From Classification to Regression: Using a Fruitfly to Solve Equations

2026-07-29

AI Summary

This work addresses the challenge in scientific regression tasks where input data are often confined to localized regions, hindering efficient modeling of nonlinear input–output relationships. Inspired by the olfactory processing mechanism of fruit flies, the authors propose a general framework that reformulates regression as classification: a finite library of local patterns is constructed offline, and predictions at query time are generated through similarity-based matching followed by weighted reconstruction. By integrating embedding techniques with physics-informed learning strategies, the method explicitly balances trade-offs among prediction accuracy, memory usage, and inference cost. Experiments on nonlinear dynamical systems, data-driven regression, and physics-informed learning demonstrate that the approach substantially reduces computational and memory overhead while maintaining high predictive accuracy.

Abstract

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 workflow extracts patterns from data or governing equations during the offline phase, while online prediction requires only similarity evaluation and response aggregation. This structure helps us reduce computational and memory demands while providing explicit control over the trade-off among accuracy, storage, and inference cost.

Problem

• regression
• nonlinear input-output relationships
• scientific data
• computational efficiency
• memory cost

Innovation

• fruitfly-inspired learning
• regression via classification
• local pattern library
• similarity-based reconstruction
• offline-online workflow