L-FNO：用于随机事件动力学的洛伦兹傅里叶神经算子
L-FNO: Lorentzian Fourier Neural Operator for Stochastic Event Dynamics
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中文总结 AI 辅助
该研究针对稀疏事件场景下标准神经算子的适用性局限，提出L-FNO随机神经算子，经8个合成基准和3个真实世界数据集验证，其在事件似然等指标上优于基线模型，为随机事件动力学建模提供有效方法
中文摘要 AI 辅助
现代运行系统即便在常规条件下也面临不确定性，其中罕见、爆发性且自激的事件同时源于外生协变量和内生事件动力学。标准神经算子通常被训练为回归式的函数到函数模型，而非条件强度估计器，这限制了它们在稀疏事件场景中的适用性。我们提出洛伦兹傅里叶神经算子（L-FNO），一种随机神经算子，它结合了FNO风格的协变量路径、用于依赖历史的激发的洛伦兹谱核以及基于似然的训练目标。我们在8个合成点过程基准和3个真实世界数据集（涵盖疾病暴发预测、半导体故障或缺陷检测）上评估了L-FNO。与基于回归和基于似然的神经算子基线相比，L-FNO在事件似然、校准诊断和罕见事件检测方面均有所提升。这些结果表明，结构化谱记忆和基于似然的学习为随机事件动力学的神经算子模型提供了有效的归纳偏置。
英文摘要
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.
发表机构
- Tech University of Korea（韩国技术大学）
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