用强化学习自动发现数学方程,提升科学建模效率。
Deep Symbolic Optimization: Reinforcement Learning for Symbolic Mathematics
- 将方程发现转化为序列决策问题,结合神经网络与强化学习
- 在基准测试中达到当前最优的准确率与可解释性
- 适合需要自动化建模的科研人员,尤其擅长复杂符号结构搜索
深度符号优化(Deep Symbolic Optimization, DSO)是一种新型计算框架,用于科学发现中的符号优化,尤其适用于寻找复杂符号结构的任务。典型应用如方程发现,旨在自动推导以符号形式表达的数学模型。在DSO中,发现过程被建模为序列决策任务:生成式神经网络学习候选符号表达式的概率分布,强化学习策略引导搜索向最有希望的区域推进。该方法融合梯度优化、进化与局部搜索技术,引入即时约束、领域先验和先进策略优化方法,构建出一个能高效探索广阔搜索空间的稳健框架,从而识别出可解释且物理意义明确的模型。在基准问题上的广泛评估表明,DSO在准确率与可解释性方面均达到当前最优水平。本章全面概述了DSO框架,并展示其在自动化科学发现中符号优化的变革潜力。
原文摘要 · Abstract (English)
Deep Symbolic Optimization (DSO) is a novel computational framework that enables symbolic optimization for scientific discovery, particularly in applications involving the search for intricate symbolic structures. One notable example is equation discovery, which aims to automatically derive mathematical models expressed in symbolic form. In DSO, the discovery process is formulated as a sequential decision-making task. A generative neural network learns a probabilistic model over a vast space of candidate symbolic expressions, while reinforcement learning strategies guide the search toward the most promising regions. This approach integrates gradient-based optimization with evolutionary and local search techniques, and it incorporates in-situ constraints, domain-specific priors, and advanced policy optimization methods. The result is a robust framework capable of efficiently exploring extensive search spaces to identify interpretable and physically meaningful models. Extensive evaluations on benchmark problems have demonstrated that DSO achieves state-of-the-art performance in both accuracy and interpretability. In this chapter, we provide a comprehensive overview of the DSO framework and illustrate its transformative potential for automating symbolic optimization in scientific discovery.
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