用实验设计提升数据质量，自动发现系统中缺失的物理规律
Experimental Design for Missing Physics
- 通过符号回归与神经网络结合，从数据中挖掘缺失模型结构
- 提出顺序实验设计方法，最优区分多个可能模型
- 在生物反应器案例中成功识别出未知动力学规律
大多数过程系统中，模型结构知识不完整，需从实验数据中学习缺失的物理规律。近年来，通用微分方程与符号回归的结合成为发现缺失物理规律的流行工具：通用微分方程用神经网络表示模型中缺失部分，符号回归则使这些神经网络可解释。这类机器学习方法依赖高质量数据才能准确恢复真实模型结构。为此，本文提出一种基于最优区分符号回归生成的多个合理模型结构的顺序实验设计方法，以获取信息量最大的数据。该方法被应用于生物反应器中缺失物理规律的发现任务，显著提升了模型识别精度。
原文摘要 · Abstract (English)
For most process systems, knowledge of the model structure is incomplete. This missing physics must then be learned from experimental data. Recently, a combination of universal differential equations and symbolic regression has become a popular tool to discover these missing physics. Universal differential equations employ neural networks to represent missing parts of the model structure, and symbolic regression aims to make these neural networks interpretable. These machine learning techniques require high-quality data to successfully recover the true model structure. To gather such informative data, a sequential experimental design technique is developed which is based on optimally discriminating between the plausible model structures suggested by symbolic regression. This technique is then applied to discovering the missing physics of a bioreactor.
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