L-FNO用谱记忆建模事件自激发，提升稀疏事件预测精度。
L-FNO: Lorentzian Fourier Neural Operator for Stochastic Event Dynamics
- 融合洛伦兹谱核与傅里叶神经算子，捕捉历史事件激发效应
- 在8个合成与3个真实数据集上，事件似然与稀有事件检测均更优
- 适合医疗疫情、芯片缺陷等稀疏突发事件的建模任务
现代运行系统在常规条件下仍面临不确定性，罕见、突发且自激发的事件既源于外部协变量，也来自内部事件动态。标准神经算子通常以回归式函数到函数模型训练，而非条件强度估计器，难以适应稀疏事件场景。我们提出洛伦兹傅里叶神经算子（L-FNO），一种结合FNO风格协变量路径、洛伦兹谱核以建模历史依赖激发、以及基于似然的训练目标的随机神经算子。在八个合成点过程基准和三个真实世界数据集（涵盖疾病爆发预测及半导体故障/缺陷检测）上评估，L-FNO在事件似然、校准诊断和稀有事件检测方面均优于回归与似然基神经算子基线。结果表明，结构化的谱记忆与基于似然的学习为神经算子在随机事件动态建模中提供了有效归纳偏置。
原文摘要 · Abstract (English)
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.
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