(59o) Development of Algorithms for Mass and Energy Constrained Dynamic Neural Network Models

First-principles models can provide very good prediction even for cases when there are no or limited data or for cases where data collection is infeasible. However, constructing accurate first-principles models for complex nonlinear dynamic systems may be computationally expensive, time consuming, and intractable for online adaptation when only limited information in terms of input and output boundary conditions of the system is available. On the contrary, artificial intelligence (AI) or black-box models are relatively easier to develop, simulate, and adapt online¹. Although various types of AI modeling techniques have been widely employed for process synthesis, design and modeling², the development of such models requires large amount of data so can be infeasible where data acquisition is prohibitive or collection of certain type of data is practically impossible given the current state of the measurement technology. Moreover, the measurement data available for training the neural networks (NNs) for any chemical engineering process may not necessarily satisfy mass and energy balances and other physics of the system. If these constraints are not satisfied during machine learning and during simulation (i.e., inverse and forward problems), model predictions can violate the conservation laws and therefore may not be meaningful. This work develops algorithms for NNs where mass and energy constraints are exactly satisfied during inverse and forward problems, even though the corresponding training data violate the same.

Recent years have seen the development of a relatively new branch of supervised data-driven modeling of nonlinear systems known as physics-informed neural networks³ (PINNs) which aim to impose certain physics constraints by penalizing the objective function of typical NN training algorithms, thus ‘approximately’ satisfying such constraints during optimal network synthesis and parameter estimation. But in most chemical engineering applications, it is expected that certain mathematical relationships are exactly satisfied, which cannot be guaranteed by typical PINNs⁴. Moreover, most hybrid mechanistic approaches focused on exactly conserving mass and/or energy of a system require rigorous understanding of the process for formulating the physics-based differential or algebraic constraints and hence become system-specific⁵. In this work, a novel class of network models in proposed, namely the Mass-Energy Constrained Neural Networks (MECNNs), that exactly satisfies the mass and energy constraints using only a subset of input and output boundary conditions. The mass and energy conservation laws, expressed in terms of the species molar/atom or enthalpy balance equations are posed as equality constraints in the nonlinear parameter estimation problem, thus providing flexibility to apply this algorithm to model any generic nonlinear chemical system. Efficient training algorithms are developed for optimal synthesis of the network and estimation of parameters. The proposed algorithms for solving both the inverse and forward problems are tested by injecting noise to the simulated data for generating steady-state as well as dynamic training data for the MECNNs. Furthermore, 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 MECNNs developed in this work have been shown to accurately capture the system truth, provided the data for model training is sufficiently rich.

Unlike steady-state, developing a fully data-driven dynamic modeling approach by exactly satisfying the mass and energy balance equations can be significantly challenging, since conservation of mass/energy during transience is difficult to check in general due to insufficient information about the holdup of a system. Therefore, in addition to steady-state modeling, efficient algorithms have been developed for estimating optimal parameters also for dynamic MECNNs represented by hybrid series/parallel all-nonlinear static-dynamic neural network models (developed as part of our previous work⁶), which have been shown to perform significantly superior to many existing state-of-the-art approaches in terms of both computational expense as well as predictive capability, while modeling any generic nonlinear dynamic chemical process system⁶. The proposed structures and algorithms are applied to model two nonlinear dynamic chemical processes, namely the nonisothermal Van de Vusse reactor system and a post-combustion CO₂ capture model⁷. It is observed that the outputs from the MECNN exactly satisfy mass and energy conservation, even though the data used for training the network violates the same.

References

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