PIEFS: Physics-Informed Eigenfunction Features with Learnable Scaling
Spectral methods are widely used to construct representations from the geometry of data, but they often rely on a fixed kernel, graph Laplacian, or manually selected feature scaling. We propose Physics-Informed Eigenfunction Features with Learnable Scaling (PIEFS), a supervised neural representation-learning framework with a spectral inductive bias, based on a modified Dirichlet energy. In PIEFS, scalar coordinate maps are trained under empirical Gram orthogonality, a supervised linear readout, and a Dirichlet penalty in which the input gradient is transformed by a learnable metric $A(x)=Λ(x)U(x)$. The diagonal factor $Λ(x)$ controls anisotropic scaling, while the orthogonal factor $U(x)$...
| Authors | Varvara Nazarenko, Timur Lidzhiev, Alexander Tarakanov |
|---|---|
| Primary category | cs.LG |
| Published | 4 July 2026 |
| Last updated at source | 7 July 2026 |
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