Traditional models grounded in first principles often struggle with accuracy as the system's complexity increases. Conversely, machine learning approaches, while powerful, face challenges in interpretability and in handling physical constraints. Efforts to combine these models often often stumble upon difficulties in finding a balance between accuracy and complexity. To address these issues, we propose a comprehensive framework based on a "mixture of experts" rationale. This approach enables the data-based fusion of diverse local models, leveraging the full potential of first-principle-based priors. Our solution allows independent training of experts, drawing on techniques from both machine learning and system identification, and it supports both collaborative and competitive learning paradigms. To enhance interpretability, we penalize abrupt variations in the expert's combination. Experimental results validate the effectiveness of our approach in producing an interpretable combination of models closely resembling the target phenomena.

翻译：基于第一原理的传统模型在系统复杂性增加时往往难以保证精度。而机器学习方法尽管功能强大，却在可解释性和物理约束处理方面面临挑战。将两类模型结合的尝试常因难以在精度与复杂度间取得平衡而受阻。针对这些问题，我们提出基于"专家混合"机制的综合性框架。该方法通过数据驱动方式融合多样化的局部模型，充分发挥基于第一原理的先验知识潜力。我们的方案允许专家模型独立训练，借鉴机器学习和系统辨识技术，同时支持协作与竞争两种学习范式。通过惩罚专家组合中的突变现象提升可解释性。实验结果验证了该方法在生成与目标现象高度相似的可解释模型组合方面的有效性。