L-FNO Models Stochastic Events with Spectral Memory

Modern operational systems frequently encounter uncertainty, even under routine conditions, where rare, bursty, and self-exciting events can emerge from both external factors (exogenous covariates) and internal event dynamics. Traditional neural operators are typically trained as regression-style function-to-function models, which limits their effectiveness in sparse event regimes where the focus is on estimating conditional intensity rather than continuous values. To address this, researchers introduce the Lorentzian Fourier Neural Operator (L-FNO). This novel stochastic neural operator integrates several key components: an FNO-style path for processing covariates, Lorentzian spectral kernels to capture history-dependent excitation, and a likelihood-based training objective. This combination provides effective inductive biases for modeling stochastic event dynamics. L-FNO was evaluated on eight synthetic point-process benchmarks and three real-world datasets, including disease outbreak prediction and semiconductor fault detection. The results demonstrated that L-FNO significantly improved event likelihood, calibration diagnostics, and rare-event detection compared to both regression-based and likelihood-based neural operator baselines. These findings highlight the benefits of structured spectral memory and likelihood-based learning for neural operator models dealing with complex, uncertain event patterns.