Optimality Principles and Neural Ordinary Differential Equations-based Process Modeling for Distributed Control
Most recent advances in machine learning and analytics for process control pose the question of how to naturally integrate new data-driven methods with classical process models and control. We propose a process modeling framework enabling integration of data-driven algorithms through consistent topological properties and conservation of extensive quantities. Interconnections among process network units are represented through connectivity matrices and network graphs. We derive the system's natural objective function equivalent to the non-equilibrium entropy production in a steady state system as a driving force for the process dynamics. We illustrate how distributed control and optimization can be implemented into process network structures and how control laws and algorithms alter the system's natural equilibrium towards engineered objectives. The basic requirement is that the flow conditions can be expressed in terms of conic sector (passivity) conditions. Our formalism allows integration of fundamental conservation properties from topology with learned dynamic relations from data through sparse deep neural networks. We demonstrate in a practical example of a simple inventory control system how to integrate the basic topology of a process with a neural network ordinary differential equation model. The system specific constitutive equations are left undescribed and learned by the neural ordinary differential equation algorithm using the adjoint method in combination with an adaptive ODE solver from synthetic time-series data. The resulting neural network forms a state space model for use in e.g. a model predictive control algorithm.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Solving differential equations using physics informed deep learning: a hand-on tutorial with benchmark tests
We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function dur…
Practical Aspects on Solving Differential Equations Using Deep Learning: A Primer
Deep learning has become a popular tool across many scientific fields, including the study of differential equations, particularly partial differential equations. This work introduces the basic principles of deep learnin…
Deep LearningGPUModelling Chemical Reaction Networks using Neural Ordinary Differential Equations
In chemical reaction network theory, ordinary differential equations are used to model the temporal change of chemical species concentration. As the functional form of these ordinary differential equations systems is der…
FormOn solving Ordinary Differential Equations using Gaussian Processes
We describe a set of Gaussian Process based approaches that can be used to solve non-linear Ordinary Differential Equations. We suggest an explicit probabilistic solver and two implicit methods, one analogous to Picard i…
Gaussian ProcessesResQ: A Novel Framework to Implement Residual Neural Networks on Analog Rydberg Atom Quantum Computers
Research in quantum machine learning has recently proliferated due to the potential of quantum computing to accelerate machine learning. An area of machine learning that has not yet been explored is neural ordinary diffe…
Quantum Machine Learning