[论文] From Classification to Regression: Using a Fruitfly to Solve Equations

论文概要

研究领域: ML
作者: Shady E. Ahmed, Panos Stinis
发布时间: 2026-07-29
arXiv: 2607.27196

中文摘要

本文提出一种受果蝇感知环境机制启发的新型回归方法——用分类来做回归。具体来说，我们通过用有限库的代表性局部模式替代复杂的全局代理模型，构建了一个学习非线性输入-输出关系的一般框架。由于科学数据通常占据输入空间中有限且重复的区域，我们通过度量查询与存储模式之间的相似性来生成预测，然后通过加权重构组合其关联响应。我们将该方法应用于非线性动力系统、数据驱动回归和物理信息学习，使用合适的嵌入和相似性度量。对于动力系统，我们的离线-在线工作流在离线阶段从数据或控制方程中提取模式，而在线预测仅需相似性评估和响应聚合。这种结构有助于降低计算和内存需求，同时提供对精度、存储和推理成本之间权衡的显式控制。

原文摘要

We present a novel approach to regression tasks using classification which is motivated by the mechanism used by fruitflies to sense their environment. Specifically, we formulate a general framework for learning nonlinear input-output relationships by replacing complex global surrogate models with a finite library of representative local patterns. Since scientific data often occupy limited and recurring regions of the input space, we generate predictions by measuring similarities between a query and stored patterns, then combining their associated responses through weighted reconstruction. We apply this approach to nonlinear dynamical systems, data-driven regression, and physics-informed learning using suitable embeddings and similarity measures. For dynamical systems, our offline-online w...

自动采集于 2026-07-31

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