arXiv subjects

Alexander Mitsos

Publications and source records attributed to Alexander Mitsos.

At least 55 records · Page 3Linked to original sources

arXiv2023

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.

physics.chem-ph↗

arXiv2023

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 %.

eess.SY↗

arXiv2023

Data-driven Product-Process Optimization of N-isopropylacrylamide Microgel Flow-Synthesis

Microgels are cross-linked, colloidal polymer networks with great potential for stimuli-response release in drug-delivery applications, as their size in the nanometer range allows them to pass human cell boundaries. For applications with specified requirements regarding size, producing tailored microgels in a continuous flow reactor is advantageous because the microgel properties can be controlled tightly. However, no fully-specified mechanistic models are available for continuous microgel synthesis, as the physical properties of the included components are only studied partly. To address this gap and accelerate tailor-made microgel development, we propose a data-driven optimization in a hardware-in-the-loop approach to efficiently synthesize microgels with defined sizes. We optimize the synthesis regarding conflicting objectives (maximum production efficiency, minimum energy consumption, and the desired microgel radius) by applying Bayesian optimization via the solver ``Thompson sampling efficient multi-objective optimization'' (TS-EMO). We validate the optimization using the deterministic global solver ``McCormick-based Algorithm for mixed-integer Nonlinear Global Optimization'' (MAiNGO) and verify three computed Pareto optimal solutions via experiments. The proposed framework can be applied to other desired microgel properties and reactor setups and has the potential of efficient development by minimizing number of experiments and modelling effort needed.

cs.CE↗

arXiv2023

Optimal Design and Flexible Operation of a Fully Electrified Biodiesel Production Process

The flexible operation of electrified chemical processes, powered by renewable electricity, offers economic and ecological incentives, paving the way for a more sustainable chemical industry. However, this requires a departure from the traditional steady-state operation, posing a challenge to process design and operation. We propose an approach for flexible biodiesel production by utilizing intermediate and final buffer tanks. These tanks serve to decouple the dynamics between different process unit operations. We investigate the flexibility of three different process configurations and compare the outcomes of their dynamic optimization strategies with those of a steady-state operation, considering a typical demand-side response scenario. For all strategies, we employ local gradient-based optimization and solve them using our open-source optimization framework DyOS. Our findings indicate that by incorporating intermediate buffer tanks, we fully exploit the process flexibility potential, leading to total energy savings of up to 29%. We also propose an implementation based on distributed optimization problems, yielding similar savings while significantly reducing computational costs by over 10-fold and improving convergence, thus paving the way toward online application. Overall, this study highlights the potential benefits of incorporating buffer tanks and optimization strategies in the flexible operation of electrified chemical processes, even those initially designed solely for steady-state operation.

math.OC↗

arXiv2023

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

Meta-learning of numerical algorithms for a given task consists 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.

cs.LG↗

arXiv2023

Cost-Optimal Power-to-Methanol: Flexible Operation or Intermediate Storage?

The synthesis of methanol from captured carbon dioxide and green hydrogen could be a promising replacement for the current fossil-based production. The major energy input and cost driver for such a process is the electricity for hydrogen production. Time-variable electricity cost or availability thus motivates flexible operation. However, it is unclear if each unit of the process should be operated flexibly, and if storage of electricity or hydrogen reduces the methanol production cost. To answer these questions, we modeled a Power-to-Methanol plant with batteries and hydrogen storage. Using this model, we solved a combined design and scheduling optimization problem, which provides the optimal size of the units of the plant and their optimal (quasi-stationary) operation. The annualized cost of methanol was minimized for a grid-connected and a stand-alone case study. The optimization results confirm that storage, especially hydrogen storage, is particularly beneficial when the electricity price is high and highly fluctuating. Irrespective of the presence of storage, the whole Power-to-Methanol plant should be operated flexibly: even moderate flexibility of the methanol synthesis unit significantly reduces the production cost.

math.OC↗

arXiv2023

Nonlinear Isometric Manifold Learning for Injective Normalizing Flows

To model manifold data using normalizing flows, we employ isometric autoencoders to design embeddings with explicit inverses that do not distort the probability distribution. Using isometries separates manifold learning and density estimation and enables training of both parts to high accuracy. Thus, model selection and tuning are simplified compared to existing injective normalizing flows. Applied to data sets on (approximately) flat manifolds, the combined approach generates high-quality data.

cs.LG↗

arXiv2023

Multivariate Probabilistic Forecasting of Intraday Electricity Prices using Normalizing Flows

Electricity is traded on various markets with different time horizons and regulations. Short-term intraday trading becomes increasingly important due to the higher penetration of renewables. In Germany, the intraday electricity price typically fluctuates around the day-ahead price of the European Power EXchange (EPEX) spot markets in a distinct hourly pattern. This work proposes a probabilistic modeling approach that models the intraday price difference to the day-ahead contracts. The model captures the emerging hourly pattern by considering the four 15 min intervals in each day-ahead price interval as a four-dimensional joint probability distribution. The resulting nontrivial, multivariate price difference distribution is learned using a normalizing flow, i.e., a deep generative model that combines conditional multivariate density estimation and probabilistic regression. Furthermore, this work discusses the influence of different external impact factors based on literature insights and impact analysis using explainable artificial intelligence (XAI). The normalizing flow is compared to an informed selection of historical data and probabilistic forecasts using a Gaussian copula and a Gaussian regression model. Among the different models, the normalizing flow identifies the trends with the highest accuracy and has the narrowest prediction intervals. Both the XAI analysis and the empirical experiments highlight that the immediate history of the price difference realization and the increments of the day-ahead price have the most substantial impact on the price difference.

cs.LG↗

arXiv2022

Graph Machine Learning for Design of High-Octane Fuels

Fuels with high-knock resistance enable modern spark-ignition engines to achieve high efficiency and thus low CO2 emissions. Identification of molecules with desired autoignition properties indicated by a high research octane number and a high octane sensitivity is therefore of great practical relevance and can be supported by computer-aided molecular design (CAMD). Recent developments in the field of graph machine learning (graph-ML) provide novel, promising tools for CAMD. We propose a modular graph-ML CAMD framework that integrates generative graph-ML models with graph neural networks and optimization, enabling the design of molecules with desired ignition properties in a continuous molecular space. In particular, we explore the potential of Bayesian optimization and genetic algorithms in combination with generative graph-ML models. The graph-ML CAMD framework successfully identifies well-established high-octane components. It also suggests new candidates, one of which we experimentally investigate and use to illustrate the need for further auto-ignition training data.

cs.LG↗

arXiv2022

Physical Pooling Functions in Graph Neural Networks for Molecular Property Prediction

Graph neural networks (GNNs) are emerging in chemical engineering for the end-to-end learning of physicochemical properties based on molecular graphs. A key element of GNNs is the pooling function which combines atom feature vectors into molecular fingerprints. Most previous works use a standard pooling function to predict a variety of properties. However, unsuitable pooling functions can lead to unphysical GNNs that poorly generalize. We compare and select meaningful GNN pooling methods based on physical knowledge about the learned properties. The impact of physical pooling functions is demonstrated with molecular properties calculated from quantum mechanical computations. We also compare our results to the recent set2set pooling approach. We recommend using sum pooling for the prediction of properties that depend on molecular size and compare pooling functions for properties that are molecular size-independent. Overall, we show that the use of physical pooling functions significantly enhances generalization.

cs.LG↗

arXiv2022

Optimization with Trained Machine Learning Models Embedded

Trained ML models are commonly embedded in optimization problems. In many cases, this leads to large-scale NLPs that are difficult to solve to global optimality. While ML models frequently lead to large problems, they also exhibit homogeneous structures and repeating patterns (e.g., layers in ANNs). Thus, specialized solution strategies can be used for large problem classes. Recently, there have been some promising works proposing specialized reformulations using mixed-integer programming or reduced space formulations. However, further work is needed to develop more efficient solution approaches and keep up with the rapid development of new ML model architectures.

math.OC↗

arXiv2022

Graph neural networks for the prediction of molecular structure-property relationships

Molecular property prediction is of crucial importance in many disciplines such as drug discovery, molecular biology, or material and process design. The frequently employed quantitative structure-property/activity relationships (QSPRs/QSARs) characterize molecules by descriptors which are then mapped to the properties of interest via a linear or nonlinear model. In contrast, graph neural networks, a novel machine learning method, directly work on the molecular graph, i.e., a graph representation where atoms correspond to nodes and bonds correspond to edges. GNNs allow to learn properties in an end-to-end fashion, thereby avoiding the need for informative descriptors as in QSPRs/QSARs. GNNs have been shown to achieve state-of-the-art prediction performance on various property predictions tasks and represent an active field of research. We describe the fundamentals of GNNs and demonstrate the application of GNNs via two examples for molecular property prediction.

q-bio.BM↗

arXiv2022

Normalizing Flow-based Day-Ahead Wind Power Scenario Generation for Profitable and Reliable Delivery Commitments by Wind Farm Operators

We present a specialized scenario generation method that utilizes forecast information to generate scenarios for day-ahead scheduling problems. In particular, we use normalizing flows to generate wind power scenarios by sampling from a conditional distribution that uses wind speed forecasts to tailor the scenarios to a specific day. We apply the generated scenarios in a stochastic day-ahead bidding problem of a wind electricity producer and analyze whether the scenarios yield profitable decisions. Compared to Gaussian copulas and Wasserstein-generative adversarial networks, the normalizing flow successfully narrows the range of scenarios around the daily trends while maintaining a diverse variety of possible realizations. In the stochastic day-ahead bidding problem, the conditional scenarios from all methods lead to significantly more stable profitable results compared to an unconditional selection of historical scenarios. The normalizing flow consistently obtains the highest profits, even for small sets scenarios.

math.OC↗

arXiv2022

Graph Neural Networks for Temperature-Dependent Activity Coefficient Prediction of Solutes in Ionic Liquids

Ionic liquids (ILs) are important solvents for sustainable processes and predicting activity coefficients (ACs) of solutes in ILs is needed. Recently, matrix completion methods (MCMs), transformers, and graph neural networks (GNNs) have shown high accuracy in predicting ACs of binary mixtures, superior to well-established models, e.g., COSMO-RS and UNIFAC. GNNs are particularly promising here as they learn a molecular graph-to-property relationship without pretraining, typically required for transformers, and are, unlike MCMs, applicable to molecules not included in training. For ILs, however, GNN applications are currently missing. Herein, we present a GNN to predict temperature-dependent infinite dilution ACs of solutes in ILs. We train the GNN on a database including more than 40,000 AC values and compare it to a state-of-the-art MCM. The GNN and MCM achieve similar high prediction performance, with the GNN additionally enabling high-quality predictions for ACs of solutions that contain ILs and solutes not considered during training.

cs.LG↗

arXiv2022

Multi-scale membrane process optimization with high-fidelity ion transport models through machine learning

Innovative membrane technologies optimally integrated into large separation process plants are essential for economical water treatment and disposal. However, the mass transport through membranes is commonly described by nonlinear differential-algebraic mechanistic models at the nano-scale, while the process and its economics range up to large-scale. Thus, the optimal design of membranes in process plants requires decision making across multiple scales, which is not tractable using standard tools. In this work, we embed artificial neural networks~(ANNs) as surrogate models in the deterministic global optimization to bridge the gap of scales. This methodology allows for deterministic global optimization of membrane processes with accurate transport models -- avoiding the utilization of inaccurate approximations through heuristics or short-cut models. The ANNs are trained based on data generated by a one-dimensional extended Nernst-Planck ion transport model and extended to a more accurate two-dimensional distribution of the membrane module, that captures the filtration-related decreasing retention of salt. We simultaneously design the membrane and plant layout yielding optimal membrane module synthesis properties along with the optimal plant design for multiple objectives, feed concentrations, filtration stages, and salt mixtures. The developed process models and the optimization solver are available open-source, enabling computational resource-efficient multi-scale optimization in membrane science.

physics.comp-ph↗

arXiv2022

Identification of MIMO Wiener-type Koopman Models for Data-Driven Model Reduction using Deep Learning

We use Koopman theory to develop a data-driven nonlinear model reduction and identification strategy for multiple-input multiple-output (MIMO) input-affine dynamical systems. While the present literature has focused on linear and bilinear Koopman models, we derive and use a Wiener-type Koopman formulation. We discuss that the Wiener structure is particularly suitable for model reduction, and can be naturally derived from Koopman theory. Moreover, the Wiener block-structure unifies the mathematical simplicity of linear dynamical blocks and the accuracy of bilinear dynamics. We present a Koopman deep-learning strategy combining autoencoders and linear dynamics that generates low-order surrogate models of MIMO Wiener type. In three case studies, we apply our framework for identification and reduction of a system with input multiplicity, a chemical reactor and a high-purity distillation column. We compare the prediction performance of the identified Wiener models to linear and bilinear Koopman models. We observe the highest accuracy and strongest model reduction capabilities of low-order Wiener-type Koopman models, making them promising for control.

math.OC↗

arXiv2022

Principal Component Density Estimation for Scenario Generation Using Normalizing Flows

Neural networks-based learning of the distribution of non-dispatchable renewable electricity generation from sources such as photovoltaics (PV) and wind as well as load demands has recently gained attention. Normalizing flow density models are particularly well suited for this task due to the training through direct log-likelihood maximization. However, research from the field of image generation has shown that standard normalizing flows can only learn smeared-out versions of manifold distributions. Previous works on normalizing flow-based scenario generation do not address this issue, and the smeared-out distributions result in the sampling of noisy time series. In this paper, we exploit the isometry of the principal component analysis (PCA), which sets up the normalizing flow in a lower-dimensional space while maintaining the direct and computationally efficient likelihood maximization. We train the resulting principal component flow (PCF) on data of PV and wind power generation as well as load demand in Germany in the years 2013 to 2015. The results of this investigation show that the PCF preserves critical features of the original distributions, such as the probability density and frequency behavior of the time series. The application of the PCF is, however, not limited to renewable power generation but rather extends to any data set, time series, or otherwise, which can be efficiently reduced using PCA.

cs.LG↗

arXiv2021

Validation Methods for Energy Time Series Scenarios from Deep Generative Models

The design and operation of modern energy systems are heavily influenced by time-dependent and uncertain parameters, e.g., renewable electricity generation, load-demand, and electricity prices. These are typically represented by a set of discrete realizations known as scenarios. A popular scenario generation approach uses deep generative models (DGM) that allow scenario generation without prior assumptions about the data distribution. However, the validation of generated scenarios is difficult, and a comprehensive discussion about appropriate validation methods is currently lacking. To start this discussion, we provide a critical assessment of the currently used validation methods in the energy scenario generation literature. In particular, we assess validation methods based on probability density, auto-correlation, and power spectral density. Furthermore, we propose using the multifractal detrended fluctuation analysis (MFDFA) as an additional validation method for non-trivial features like peaks, bursts, and plateaus. As representative examples, we train generative adversarial networks (GANs), Wasserstein GANs (WGANs), and variational autoencoders (VAEs) on two renewable power generation time series (photovoltaic and wind from Germany in 2013 to 2015) and an intra-day electricity price time series form the European Energy Exchange in 2017 to 2019. We apply the four validation methods to both the historical and the generated data and discuss the interpretation of validation results as well as common mistakes, pitfalls, and limitations of the validation methods. Our assessment shows that no single method sufficiently characterizes a scenario but ideally validation should include multiple methods and be interpreted carefully in the context of scenarios over short time periods.

cs.LG↗