Sound field reconstruction from sparse microphone measurements is a highly ill-posed inverse problem, particularly at high frequencies and under sub-Nyquist spatial sampling. We propose the Physics-Informed Neural Equivalent Source Method (PINES), representing an equivalent-source density as a coordinate-based neural function over a prescribed source manifold. A multilayer perceptron maps virtual-source coordinates to samples of a complex-valued equivalent-source density, which are then propagated to microphone and reconstruction locations using precomputed Green's-function transfer matrices. Since the acoustic field is synthesized through Green's-function superposition, the reconstructed field satisfies the homogeneous Helmholtz equation by construction. Consequently, PINES is trained solely with a normalized microphone pressure data loss. In simulated reverberant room scenarios, PINES achieves competitive reconstruction accuracy with a 7.1--8.0$\times$ runtime speedup over the conventional Physics-Informed Neural Network baseline.