Tian Yuan, Zhou Wenqi, Viscione Michele, Dong Hao, Kammer David S, Fink Olga
Institute for Building Materials, ETH Zürich, Zürich, Switzerland.
China Yangtze Power Co., Ltd, Yichang, Hubei, China.
Nat Commun. 2025 Apr 26;16(1):3930. doi: 10.1038/s41467-025-59288-y.
Symbolic Regression holds great potential for uncovering underlying mathematical and physical relationships from observed data. However, the vast combinatorial space of possible expressions poses significant challenges for previous online search methods and pre-trained transformer models, which mostly do not consider the integration of domain experts' prior knowledge. To address these challenges, we propose the Symbolic Q-network, an advanced interactive framework for large-scale symbolic regression. Unlike previous transformer-based SR approaches, Symbolic Q-network leverages reinforcement learning without relying on a transformer-based decoder. Furthermore, we propose a co-design mechanism, where the Symbolic Q-network facilitates effective interaction with domain experts at any stage of the equation discovery process. Our extensive experiments demonstrate Sym-Q performs comparably to existing pretrained models across multiple benchmarks. Furthermore, our experiments on real-world cases demonstrate that the interactive co-design mechanism significantly enhances Symbolic Q-network's performance, achieving greater performance gains than standard autoregressive models.
符号回归在从观测数据中揭示潜在的数学和物理关系方面具有巨大潜力。然而，对于先前的在线搜索方法和预训练的变压器模型而言，可能表达式的巨大组合空间带来了重大挑战，这些方法大多没有考虑领域专家先验知识的整合。为应对这些挑战，我们提出了符号Q网络，这是一种用于大规模符号回归的先进交互式框架。与先前基于变压器的符号回归方法不同，符号Q网络利用强化学习，而不依赖基于变压器的解码器。此外，我们提出了一种协同设计机制，在该机制中，符号Q网络在方程发现过程的任何阶段都便于与领域专家进行有效交互。我们广泛的实验表明，在多个基准测试中，Sym-Q的表现与现有预训练模型相当。此外，我们在实际案例上的实验表明，交互式协同设计机制显著提高了符号Q网络的性能，比标准自回归模型实现了更大的性能提升。
