Physics-Informed Neural Networks for Dynamic Process Operations with Limited Physical Knowledge and Data

In chemical engineering, process data is often expensive to acquire, and complex phenomena are difficult to model rigorously, rendering both entirely data-driven and purely mechanistic modeling approaches impractical. We explore using physics-informed neural networks (PINNs) for modeling dynamic processes governed by differential-algebraic equation systems when process data is scarce and complete mechanistic knowledge is missing. In particular, we focus on estimating states for which neither direct observational data nor constitutive equations are available. For demonstration purposes, we study a continuously stirred tank reactor and a liquid-liquid separator. We find that PINNs can infer unmeasured states with reasonable accuracy, and they generalize better in low-data scenarios than purely data-driven models. We thus show that PINNs, similar to hybrid mechanistic/data-driven models, are capable of modeling processes when relatively few experimental data and only partially known mechanistic descriptions are available, and conclude that they constitute a promising avenue that warrants further investigation.

Task-optimal data-driven surrogate models for eNMPC via differentiable simulation and optimization

We present a method for end-to-end learning of Koopman surrogate models for optimal performance in control. In contrast to previous contributions that employ standard reinforcement learning (RL) algorithms, we use a training algorithm that exploits the potential differentiability of environments based on mechanistic simulation models. We evaluate the performance of our method by comparing it to that of other controller type and training algorithm combinations on a literature known eNMPC case study. Our method exhibits superior performance on this problem, thereby constituting a promising avenue towards more capable controllers that employ dynamic surrogate models.

Nonlinear Manifold Learning Determines Microgel Size from Raman Spectroscopy

Polymer particle size constitutes a crucial characteristic of product quality in polymerization. Raman spectroscopy is an established and reliable process analytical technology for in-line concentration monitoring. Recent approaches and some theoretical considerations show a correlation between Raman signals and particle sizes but do not determine polymer size from Raman spectroscopic measurements accurately and reliably. With this in mind, we propose three alternative machine learning workflows to perform this task, all involving diffusion maps, a nonlinear manifold learning technique for dimensionality reduction: (i) directly from diffusion maps, (ii) alternating diffusion maps, and (iii) conformal autoencoder neural networks. We apply the workflows to a data set of Raman spectra with associated size measured via dynamic light scattering of 47 microgel (cross-linked polymer) samples in a diameter range of 208nm to 483 nm. The conformal autoencoders substantially outperform state-of-the-art methods and results for the first time in a promising prediction of polymer size from Raman spectra.

Predicting the Temperature Dependence of Surfactant CMCs Using Graph Neural Networks

The critical micelle concentration (CMC) of surfactant molecules is an essential property for surfactant applications in industry. Recently, classical QSPR and Graph Neural Networks (GNNs), a deep learning technique, have been successfully applied to predict the CMC of surfactants at room temperature. However, these models have not yet considered the temperature dependency of the CMC, which is highly relevant for practical applications. We herein develop a GNN model for temperature-dependent CMC prediction of surfactants. We collect about 1400 data points from public sources for all surfactant classes, i.e., ionic, nonionic, and zwitterionic, at multiple temperatures. We test the predictive quality of the model for following scenarios: i) when CMC data for surfactants are present in the training of the model in at least one different temperature, and ii) CMC data for surfactants are not present in the training, i.e., generalizing to unseen surfactants. In both test scenarios, our model exhibits a high predictive performance of R$^2 \geq $ 0.94 on test data. We also find that the model performance varies by surfactant class. Finally, we evaluate the model for sugar-based surfactants with complex molecular structures, as these represent a more sustainable alternative to synthetic surfactants and are therefore of great interest for future applications in the personal and home care industries.

Data-driven Nonlinear Model Reduction using Koopman Theory: Integrated Control Form and NMPC Case Study

We use Koopman theory for data-driven model reduction of nonlinear dynamical systems with controls. We propose generic model structures combining delay-coordinate encoding of measurements and full-state decoding to integrate reduced Koopman modeling and state estimation. We present a deep-learning approach to train the proposed models. A case study demonstrates that our approach provides accurate control models and enables real-time capable nonlinear model predictive control of a high-purity cryogenic distillation column.

Graph Neural Networks for Surfactant Multi-Property Prediction

Surfactants are of high importance in different industrial sectors such as cosmetics, detergents, oil recovery and drug delivery systems. Therefore, many quantitative structure-property relationship (QSPR) models have been developed for surfactants. Each predictive model typically focuses on one surfactant class, mostly nonionics. Graph Neural Networks (GNNs) have exhibited a great predictive performance for property prediction of ionic liquids, polymers and drugs in general. Specifically for surfactants, GNNs can successfully predict critical micelle concentration (CMC), a key surfactant property associated with micellization. A key factor in the predictive ability of QSPR and GNN models is the data available for training. Based on extensive literature search, we create the largest available CMC database with 429 molecules and the first large data collection for surface excess concentration ($\Gamma$$_{m}$), another surfactant property associated with foaming, with 164 molecules. Then, we develop GNN models to predict the CMC and $\Gamma$$_{m}$ and we explore different learning approaches, i.e., single- and multi-task learning, as well as different training strategies, namely ensemble and transfer learning. We find that a multi-task GNN with ensemble learning trained on all $\Gamma$$_{m}$ and CMC data performs best. Finally, we test the ability of our CMC model to generalize on industrial grade pure component surfactants. The GNN yields highly accurate predictions for CMC, showing great potential for future industrial applications.

Data-Driven Model Reduction and Nonlinear Model Predictive Control of an Air Separation Unit by Applied Koopman Theory

Achieving real-time capability is an essential prerequisite for the industrial implementation of nonlinear model predictive control (NMPC). Data-driven model reduction offers a way to obtain low-order control models from complex digital twins. In particular, data-driven approaches require little expert knowledge of the particular process and its model, and provide reduced models of a well-defined generic structure. Herein, we apply our recently proposed data-driven reduction strategy based on Koopman theory [Schulze et al. (2022), Comput. Chem. Eng.] to generate a low-order control model of an air separation unit (ASU). The reduced Koopman model combines autoencoders and linear latent dynamics and is constructed using machine learning. Further, we present an NMPC implementation that uses derivative computation tailored to the fixed block structure of reduced Koopman models. Our reduction approach with tailored NMPC implementation enables real-time NMPC of an ASU at an average CPU time decrease by 98 %.

End-to-End Reinforcement Learning of Koopman Models for Economic Nonlinear MPC

(Economic) nonlinear model predictive control ((e)NMPC) requires dynamic system models that are sufficiently accurate in all relevant state-space regions. These models must also be computationally cheap enough to ensure real-time tractability. Data-driven surrogate models for mechanistic models can be used to reduce the computational burden of (e)NMPC; however, such models are typically trained by system identification for maximum average prediction accuracy on simulation samples and perform suboptimally as part of actual (e)NMPC. We present a method for end-to-end reinforcement learning of dynamic surrogate models for optimal performance in (e)NMPC applications, resulting in predictive controllers that strike a favorable balance between control performance and computational demand. We validate our method on two applications derived from an established nonlinear continuous stirred-tank reactor model. We compare the controller performance to that of MPCs utilizing models trained by the prevailing maximum prediction accuracy paradigm, and model-free neural network controllers trained using reinforcement learning. We show that our method matches the performance of the model-free neural network controllers while consistently outperforming models derived from system identification. Additionally, we show that the MPC policies can react to changes in the control setting without retraining.

Gibbs-Duhem-Informed Neural Networks for Binary Activity Coefficient Prediction

We propose Gibbs-Duhem-informed neural networks for the prediction of binary activity coefficients at varying compositions. That is, we include the Gibbs-Duhem equation explicitly in the loss function for training neural networks, which is straightforward in standard machine learning (ML) frameworks enabling automatic differentiation. In contrast to recent hybrid ML approaches, our approach does not rely on embedding a specific thermodynamic model inside the neural network and corresponding prediction limitations. Rather, Gibbs-Duhem consistency serves as regularization, with the flexibility of ML models being preserved. Our results show increased thermodynamic consistency and generalization capabilities for activity coefficient predictions by Gibbs-Duhem-informed graph neural networks and matrix completion methods. We also find that the model architecture, particularly the activation function, can have a strong influence on the prediction quality. The approach can be easily extended to account for other thermodynamic consistency conditions.

A Recursively Recurrent Neural Network (R2N2) Architecture for Learning Iterative Algorithms

Meta-learning of numerical algorithms for a given task consist of the data-driven identification and adaptation of an algorithmic structure and the associated hyperparameters. To limit the complexity of the meta-learning problem, neural architectures with a certain inductive bias towards favorable algorithmic structures can, and should, be used. We generalize our previously introduced Runge-Kutta neural network to a recursively recurrent neural network (R2N2) superstructure for the design of customized iterative algorithms. In contrast to off-the-shelf deep learning approaches, it features a distinct division into modules for generation of information and for the subsequent assembly of this information towards a solution. Local information in the form of a subspace is generated by subordinate, inner, iterations of recurrent function evaluations starting at the current outer iterate. The update to the next outer iterate is computed as a linear combination of these evaluations, reducing the residual in this space, and constitutes the output of the network. We demonstrate that regular training of the weight parameters inside the proposed superstructure on input/output data of various computational problem classes yields iterations similar to Krylov solvers for linear equation systems, Newton-Krylov solvers for nonlinear equation systems, and Runge-Kutta integrators for ordinary differential equations. Due to its modularity, the superstructure can be readily extended with functionalities needed to represent more general classes of iterative algorithms traditionally based on Taylor series expansions.