Physics Informed Piecewise Linear Neural Networks for Process Optimization

TL;DR

This paper introduces physics-informed training for piecewise linear neural networks to improve process optimization, achieving results closer to global optima with reduced computational time across multiple industrial case studies.

Contribution

It proposes a novel physics-informed training method for piecewise linear neural networks, enhancing their accuracy and efficiency in process optimization tasks.

Findings

Physics-informed neural networks yield more accurate optimal solutions.

Optimization times are significantly reduced compared to standard methods.

Results are closer to global optimality in all case studies.

Abstract

Constructing first-principles models is usually a challenging and time-consuming task due to the complexity of the real-life processes. On the other hand, data-driven modeling, and in particular neural network models often suffer from issues such as overfitting and lack of useful and highquality data. At the same time, embedding trained machine learning models directly into the optimization problems has become an effective and state-of-the-art approach for surrogate optimization, whose performance can be improved by physics-informed training. In this study, it is proposed to upgrade piece-wise linear neural network models with physics informed knowledge for optimization problems with neural network models embedded. In addition to using widely accepted and naturally piece-wise linear rectified linear unit (ReLU) activation functions, this study also suggests piece-wise linear approximations for the hyperbolic tangent activation function to widen the domain. Optimization of three case studies, a blending process, an industrial distillation column and a crude oil column are investigated. For all cases, physics-informed trained neural network based optimal results are closer to global optimality. Finally, associated CPU times for the optimization problems are much shorter than the standard optimization results.