(14i) Development of Steady-State and Dynamic Mass-Energy-Thermodynamics Constrained Neural Network (MET-CNN) Models for Interconnected Systems Using Noisy Transient Data

Complex first-principles models are often needed to represent the complicated physics and chemistry associated with many chemical engineering applications. While the first-principles models can exactly satisfy mass and energy conservation, as well as specific thermodynamics constraints, their development can consume considerable time, computational resources, and require a rigorous understanding of the system physics / chemistry that be unavailable or difficult to obtain. On the contrary, data-driven models such as those generated by using artificial intelligence (AI) or other black-box modeling approaches are relatively easier to develop, simulate, and adapt online¹. Although AI-generated models are becoming increasingly popular for many chemical engineering applications, the development of such models can be challenging. Moreover, the measurement data available for training the data-driven models such as neural networks (NNs) for any chemical process may not necessarily satisfy mass / energy balances and other system physics / chemistry. If these constraints are not satisfied during inverse (training) and forward (simulation) problems, model predictions can violate conservation laws and therefore results produced from these results for optimization, control, prediction, etc. may not be meaningful. This work develops algorithms for steady-state and dynamic NN models aimed at exactly satisfying mass and energy balance equations, as well as thermodynamics constraints for interconnected systems during inverse and forward problems, even though the corresponding noisy training data violate the same.

Recent years have seen considerable effort in developing data-driven models that satisfy physics constraints, often denoted as physics-constrained² or physics-informed³ NN (PCNN / PINN) which aim to impose physics constraints by augmenting the objective function of typical NN training algorithms with additional penalty terms, that serve as soft penalty for violation of physics constraints. But in most chemical engineering applications, it is desired that certain constraints are exactly satisfied, which cannot be guaranteed by typical PINNs⁴. Moreover, most hybrid approaches focused on exactly conserving mass and/or energy of an interconnected system require rigorous understanding of each underlying process within the interconnection for formulating physics-based differential or algebraic constraints and hence become system-specific. In this work, a novel class of physics-constrained network models is proposed, namely the Mass-Energy-Thermodynamics Constrained Neural Networks (MET-CNN), that can exactly satisfy mass and energy constraints, along with desired thermodynamics constraints for interconnected systems. These constraints are posed as equality constraints in the nonlinear parameter estimation problem such as species molar/atom constraints, enthalpy balance equations, etc. thus providing sufficient flexibility to incorporate any additional physics constraints such as those stemming from addition/removal of mass and/or heat to/from the system, transformation of energy from one form to another, change of phase within the system, etc. as necessary for modeling distributed process systems. The proposed approaches can also accommodate nonlinear transformation for constraint satisfaction, even when there is no close-form equation available for the same (e.g., exactly satisfying desired constraints may require solution of an optimization problem). Efficient algorithms are developed for optimal network synthesis and parameter estimation involving the incorporation of local measurements especially while modeling distributed systems within the interconnected framework, without requiring a rigorous understanding of the underlying processes. The proposed algorithms for solving both the inverse and forward problems are tested by contaminating the steady-state and dynamic data with time-independent and time-varying bias / noise. Furthermore, it is worth mentioning that most data-driven approaches for modeling complex nonlinear dynamic systems with respect to available measurements may not provide any information about the ‘true’ data. The optimal MET-CNN models developed in this work have been shown to accurately capture the actual system truth with minimum bias, even when trained against data that are corrupted with time-invariant as well as time-varying uncertainties (noise).

Unlike steady-state, developing a fully data-driven dynamic modeling approach by exactly satisfying the mass, energy, and thermodynamics-based conservation equations can be significantly challenging, since such constraints, especially mass and energy balances during transience are difficult to satisfy in a data-driven framework due to insufficient information about the holdup of a system. In this work, efficient algorithms have been developed for estimating optimal parameters also for dynamic MET-CNN, represented by the hybrid series/parallel all-nonlinear static-dynamic neural network models (developed as part of our previous work⁵), which have been shown to perform significantly superior to many existing state-of-the-art approaches for performance measures such as the computational expense and predictive capability⁵. The proposed architectures and algorithms for MET-CNN are applied to several interconnected systems consisting of various dynamic reactive and non-reactive chemical processes involving change of phase as well as addition/removal of mass/energy to/from the system under consideration. It is observed that the outputs from the proposed MET-CNN can exactly satisfy mass, energy and thermodynamics constraints, even though the data used for training the optimal network models violate the same.

References

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