用神经网络直接预测复杂系统的统计量，速度提升百倍。
Neural Statistical Functions
- 基于预训练模型和零散数据，构建可直接推断统计量的神经函数
- 在动力系统能量、气动响应分位数等任务上表现优异，评估次数减少100倍
- 适合需要快速估计不确定性或极端值的工程仿真与决策场景
传统深度学习多针对单一样本，但在实际应用中常需多次推理以估计复杂决策任务中的统计量（如不确定性分析或极值分析），导致显著延迟。本文提出神经统计函数，一种从预训练单样本预测器和零散数据样本中学习的新模型家族，可直接在连续运行条件范围内推断统计量，无需显式采样。通过引入前缀统计量概念，将积分、分位数、最大值等多种统计函数统一为区间条件框架，并以前缀统计量与个体样本回归之间的原则性对应关系作为学习目标。该方法在复杂物理过程的关键统计量估计中表现良好，包括动力系统累积能量、气动响应分位数及碰撞过程最大应力，同时实现最高达100倍的模型评估次数降低。
原文摘要 · Abstract (English)
Classical deep learning typically operates on individual cases. Despite its success, real-world usage often requires repeated inference to estimate statistical quantities for complex decision-making tasks involving uncertainty or extreme-value analysis, resulting in substantial latency. We introduce neural statistical functions, a new family of models learned from pre-trained single-sample predictors and scattered data samples, which can directly infer statistics over continuous operating condition ranges without explicit sampling. By introducing the notion of prefix statistics, we transform and unify diverse statistical functions (e.g., integrals, quantiles, and maxima) into an interval-conditional framework, in which a principled identity between the prefix statistics and the individual-case regression serves as the learning objective. Neural statistical functions achieve strong performance in estimating essential statistics of complex physical processes, including accumulated energy in dynamical systems, quantiles of aerodynamic responses, and maximum stress in crash processes, while achieving up to a 100$\times$ reduction in model evaluations.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。