发表机构
Universidad Politecnica de Madrid（马德里理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出神经进化符号回归方法，以共享符号主干实现耦合多输出系统的物理一致性，在弱可识别共享因子场景下优于独立方法，是结构化共享机制提取器。
AI 中文摘要
符号回归可生成解析表达式，但通常一次仅适用于一个输出，这在过程系统中存在局限——状态变量常通过共享物理参数耦合。独立符号回归虽能给出准确的单个方程，但难以将其解释为统一模型。本文提出一种用于耦合多输出系统的神经进化符号回归方法，该方法搜索共享符号主干：一组潜在符号单元，经一次发现后，通过稀疏加性或乘性读出被多个输出复用。离散模型结构通过变异与交叉进化，连续参数则通过梯度下降调整并遗传给后代。该方法在含已知真值的基准集和水热液化产率案例中进行评估，结果显示耦合并非降低预测误差的通用途径。其主要贡献在于，当潜在表达式中嵌入物理共享因子且该因子从数据中弱可识别时，可实现并诊断跨输出一致性，这种情况发生在Langmuir-Hinshelwood和位点覆盖率分母中，独立PySR方法无法缩小一致性差距或恢复相同的共享形式；反之，当每个输出已可识别时，如Van de Vusse基准，独立符号回归与耦合模型表现相当或更优。所提框架并非通用预测器，而是结构化共享机制提取器，其价值在目标结构稀疏、共享、弱可识别或受闭合约束时最为显著。
英文摘要
Symbolic regression provides analytical expressions, but it is usually applied one output at a time. This is limiting in process systems, where state variables are often coupled through shared physical parameters. Independent symbolic regression can give accurate individual equations that are difficult to interpret as one model. We present a neuro-evolutionary symbolic regression method for coupled multi-output systems. The method searches for a shared symbolic backbone: a set of latent symbolic units that is discovered once and reused by several outputs through sparse additive or multiplicative read-outs. The discrete model structure is evolved by mutation and crossover, whereas the continuous parameters are tuned by gradient descent and inherited by the offspring. The method is assessed on a set of benchmarks with known ground truth and on a hydrothermal liquefaction yield case. The results show that coupling is not a general route to lower prediction error. Its main contribution is the enforcement and diagnosis of cross-output consistency when a physically shared factor is embedded in a latent expression and is weakly identifiable from the data. This occurs for Langmuir-Hinshelwood and site-coverage denominators, for which independent PySR does not close the consistency gap or recover the same shared form. Conversely, when each output is already identifiable, as in the Van de Vusse benchmark, independent symbolic regression matches or improves the coupled model. The proposed framework, rather than a general purpose predictor, is a structured shared-mechanism extractor. Its value is highest when the target structure is sparse, shared, weakly identifiable or constrained by closure.
Comments20 pages, 1 figure
