This paper presents a novel approach for parameterizing Fourier modes using artificial neural networks to compute three-dimensional magnetohydrodynamic (MHD) equilibrium, and compares it with existing computational methods. The global nonlinear force residual is minimized across the entire real-space volume using a first-order optimizer. Compared to existing codes, we achieve the same minimum residual at a competitive computational cost. Furthermore, increasing the computational cost allows the neural network to achieve a lower residual minimum, establishing a new lower bound on the force residual. Using a neural network with minimal complexity, we anticipate significant improvements not only in single-equilibrium computations but also in computing neural network models valid for continuous equilibrium distributions.
