Open Access

Uncertainty quantification plays a crucial role in process systems engineering, where reliable decision-making depends on the accurate characterization of model uncertainty. A principled framework for this purpose is provided by Bayesian inference, which updates prior knowledge about model parameters based on experimental or simulated data. The resulting posterior distributions, and the quantities derived from them, are essential for informed decision-making, robust prediction, and process optimization. However, computing these quantities of interest is often intractable, as it requires solving high-dimensional integrals over the parameter space. In contrast to full Bayesian inference, an approach to solve the issue of intractablility that remains widely used in process engineering is to approximate the posterior and related quantities by linearizing the model through local sensitivity analysis, thereby enabling the use of analytical solutions from linear regression analysis. While computationally efficient, these approximations can introduce significant error, particularly for highly nonlinear systems [3]. On the other hand, sampling-based methods such as Markov Chain Monte Carlo (MCMC) approximate the posterior distribution by drawing samples from it. These sampling-based methods are asymptotically exact but often prohibitively expensive in practice due to the large number of posterior samples required for convergence. In this work, we present a comprehensive benchmark of state-of-the-art methodologies for uncertainty quantification in chemical process engineering. Specifically, we systematically evaluate inverse uncertainty quantification methods for estimating posterior means and variances, thereby providing insights into their accuracy, robustness, and practical applicability in process modeling. The evaluated methods comprise cubature-based uncertainty quantification and variational inference using normalizing flows. Cubature methods provide a general numerical framework for approximating multidimensional integrals and are therefore particularly suitable for uncertainty quantification in nonlinear systems. Moreover, cubature methods use a fixed set of deterministically chosen samples and evaluate the integral through weighted sums of function evaluations, resulting in high computational efficiency. Here, we extend the approach presented in [1], which employs the fifth-degree cubature formula proposed by Lu and Darmofal [4]. In addition, the present study evaluates approximation error from variational inference with normalizing flows as flexible variational distributions. In variational inference, the posterior distribution is approximated by a family of parametric distributions, whose parameters are optimized to minimize the Kullback–Leibler divergence from the true posterior [7]. A common limitation of this approach lies in the restricted expressiveness of simple distribution families, which can lead to suboptimal approximations. Normalizing flows overcome this limitation by applying a sequence of invertible transformations to a simple base distribution, thereby enabling the representation of highly complex posterior distributions while maintaining efficient sampling and density evaluation [2], [7]. In contrast to cubature-based methods, normalizing flows can represent a wider range of posterior distributions, including highly complex and multimodal ones. However, they typically require more data points during both training and evaluation. Both methods are benchmarked against the widely used linearization-based approach to uncertainty quantification. The benchmark is conducted on two problems in chemical process engineering: (i) the parameter estimation of a zero-order ammonia decomposition kinetic on nickel [5] as an example of an explicit model, and (ii) the inference of activity coefficients based on a binary NRTL model [6] as an example of an implict model. Each method is evaluated in terms of accuracy and computational efficiency. Since the computation of an analytic posterior is not available due to the inherent nonlinearity of the problems, an exhaustive MCMC sampling scheme is employed as a reference solution for the comparison of the predicitve accuracy. The computational cost is generally related with two components: the training of the uncertainty quantification model and the subsequent evaluation of the trained model to obtain posterior estimates. Since the computational costs of the benchmarked methods cannot be clearly categorized in this manner, all methods are compared based on their total time required for both training and evaluation. The results highlight the respective strengths and limitations of the evaluated approaches and provide practical guidance for selecting suitable Bayesian inference techniques in process engineering applications. The findings contribute to more reliable and robust simulation-based decision-making in the field.

Polymer membranes are critical functional components in proton-exchange membrane water electrolyzers (PEMWEs), where they simultaneously enable ionic transport, separate reactive gases, and Sustain mechanical loads. Despite their central role, membrane failure remains a key limitation for System reliability and safety, driven by the complex interaction of electrochemical reactions, two-phase flow, transport processes, and material degradation due to mechanical, chemical, and thermal loads. In particular, gas-liquid flow regimes in catalyst layers, porous transport layers, and flow channels strongly influence local pressure, temperature, and concentrations at the membrane interface. These impact the membrane’s hydration conditions, inducing heterogeneous swelling, stress concentrations, and Membrane thinning, which accelerates the aging process. This contribution presents a multiphysics modeling framework for the simulation-based investigation of membrane degradation and failure mechanisms in PEMWEs, synthesizing ideas from previous works into a novel integrated modeling approach. Two-phase flow in the adjacent porous and free-flow regions is described using porous-media formulations and phase-field computational fluid dynamics, resolving gas generation, saturation, and pressure fields under different operating conditions. The resulting interface quantities are coupled to a porous-mixture-based finite strain membrane model that accounts for hydration-dependent transport and swelling-induced deformation. Damage or failure indicators are introduced to capture the onset of critical membrane degradation driven by cyclic loading, dehydration, or pressure fluctuations. This modeling concept enables systematic analysis of how operating conditions and flow regimes, including annular or mist-like patterns, contribute to membrane stress and failure risk. The Framework provides a foundation for predictive lifetime assessment and supports the design of more durable and safer electrolyzer systems.

Introduction: Mitral regurgitation (MR) is a common valvular disease associated with complications such as pulmonary hypertension, atrial fibrillation, and heart failure. However, its full impact on the cardiovascular system, especially on right heart function, is not yet fully understood. Understanding this relationship is important because the right ventricle (RV) is critical for maintaining cardiovascular function. Dysfunction of the RV, which may be contributed by conditions like MR, is strongly associated with poor clinical outcomes. Despite its importance, comprehensively studying MR's effect on the RV has been challenging due to the complex, interdependent nature of cardiovascular dynamics, limited patient data, and the difficulty in synthesizing disparate information to clarify the left heart-right heart connection. Methods: The primary goal of this study is to investigate the effects of MR on cardiovascular hemodynamics and RV function by integrating 3D models of the left heart with a closed-loop 0D models of the entire cardiovascular system. We further conduct detailed analyses using patient-specific models to explore how various system modifications impact the RV, providing insights into the nuanced effects of MR on the right heart. Results and Discussion: This analysis provides several clinically relevant insights. First, progressive MR markedly increases RV afterload and predisposes the RV to dysfunction, even when intrinsic RV contractility is preserved or enhanced. Second, MR-specific severity indices and left-heart metrics alone fail to capture the true burden on the right heart; RV impairment can progress despite stable or only modestly changing MR descriptors. Finally, these findings highlight the need to incorporate direct assessment of RV structure and function into the evaluation of MR, as RV vulnerability plays a critical role in determining patient risk and guiding management decisions.

The Data Exchange in the Process Industry (DEXPI) standardization group has recently released a new specification addressing early process design information, particularly information found in block flow diagrams (BFDs) and process flow diagrams (PFDs). The specification provides an information model and exchange format for such design information, but it does not yet define a graphical notation or modeling approach for creating and exchanging compliant BFDs or PFDs. Our work investigates the structural and semantic correspondence between the DEXPI Process information model and the Business Process Model and Notation 2.0 (BPMN 2.0) standard and proposes a BPMN 2.0-based representation for DEXPI’s BFDs and PFDs. The approach is validated using the Tennessee Eastman process as a case study. The results show that BPMN 2.0 can represent and exchange DEXPI Process-relevant design information in a semantic and standardized way, that the resulting models can be transformed into schema-valid DEXPI 2.0 XML, and that it provides a practical and tool-supported basis for graphical modeling of BFDs and PFDs. To support adoption, we provide an open-source reference implementation, bpmn2dexpi, that realizes the proposed representation, transforms BPMN 2.0 models into DEXPI 2.0-compliant XML, and validates the output against the DEXPI 2.0 XML Schema and information model.

Kurze Vorstellung des Forschungsprojektes zum Thema sichere Wasserstoffnetze und die Motivierung, wieso eine digitale, teilautonome, quantifizierte und ML-gestützte Sicherheitsanalyse sinnvoll ist und wie die neue Anlage ModuH2Pipe dafür hervorragende Validierungsmethoden bietet.