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arXiv 2204.02488cs.LGnlin.CDphysics.data-anstat.ML
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通过神经运算符中的主动学习发现和预测极端事件

Discovering and forecasting extreme events via active learning in neural operators

Massachusetts Institute of Technology(麻省理工学院);Brown University(布朗大学)

Ethan Pickering, Stephen Guth, George Em Karniadakis, Themistoklis P. Sapsis

摘要:

社会和自然界中的极端事件,如流行病高峰,流氓波或结构故障,可能会产生灾难性的后果。描述极端情况是困难的,因为它们很少发生,从看似良性的条件下产生,属于复杂的,往往是未知的无限维系统。这些挑战使得将其定性为无实际意义的尝试成为可能。我们通过将贝叶斯实验设计(BED)中的新型训练方案与深度神经运算符(DNO)集成相结合来解决这些困难。这个模型不可知的框架对BED计划,积极选择数据量化极端事件与DNO的合奏,近似无限维非线性算子。我们发现,这个框架不仅明显优于高斯过程(GP),而且1)只有两个成员的浅集合表现最好; 2)无论初始数据的状态如何,极端都被发现(即有或没有极端); 3)我们的方法消除了“双下降”现象; 4)与逐步全局最优相比,使用批量次优采集点不会妨碍BED性能;以及5)蒙特卡洛采集在高维中优于标准优化器。这些结论共同构成了人工智能辅助实验基础设施的基础,该基础设施可以有效地推断和确定从物理到社会系统的许多领域的关键情况。

英文摘要:

Extreme events in society and nature, such as pandemic spikes, rogue waves, or structural failures, can have catastrophic consequences. Characterizing extremes is difficult as they occur rarely, arise from seemingly benign conditions, and belong to complex and often unknown infinite-dimensional systems. Such challenges render attempts at characterizing them as moot. We address each of these difficulties by combining novel training schemes in Bayesian experimental design (BED) with an ensemble of deep neural operators (DNOs). This model-agnostic framework pairs a BED scheme that actively selects data for quantifying extreme events with an ensemble of DNOs that approximate infinite-dimensional nonlinear operators. We find that not only does this framework clearly beat Gaussian processes (GPs) but that 1) shallow ensembles of just two members perform best; 2) extremes are uncovered regardless of the state of initial data (i.e. with or without extremes); 3) our method eliminates "double-descent" phenomena; 4) the use of batches of suboptimal acquisition points compared to step-by-step global optima does not hinder BED performance; and 5) Monte Carlo acquisition outperforms standard optimizers in high-dimensions. Together these conclusions form the foundation of an AI-assisted experimental infrastructure that can efficiently infer and pinpoint critical situations across many domains, from physical to societal systems.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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