Juan Diego Toscano, Sascha Ranftl, Zhiwei Gao, Li-Lian Wang, George Em Karniadakis · 2026 · arXiv
DOI: 10.48550/arXiv.2610.29909 · open-access PDF
Las sustitutas de aprendizaje automático en la ciencia computacional a menudo requieren no sólo predicciones precisas, sino también expectativas, variaciones, integrales conservados y constantes de normalización. Las redes neuronales convencionales, incluyendo las redes de Kolmogorov-Arnold (KANs), generalmente evalúan estas cantidades a través de la muestra de Monte Carlo o la cuadratura multidimensional, haciendo que la inferencia repetida sea costosa, particularmente en dimensiones altas.
Machine translation (Meta M2M100); the English original follows.
Machine-learning surrogates in computational science often require not only accurate predictions but also expectations, variances, conserved integrals, and normalization constants. Conventional neural networks, including Kolmogorov--Arnold networks (KANs), generally evaluate these quantities through Monte Carlo sampling or multidimensional quadrature, making repeated inference costly, particularly in high dimensions. We introduce KANs with Tractable Operators for Uncertainty and Constraints (TOUCKANs), whose finite-degree polynomial outer functions yield a decomposable sum--product representat
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