[Submitted on 7 May 2026]
Title:L-FNO: Lorentzian Fourier Neural Operator for Stochastic Event Dynamics
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Abstract:Modern operational systems face uncertainty even in routine conditions, where rare, bursty, and self-exciting events emerge from both exogenous covariates and endogenous event dynamics. Standard neural operators are typically trained as regression-style function-to-function models rather than conditional-intensity estimators, limiting their suitability for sparse event regimes. We introduce the Lorentzian Fourier Neural Operator (L-FNO), a stochastic neural operator that combines an FNO-style covariate path, Lorentzian spectral kernels for history-dependent excitation, and a likelihood-based training objective. We evaluate L-FNO on eight synthetic point-process benchmarks and three real-world datasets covering disease outbreak prediction and semiconductor fault or defect detection. L-FNO improves event likelihood, calibration diagnostics, and rare-event detection over regression- and likelihood-based neural operator baselines. These results show that structured spectral memory and likelihood-based learning provide effective inductive biases for neural operator models of stochastic event dynamics.
Comments: 21 pages, 5 figures (9 pages for the main text)
Subjects:
Machine Learning (cs.LG); Machine Learning (stat.ML)
Cite as: arXiv:2608.13562 [cs.LG]
(or arXiv:2608.13562v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2608.13562
arXiv-issued DOI via DataCite
Submission history
From: Songhee Kang Dr. [view email] [v1] Thu, 7 May 2026 04:46:21 UTC (1,046 KB)
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