L-FNO: Lorentzian Fourier Neural Operator for Stochastic Event Dynamics
L-FNO is a stochastic neural operator that reframes neural operators from regression-style function-to-function models to conditional-intensity estimators for sparse event regimes It combines an FNO-style covariate path with Lorentzian spectral kernels for history-dependent excitation and a likelihood-based training objective Evaluated on eight synthetic point-process benchmarks and three real-world datasets spanning disease outbreak prediction and semiconductor fault/defect detection L-FNO outp
Analysis
TL;DR
- L-FNO is a stochastic neural operator that reframes neural operators from regression-style function-to-function models to conditional-intensity estimators for sparse event regimes
- It combines an FNO-style covariate path with Lorentzian spectral kernels for history-dependent excitation and a likelihood-based training objective
- Evaluated on eight synthetic point-process benchmarks and three real-world datasets spanning disease outbreak prediction and semiconductor fault/defect detection
- L-FNO outperforms both regression- and likelihood-based neural operator baselines on event likelihood, calibration diagnostics, and rare-event detection
- The work demonstrates that structured spectral memory and likelihood-based learning provide effective inductive biases for modeling stochastic event dynamics
Why It Matters
This work addresses a critical gap in applying neural operators to real-world scenarios involving rare, bursty, and self-exciting events—situations where standard regression-based neural operators fundamentally fall short. By rethinking neural operators as conditional-intensity estimators with proper likelihood objectives, it opens the door to more reliable deployment in high-stakes domains like healthcare and manufacturing.
Technical Details
- Architecture: L-FNO integrates an FNO-style covariate path (processing exogenous inputs) with Lorentzian spectral kernels that capture history-dependent excitation, enabling the model to represent self-exciting point-process dynamics
- Training objective: Replaces standard regression loss with a likelihood-based training objective, aligning the model with the probabilistic nature of event data rather than treating it as deterministic function approximation
- Evaluation: Tested on eight synthetic point-process benchmarks and three real-world datasets, including disease outbreak prediction and semiconductor fault/defect detection
- Key finding: Structured spectral memory combined with likelihood-based learning serves as a strong inductive bias, improving not only predictive accuracy but also calibration and rare-event detection performance
Industry Insight
- Neural operators are increasingly being adapted beyond traditional PDE-solving domains into probabilistic and event-driven applications, signaling a broader shift toward uncertainty-aware operator learning
- The likelihood-based training paradigm introduced here could become a template for adapting other deterministic neural operator architectures to stochastic settings
- For practitioners in healthcare, manufacturing, or any domain dealing with rare-event detection, L-FNO offers a principled alternative to ad-hoc thresholding approaches on regression-based models, with improved calibration reducing false alarms in critical systems
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