An LLM-Driven Workflow for Automated Process Control Strategy Generation and Tuning from Dynamic Process Models

We present a structured large-language-model-driven workflow for automated multi-variable control design from dynamic process models. The workflow decomposes the design task into constrained code-generation steps: plant-interface construction, normalization, manipulated-variable controlled-variable (MV-CV) pairing, controller specification, closed loop simulation, scenario generation, performance evaluation and Bayesian-optimization (BO) based tuning. Generated artifacts are executed and validated before downstream tasks proceed, and failed artifacts are repaired using validation feedback. The proposed approach is demonstrated on a nonlinear gas-preheater benchmark with coupled pressure and temperature dynamics. The generated workflow produces a physically consistent decentralized PI (proportional-integral) feedback-feedforward control structure and an executable tuning environment. Bayesian optimization reduces the closed loop performance objective, which aggregates set-point tracking and disturbance-rejection errors for the controlled variables, by approximately 26.5% relative to the initial controller generated by the workflow, mainly through improved pressure-loop transient performance. This figure quantifies the automated tuning stage rather than a comparison against a manually designed controller. The results demonstrate the feasibility of using structured large-language-model-based code generation to construct executable control-design workflows, while also highlighting the need for broader validation on larger plantwide-control benchmarks.

Does Demand Response Increase Vulnerability to Cyber Attacks by Adversarial Data Modifications?

Adversarial attacks are crafted data manipulations that aim to deteriorate the outcomes of prediction or decision-making algorithms. In the energy systems literature, adversarial attacks have been studied with a focus on problems regarding the electricity grid. Such problems include forecasting and grid state estimation, where adversarial attacks are also known as false data injection attacks. Only few studies have analyzed the potential impact that adversarial attacks have on the demand side. We analyze how manipulated price forecasts impact the decision-making in industrial demand response. To this end, we design adversarial attacks that aim to deteriorate the output of electricity price forecasting models and solve scheduling optimization problems of energy-intensive production processes using the distorted price forecasts. We make use of a generalized process model to investigate the vulnerability to adversarial attacks for a range of production scheduling problems with different levels of process flexibility. We find that adversarial attacks can erode the profits gained from demand response. However, when perturbations are limited in extent (so that they are hard to detect by the human user), demand response preserves about 90\% of its financial advantage compared to steady-state process operation. Further, we find that the impact of adversarial attacks on demand response does not only depend on the magnitude of the perturbations but rather on the orientation of the adversarial perturbations. Therefore, we argue that attack analyses should explicitly incorporate the sensitivities of scheduling optimization models into the attack design to enable more rigorous assessments of decision-making under adversarial attacks.

Hybrid Neural Ordinary Differential Equations for Data-Efficient Polymerization Modeling with Incomplete Kinetics

Accurate prediction of polymerization dynamics is essential for process design, control, and optimization. Yet, purely mechanistic models require labor-intensive parameterization of partially characterized kinetics, while purely data-driven models demand large, diverse datasets that are costly to obtain, particularly in early-design stages. We propose a hybrid Neural Ordinary Differential Equation (NODE) framework for data-efficient modeling of free-radical polymerization. Using batch polymerization of methyl methacrylate (MMA) as a case study, the mechanistic mass balances are retained explicitly, and only the partially-characterized effective radical concentration governing monomer consumption is learned from data through a neural network surrogate, while established reactions such as initiator decomposition, propagation, and termination remain physically modeled. The hybrid NODE is evaluated against a discrete-time feedforward neural network and a purely data-driven NODE under sparse data conditions, with models trained on as few as ten measurements under both regular and irregular sampling. The hybrid NODE consistently achieves lower prediction errors and more physically consistent extrapolations than both purely data-driven baselines. In a generalization scenario with noisy data and unseen operating conditions, the hybrid NODE achieves an RMSE of 0.013, compared to 0.31 for the data-driven NODE and 0.68 for the discrete-time model, demonstrating that learning only a closure term rather than the full dynamics is sufficient for reliable prediction under limited data availability.

Iterative Model-Learning Scheme via Gaussian Processes for Nonlinear Model Predictive Control of (Semi-)Batch Processes

Batch processes are inherently transient and typically nonlinear, motivating nonlinear model predictive control (NMPC). However, adopting NMPC is hindered by the cost and unavailability of dynamic models. Thus, we propose to use Gaussian Processes (GP) in a model-learning NMPC scheme (GP-MLMPC) for batch processes. We initialize the GP-MLMPC using data from a single initial trajectory, e.g., from a PI controller. We iteratively apply the NMPC embedded with GPs to run batches and update the GP with new observations from each iteration, thereby achieving batch-wise improvements. Using uncertainty quantification from the GPs, we formulate chance constraints to enforce safe operation to the required confidence levels. We demonstrate our approach in \textit{silico} on a semi-batch polymerization reactor for tracking and economic objectives over durations of two hours, and the reactor temperature is constrained in a range of $\pm2^\circ C$ around its setpoint. After only four batch iterations, tracking error from the GP-MLMPC scheme converged to a reduction of $83\%$, compared to the initial trajectory. Furthermore, under an economic objective, the GP-MLMPC resulted in a 17-fold increase in final product mass by iteration 8, compared to the initial trajectory. In both cases, the resulting GP-MLMPC performance is on par with the full-model NMPC, which shows that the optimal controller can be learned by the approach. By collecting samples around the optimal trajectory, the GP-MLMPC remains sample-efficient across iterations and achieves quick convergence. Thus, the proposed GP-MLMPC scheme presents a promising data-efficient approach for the control of nonlinear batch processes without mechanistic knowledge.

Bayesian Optimization of Partially Known Systems using Hybrid Models

Bayesian optimization (BO) has gained attention as an efficient algorithm for black-box optimization of expensive-to-evaluate systems, where the BO algorithm iteratively queries the system and suggests new trials based on a probabilistic model fitted to previous samples. Still, the standard BO loop may require a prohibitively large number of experiments to converge to the optimum, especially for high-dimensional and nonlinear systems. We present a hybrid model-based BO formulation that combines the iterative Bayesian learning of BO with partially known mechanistic physical models. Instead of learning a direct mapping from inputs to the objective, we write all known equations for a physics-based model and infer expressions for variables missing equations using a probabilistic model, in our case, a Gaussian process (GP). The final formulation then includes the GP as a constraint in the hybrid model, thereby allowing other physics-based nonlinear and implicit model constraints. This hybrid model formulation yields a constrained, nonlinear stochastic program, which we discretize using the sample-average approximation. In an in-silico optimization of a single-stage distillation, the hybrid BO model based on mass conservation laws yields significantly better designs than a standard BO loop. Furthermore, the hybrid model converges in as few as one iteration, depending on the initial samples, whereas, the standard BO does not converge within 25 for any of the seeds. Overall, the proposed hybrid BO scheme presents a promising optimization method for partially known systems, leveraging the strengths of both mechanistic modeling and data-driven optimization.

Data-Driven Conditional Flexibility Index

With the increasing flexibilization of processes, determining robust scheduling decisions has become an important goal. Traditionally, the flexibility index has been used to identify safe operating schedules by approximating the admissible uncertainty region using simple admissible uncertainty sets, such as hypercubes. Presently, available contextual information, such as forecasts, has not been considered to define the admissible uncertainty set when determining the flexibility index. We propose the conditional flexibility index (CFI), which extends the traditional flexibility index in two ways: by learning the parametrized admissible uncertainty set from historical data and by using contextual information to make the admissible uncertainty set conditional. This is achieved using a normalizing flow that learns a bijective mapping from a Gaussian base distribution to the data distribution. The admissible latent uncertainty set is constructed as a hypersphere in the latent space and mapped to the data space. By incorporating contextual information, the CFI provides a more informative estimate of flexibility by defining admissible uncertainty sets in regions that are more likely to be relevant under given conditions. Using an illustrative example, we show that no general statement can be made about data-driven admissible uncertainty sets outperforming simple sets, or conditional sets outperforming unconditional ones. However, both data-driven and conditional admissible uncertainty sets ensure that only regions of the uncertain parameter space containing realizations are considered. We apply the CFI to a security-constrained unit commitment example and demonstrate that the CFI can improve scheduling quality by incorporating temporal information.

Model-Free Stochastic Process Modeling and Optimization using Normalizing Flows

Real-world chemical processes often exhibit stochastic dynamics with non-trivial correlations and state-dependent fluctuations. However, most process models simply add stationary noise terms to a deterministic prediction, which can lead to inaccurate predictions. This work proposes using conditional normalizing flows as discrete-time models (DTMs) to learn the stochastic dynamics of chemical processes. Normalizing flows learn an explicit expression of the system states' probability density function (PDF) given prior states and control inputs. The resulting model naturally allows for formulating stochastic and probabilistic setpoint-tracking objectives and chance constraints. In applications to a continuous reactor and a reactor cascade, the normalizing flow yields stable simulations over long time horizons and high-quality results in stochastic and probabilistic MPC formulation for open-loop control. Furthermore, a chance-constrained optimization finds reliable startup controls for the reactor cascade with stochastic reactions. In conclusion, the conditional normalizing flow presents an excellent choice for modeling nonlinear stochastic dynamics.

Multivariate Scenario Generation of Day-Ahead Electricity Prices using Normalizing Flows

Trading on electricity markets requires accurate information about the realization of electricity prices and the uncertainty attached to the predictions. We present a probabilistic forecasting approach for day-ahead electricity prices using the fully data-driven deep generative model called normalizing flows. Our modeling approach generates full-day scenarios of day-ahead electricity prices based on conditional features such as residual load forecasts. Furthermore, we propose extended feature sets of prior realizations and a periodic retraining scheme that allows the normalizing flow to adapt to the changing conditions of modern electricity markets. In particular, we investigate the impact of the energy crisis ensuing from the Russian invasion of Ukraine. Our results highlight that the normalizing flow generates high-quality scenarios that reproduce the true price distribution and yield highly accurate forecasts. Additionally, our analysis highlights how our improvements towards adaptations in changing regimes allow the normalizing flow to adapt to changing market conditions and enables continued sampling of high-quality day-ahead price scenarios.

Multivariate Probabilistic Forecasting of Intraday Electricity Prices using Normalizing Flows

Electricity is traded on various markets with different time horizons and regulations. Short-term trading becomes increasingly important due to higher penetration of renewables. In Germany, the intraday electricity price typically fluctuates around the day-ahead price of the 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 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. The normalizing flow is compared to a selection of historical data, a Gaussian copula, and a Gaussian regression model. Among the different models, the normalizing flow identifies the trends most accurately and has the narrowest prediction intervals. Notably, the normalizing flow is the only approach that identifies rare price peaks. Finally, this work discusses the influence of different external impact factors and finds that, individually, most of these factors have negligible impact. Only the immediate history of the price difference realization and the combination of all input factors lead to notable improvements in the forecasts.

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 the particular usage in day-ahead scheduling problems. In particular, we use normalizing flows to generate wind power generation scenarios by sampling from a conditional distribution that uses day-ahead wind speed forecasts to tailor the scenarios to the specific day. We apply the generated scenarios in a simple stochastic day-ahead bidding problem of a wind electricity producer and run a statistical analysis focusing on whether the scenarios yield profitable and reliable decisions. Compared to conditional scenarios generated from Gaussian copulas and Wasserstein-generative adversarial networks, the normalizing flow scenarios identify the daily trends more accurately and with a lower spread while maintaining a diverse variety. In the stochastic day-ahead bidding problem, the conditional scenarios from all methods lead to significantly more profitable and reliable results compared to an unconditional selection of historical scenarios. The obtained profits using the normalizing flow scenarios are consistently closest to the perfect foresight solution, in particular, for small sets of only five scenarios.