Machine Collective Intelligence for Explainable Scientific Discovery

2026-04-29

AI Summary

Automatically discovering interpretable and extrapolatable scientific governing equations from empirical data remains a central challenge in AI for Science. This work proposes a novel machine collective intelligence paradigm that, for the first time, unifies symbolic reasoning and metaheuristic approaches within a multi-agent collaborative framework. By enabling multiple reasoning agents to jointly generate, evaluate, critique, and integrate symbolic hypotheses, the method achieves autonomous equation discovery without relying on human-provided priors. Integrating multi-agent symbolic reasoning, co-evolution, and symbolic regression, the approach successfully recovers true governing equations across deterministic, stochastic, and unknown dynamical systems. It achieves up to six orders of magnitude lower extrapolation error compared to deep neural networks while compressing models to only 5–40 interpretable variables.

Abstract

Deriving governing equations from empirical observations is a longstanding challenge in science. Although artificial intelligence (AI) has demonstrated substantial capabilities in function approximation, the discovery of explainable and extrapolatable equations remains a fundamental limitation of modern AI, posing a central bottleneck for AI-driven scientific discovery. Here, we present machine collective intelligence, a unified paradigm that integrates two fundamental yet distinct traditions in computational intelligence--symbolism and metaheuristics--to enable autonomous and evolutionary discovery of governing equations. It orchestrates multiple reasoning agents to evolve their symbolic hypotheses through coordinated generation, evaluation, critique, and consolidation, enabling scientific discovery beyond single-agent inference. Across scientific systems governed by deterministic, stochastic, or previously uncharacterized dynamics, machine collective intelligence autonomously recovered the underlying governing equations without relying on hand-crafted domain knowledge. Furthermore, the resulting equations reduced extrapolation error by up to six orders of magnitude relative to deep neural networks, while condensing 0.5-1 million model parameters into just 5-40 interpretable parameters. This study marks an important shift in AI toward the autonomous discovery of principled scientific equations.

Problem

• scientific discovery
• governing equations
• explainable AI
• extrapolation
• symbolic reasoning

Innovation

• machine collective intelligence
• symbolic regression
• explainable AI
• scientific discovery
• metaheuristics