework for lattice fermion construction, optimizing Dirac operators based on physical constraints.
- Reproduces overlap fermion operators and learns effective sign-functions by satisfying the Ginsparg-Wilson relation.
- Discovers the standard Ginsparg-Wilson relation autonomously within a generalized polynomial ansatz.
- Finds a distinct Fujikawa-type generalized Ginsparg-Wilson relation by adjusting the initial search bias.
Why it matters
This work offers a novel, data-driven approach to a fundamental problem in lattice field theory, potentially accelerating the discovery of new fermion formulations. It demonstrates the power of PINNs in complex physics problems, moving beyond traditional approximations.
Original Abstract
We propose a novel, machine-learning-based framework for constructing lattice fermions using Physics-Informed Neural Networks (PINNs). Our approach treats the formulation of the Dirac operator as an optimization problem guided by physical requirements, such as symmetries, locality and doubler-decoupling conditions. We first demonstrate that, when trained to satisfy the Ginsparg-Wilson (GW) relation as a soft constraint, a neural network reproduces the overlap fermion operator to high numerical accuracy and learns an effective sign-function mapping without explicitly using a prescribed polynomial or rational approximation. Secondly, we extend the framework from operator construction to machine-assisted algebraic discovery. Within a generalized polynomial ansatz, the network autonomously drives higher-order terms to zero and recovers the standard Ginsparg-Wilson relation. Remarkably, by changing the initial search bias, the same framework also finds a distinct solution corresponding to a Fujikawa-type generalized GW relation.
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