提出多任务符号回归模型，可同时预测多个相关变量并保持结果可解释。
Multi-task GINN-LP for Multi-target Symbolic Regression
- 用共享主干+任务专用输出层的多任务架构，捕捉多目标间依赖关系。
- 在能源效率和可持续农业任务中表现优于单目标方法，且保持高可解释性。
- 适合需要多输出预测且重视模型解释性的实际场景，如工业优化与环境建模。
在可解释人工智能领域，符号回归（SR）通过发现可解释的数学表达式来拟合数据，展现出巨大潜力。然而，现有方法主要在科学数据集上评估，其关系结构已知，限制了泛化能力；且多数仅支持单输出回归，难以应对现实世界中多目标输出且变量相互依赖的问题。为此，本文提出多任务符号回归神经网络 MTRGINN-LP，融合图神经网络与多任务深度学习，采用包含多个幂次项近似模块的共享主干结构，配合任务特定输出层，既建模多目标间依赖，又保持模型可解释性。在能源效率预测与可持续农业等真实多目标任务上验证，该模型在预测性能上具有竞争力，同时具备高可解释性，有效将符号回归扩展至更广泛的多输出实际应用。
原文摘要 · Abstract (English)
In the area of explainable artificial intelligence, Symbolic Regression (SR) has emerged as a promising approach by discovering interpretable mathematical expressions that fit data. However, SR faces two main challenges: most methods are evaluated on scientific datasets with well-understood relationships, limiting generalization, and SR primarily targets single-output regression, whereas many real-world problems involve multi-target outputs with interdependent variables. To address these issues, we propose multi-task regression GINN-LP (MTRGINN-LP), an interpretable neural network for multi-target symbolic regression. By integrating GINN-LP with a multi-task deep learning, the model combines a shared backbone including multiple power-term approximator blocks with task-specific output layers, capturing inter-target dependencies while preserving interpretability. We validate multi-task GINN-LP on practical multi-target applications, including energy efficiency prediction and sustainable agriculture. Experimental results demonstrate competitive predictive performance alongside high interpretability, effectively extending symbolic regression to broader real-world multi-output tasks.
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