Manifold-Informed Neural Networks for Low-Label ECG Electrolyte Inference

Juntang Wang, Hao Wu, Yihan Wang, Dongmian Zou, Shixin Xu

Physics-informed neural networks (PINNs) supervise on the residual of a known differential operator. Many high-stakes inference problems admit no such operator: clinical signals, behavioral measurements, materials properties. We introduce the Manifold-Informed Neural Network (MINN), a PINN-parallel paradigm that replaces the physics operator residual with a manifold operator residual: a discrete Poisson equation $\mathbf{L}_G \mathbf{H} = s_φ(\mathbf{x}, \mathbf{m})$ on a $k$-nearest-neighbor graph in the learned latent space, with a learned, task-aware source. The construction is a structural parallel to PINNs (squared operator residual plus label data, in place of operator residual plus boundary data); the $s{=}0$ limit recovers the homogeneous Laplace equation $\mathbf{L}_G\mathbf{H}=\mathbf{0}$ (classical manifold regularization solves the same equation but minimizes the Dirichlet energy $\operatorname{tr}(\mathbf{H}^\top\mathbf{L}_G\mathbf{H})$, a different penalty form). The source $s_φ$ takes input features and auxiliary metadata directly, breaking the homogeneous smoothness prior that limits classical Laplacian penalties; gated Feature-wise Linear Modulation separately…