Ambisonics encodes spatial audio using spherical harmonics — a pressure channel for what you hear, and three velocity channels for where it comes from. The standard approach to modeling room acoustics with neural networks predicts all four channels directly, then adds penalty terms to enforce physical consistency between them. The penalties are soft constraints: violated a little, enforced approximately, never exactly satisfied.
Masuyama, Germain, Wichern, Hori, and Le Roux (arXiv:2603.22589) model the velocity potential instead. A single scalar function of space and time, from which all four ambisonics channels are recovered through partial derivatives. The pressure is one derivative. The three velocity components are three others. The physical relationship between them — the linearized momentum equation — is satisfied exactly, because it's built into the mathematical structure of taking derivatives of the same function.
No penalty terms. No soft constraints. No hyperparameter controlling how much the physics matters relative to the data. The physics is in the architecture, not the loss function.
This is the general principle of physics-informed neural networks done right: don't penalize violations of physical laws — make violations structurally impossible. Modeling the potential rather than the field is a change of representation that converts a constraint into an identity. Any function's gradient automatically satisfies curl-free conditions. Any scalar potential's Laplacian and time derivatives automatically relate pressure to velocity. The constraint disappears because it was never needed — the representation already encodes it.
The practical benefit is that the network trains faster and produces more physically consistent outputs. But the deeper benefit is architectural honesty: the model cannot represent an unphysical sound field because unphysical fields aren't in the function space.