Ellipsoidal Positivity Sets for Fractional Obstacle Problems with Quadratic Forcing

What the math gives to ML

The paper gives an exact anisotropic compact-support profile for a fractional obstacle problem: a positive-definite quadratic form clipped at zero and raised to the power 1+s. The transferable asset is the ellipsoidal support together with a smooth, learnable radial decay profile, not the PDE solver itself. This can become a sparse attention or graph-neural-network kernel with learned orientation and scale, allowing the model to select a bounded anisotropic neighborhood instead of attending to every token. The main falsifiable benefit is lower attention cost at comparable accuracy, especially for data with directional or non-axis-aligned locality.