Guilhoto Leonardo Ferreira, Perdikaris Paris
Graduate Group on Applied Mathematics & Computational Science, University of Pennsylvania, Philadelphia, PA, USA.
Mechanical Engineering & Applied Mechanics, University of Pennsylvania, Philadelphia, PA, USA.
Sci Rep. 2024 Nov 25;14(1):29199. doi: 10.1038/s41598-024-79621-7.
Operator learning is a rising field of scientific computing where inputs or outputs of a machine learning model are functions defined in infinite-dimensional spaces. In this paper, we introduce Neon (Neural Epistemic Operator Networks), an architecture for generating predictions with uncertainty using a single operator network backbone, which presents orders of magnitude less trainable parameters than deep ensembles of comparable performance. We showcase the utility of this method for sequential decision-making by examining the problem of composite Bayesian Optimization (BO), where we aim to optimize a function , where is an unknown map which outputs elements of a function space, and is a known and cheap-to-compute functional. By comparing our approach to other state-of-the-art methods on toy and real world scenarios, we demonstrate that Neon achieves state-of-the-art performance while requiring orders of magnitude less trainable parameters.
算子学习是科学计算中一个新兴的领域，其中机器学习模型的输入或输出是在无限维空间中定义的函数。在本文中，我们介绍了Neon（神经认知算子网络），这是一种使用单个算子网络主干生成具有不确定性预测的架构，与具有可比性能的深度集成相比，其可训练参数数量减少了几个数量级。我们通过研究复合贝叶斯优化（BO）问题来展示这种方法在序列决策中的效用，在该问题中，我们旨在优化一个函数，其中是一个未知映射，它输出函数空间的元素，并且是一个已知且计算成本低的泛函。通过在玩具和现实世界场景中将我们的方法与其他最新方法进行比较，我们证明Neon在实现最先进性能的同时，所需的可训练参数数量减少了几个数量级。
