Math: Fractional analysis

Machine-learning ideas tagged Fractional analysis in the Math taxonomy of the Math2NN corpus.

2 ideas found

Solves: Stability Math: Fractional analysis Clear all

△ Mechanism confirmed, baseline not beaten 2026

Adjoint-Weak Fractional Residuals

Replace pointwise fractional derivatives of noisy trajectories in a neural PDE or neural dynamics loss with weak projections in which the fractional operator acts on smooth test functions. The network is trained to match integral residuals over local space-time windows, making the residual insensitive to high-frequency measurement noise while retaining sensitivity to the underlying fractional dynamics.

Useful7/10

Difficulty4/10

Novelty5/10

Training Stability Accuracy Sample efficiency

Paper: Robust data-driven discovery of fractional differential equations via weak formulations and Pareto-based subset selection arXiv:2608.12879

✗ Mechanism failed 2026

Fractional Jacobian topology loss

Train a neural field to represent a sphere-valued phase or feature map with a prescribed codimension-two defect set. Add a fractional Sobolev energy to suppress high-frequency oscillations, but enforce topology through a discrete Jacobian or winding-current loss so that smoothing cannot remove holes, filaments, or vortex defects.

Useful6/10

Difficulty5/10

Novelty7/10

Geometry Accuracy Stability Generalization

Paper: Another look at a notion of fractional mass in codimension two arXiv:2607.00810