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Geometric mappings can dramatically improve PINN training, boosting accuracy and stability by aligning input coordinates with the underlying physics of PDEs.
Neural operators get a 30-50% accuracy boost in long-term PDE prediction with a simple, geometrically-principled "plug-in" that barely increases parameter count.
Topological data analysis reveals that structurally stable and compact soft prompts lead to better downstream performance, enabling a new loss function (TSLoss) that improves convergence and tuning performance.
