用生成式超网络实现无需似然函数的不确定性量化
GenUQ: Predictive Uncertainty Estimates via Generative Hyper-Networks
- 构建生成式超网络，直接输出与观测数据一致的参数分布
- 在三个问题上优于现有方法，准确恢复制造算子和预测材料失效位置
- 适合需要高置信度预测的物理仿真与工程建模场景
算子学习是回归在函数映射上的推广，有望将复杂偏微分方程的数值积分转化为快速的函数状态映射计算，广泛应用于海冰、燃烧和大气物理建模。现有不确定性量化方法依赖基于似然的参数分布推断，但对随机算子而言，其输出可能难以构造似然函数。本文提出GenUQ，一种基于测度论的不确定性量化新方法，通过引入生成式超网络直接生成与观测数据一致的参数分布，避免了显式似然构建。在三个案例中验证：恢复一个构造算子、学习随机椭圆PDE的解算子、预测多孔钢受拉时的失效位置，结果均优于其他现有方法。
原文摘要 · Abstract (English)
Operator learning is a recently developed generalization of regression to mappings between functions. It promises to drastically reduce expensive numerical integration of PDEs to fast evaluations of mappings between functional states of a system, i.e., surrogate and reduced-order modeling. Operator learning has already found applications in several areas such as modeling sea ice, combustion, and atmospheric physics. Recent approaches towards integrating uncertainty quantification into the operator models have relied on likelihood based methods to infer parameter distributions from noisy data. However, stochastic operators may yield actions from which a likelihood is difficult or impossible to construct. In this paper, we introduce, GenUQ, a measure-theoretic approach to UQ that avoids constructing a likelihood by introducing a generative hyper-network model that produces parameter distributions consistent with observed data. We demonstrate that GenUQ outperforms other UQ methods in three example problems, recovering a manufactured operator, learning the solution operator to a stochastic elliptic PDE, and modeling the failure location of porous steel under tension.
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