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A Physics-Guided Machine Learning Framework Enabling Interpretable and Transferable Cascade Reactor Modeling:

Yan Li^1,2,3, Chunbo Xue^1,2,3, Yuehong Zhao^1,2,3

¹Chemistry & Chemical Engineering Data Center, Chinese Academy of Sciences, Beijing 100049, China.

Environmental Science & Technology

|June 22, 2026

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We developed a physics-guided reactor network (PG-RN) to model cascade reactors for metal recovery and wastewater treatment. This hybrid approach improves accuracy and data efficiency, outperforming traditional methods in complex separation processes.

Area of Science:

Chemical Engineering
Machine Learning
Process Systems Engineering

Background:

Cascade reactors are crucial for efficient separation and purification in metal recovery and wastewater treatment.
Simulating and optimizing cascade reactors is challenging due to model complexity and data limitations.

Purpose of the Study:

To develop a data-efficient, interpretable, and transferable modeling framework for cascade reactor systems.
To address the limitations of first-principles and purely data-driven models.

Main Methods:

Proposed a physics-guided reactor network (PG-RN) integrating residence time distribution (RTD) theory with machine learning.
Developed a physics-guided transfer learning strategy for improved model adaptability across reactor configurations.

Keywords:

cascade reactor modeling metal recovery physics-guided machine learning transfer learning

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Main Results:

PG-RN demonstrated competitive accuracy in data-rich scenarios and superior performance under data scarcity.
The framework provided interpretable RTD profiles consistent with theoretical expectations.
Achieved a 22% performance improvement on experimental data for lithium-ion battery metal recovery using transfer learning.

Conclusions:

PG-RN offers a robust and data-efficient modeling solution for complex cascade reactor systems.
The framework facilitates sustainable metal recovery and separation processes through improved characterization and optimization.
This hybrid approach enhances model transferability and reduces data requirements.