PIEFS: Physics-Informed Eigenfunction Features with Learnable Scaling

arXiv:2607.03692v1 Announce Type: new Abstract: 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

Source: arXiv cs.LG — read the full report at the original publisher.

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