TLDR: A new framework combines classical process modeling with data-driven AI, using network theory and Neural Ordinary Differential Equations (Neural ODEs). It embeds fundamental conservation laws and system topology into sparse neural networks, allowing for explainable models that learn dynamic relationships from data. This approach enables distributed control and optimization by reshaping a system’s natural objective function, demonstrated through an inventory control example.
In the evolving landscape of process control, a significant challenge lies in seamlessly integrating modern data-driven machine learning techniques with established classical process models. Traditional approaches often struggle with limited data availability for specific systems and the difficulty of transferring insights between similar but distinct processes. Furthermore, deep learning models, while powerful, frequently lack explainability, making it hard to understand how their parameters relate to fundamental physical laws.
A new research paper proposes an innovative process modeling framework that addresses these critical issues. This framework enables the natural integration of data-driven algorithms by ensuring consistent topological properties and the conservation of extensive quantities, such as mass and energy, within the system. It leverages network theory, representing interconnections among process units through connectivity matrices and network graphs.
Understanding the System’s Natural Drive
The core of this approach involves deriving a system’s natural objective function, which is shown to be equivalent to the non-equilibrium entropy production in a steady-state system. This entropy production acts as a fundamental driving force for the process dynamics. Essentially, a process network naturally minimizes its own entropy production, following what can be described as the “path of least thermodynamic resistance.” This inherent self-optimizing property is crucial for understanding how these systems behave.
The paper illustrates how distributed control and optimization can be effectively implemented within these process network structures. By applying specific control laws and algorithms, the system’s natural equilibrium can be altered and guided towards desired engineered objectives. This concept introduces a form of self-optimizing control, where the addition of a control loop effectively reshapes the system’s optimization goal.
Integrating AI with Fundamental Laws
A key innovation is the integration of fundamental conservation properties, derived from the system’s topology, with learned dynamic relationships obtained from data. This is achieved through the use of sparse deep neural networks, particularly Neural Ordinary Differential Equations (Neural ODEs). Unlike traditional fully connected neural networks, this approach allows the process system’s inherent topology to be embedded directly into the neural network’s structure. This means that connections between nodes in the neural network correspond to physical connections in the process, with zero weights where no physical connection exists.
This sparse architecture offers significant advantages. It not only reduces computational effort during training but also preserves the process topology, leading to more explainable parameters. The functional values within the neural network represent meaningful physical variables, such as potentials in the input layer, flows in the hidden layer, and updates in the output layer. Activation functions at the nodes can be tailored to represent constitutive equations, which describe the relationships between efforts and flows within the system.
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Practical Demonstration and Future Potential
The researchers demonstrate their framework using a practical example: a simple inventory control system. In this scenario, the basic topology of the process is integrated with a neural ordinary differential equation model. The system-specific constitutive equations, which typically describe how the system components behave, are not pre-defined but are instead learned by the neural ODE algorithm from synthetic time-series data. This learning process utilizes the adjoint method in combination with an adaptive ODE solver.
The resulting neural network forms a robust state-space model that can be used in advanced control algorithms, such as model predictive control. This approach offers a thermodynamically consistent basis for applying artificial neural network models in chemical engineering applications. The ability to incorporate the system’s topology and fundamental laws into the neural network structure means that weight parameters become explainable and can be intuitively updated as new data becomes available or if the underlying process structure changes.
This work represents a significant step towards bridging the gap between classical process control and modern data-driven AI, offering a path to more robust, explainable, and adaptable control systems for complex industrial processes. For more details, you can read the full research paper here.
