Generative artificial intelligence suffers from critical limitations including hallucination and violation of real-world constraints. To address this, we present a physics-aware generative modeling framework combining adversarial learning with physical forward models and Normalizing Flows. Systematic evaluation across simple to complex electric circuit models and four Normalizing Flow architectures demonstrates broad applicability. Training stabilization is achieved through discriminator ensembles, instance noise scheduling, and penalty terms. Downstream supervised learning tasks validate the framework’s ability to synthesize labeled training data from unlabeled impedance measurements, achieving competitive performance across several circuit elements compared to original datasets. • Physics-Aware Normalizing Flows integrate adversarial learning with physical models. • Framework guarantees physically plausible data via embedded simulator. • Labeled training data is synthesized from unlabeled impedance measurements. • Four Normalizing Flow architectures are evaluated across simple to complex equivalent circuits. • Advanced training stabilization enables convergence for complex physical models.

We introduce Physics-Aware Normalizing Flows, a novel framework combining data-driven generative modeling with a physical layer based on an Electric Circuit Model, ensuring adherence to electricity laws, sample fidelity, and explainability.Four existing Normalizing Flow architectures, including Real-NVP and NSF, were adapted to our adversarial regime and evaluated with promising results for the ad hoc determination of value ranges of physical quantities and the generation of labeled measurements based on an unlabeled dataset.By extensive data generation according to our self-explainable approach, Random Forest regressions of underlying physical quantities could be improved significantly, compared to the original dataset including omitted ground truth labels. MotivationLately, generative artificial intelligence has attracted a high level of public attention.Despite the emergence of high-performing models, however, significant weaknesses in these methods have been revealed, such as hallucination [1] and violation of causal relationships and real-world conditions [2].Approaches that integrate explicitly represented knowledge with purely statistical generative techniques have therefore gained increasing interest recently [3].An important approach in this regard is the development of physics-aware generative modeling [2], which strengthens the credibility of the generated data as well as the explainability of the models themselves.To this end, invertible flow-based generative models, i.e.Normalizing Flows (NF) [4], deserve special attention due to their built-in self-explainability with support for both sampling and probability density estimation [5], as well as continuous improvements in modeling capacity and quality of the generated samples [6,7,5].One way to strengthen the integrity of generated data is to embed physical models in NFs.This allows ad hoc synthesis of labeled training data using the physical forward model and an unlabeled dataset.Particularly in the field of impedance spectroscopy, where electrical circuit models are used to explain observed measurements, the determination of the corresponding parameter values remains a challenge, but one that can be solved by supervised learning [8].In the following, a novel approach to combine NFs with physical models is presented, exemplary for electric circuits, but adaptable for a wide range of forward models.

Abstract Uncertainties in flood predictions complicate the planning of mitigation measures. There is a consensus that many possible incident scenarios should be considered. For each scenario, a specific response plan should be prepared which is optimal with respect to criteria such as protection, costs, or realization time. None of the existing software tools is capable of creating large scenario pools, nor do they provide means for quick exploration and assessment of the associated plans. In this paper, we present an integrated solution that is based on multidimensional, time‐dependent ensemble simulations of incident scenarios and protective measures. We provide scalable interfaces which facilitate and accelerate setting up multiple time‐varying parameters for generating a pool of pre‐cooked scenarios. In case of an emergency, disaster managers can quickly extract relevant information from the pool to deal with the situation at hand. An interactive 3D‐view conveys details about how a response plan has to be executed. Linked information visualization and ranking views allow for a quick assessment of many plans. In collaboration with flood managers, we demonstrate the practical applicability of our solution. We tackle the challenges of planning mobile water barriers for protecting important infrastructure. We account for real‐world limitations of available resources and handle the involved logistics problems.

In this paper, we present a data-flow system which supports comparative analysis of time-dependent data and interactive simulation steering. The system creates data on-the-fly to allow for the exploration of different parameters and the investigation of multiple scenarios. Existing data-flow architectures provide no generic approach to handle modules that perform complex temporal processing such as particle tracing or statistical analysis over time. Moreover, there is no solution to create and manage module data, which is associated with alternative scenarios. Our solution is based on generic data-flow algorithms to automate this process, enabling elaborate data-flow procedures, such as simulation, temporal integration or data aggregation over many time steps in many worlds. To hide the complexity from the user, we extend the World Lines interaction techniques to control the novel data-flow architecture. The concept of multiple, special-purpose cursors is introduced to let users intuitively navigate through time and alternative scenarios. Users specify only what they want to see, the decision which data are required is handled automatically. The concepts are explained by taking the example of the simulation and analysis of material transport in levee-breach scenarios. To strengthen the general applicability, we demonstrate the investigation of vortices in an offline-simulated dam-break data set.

Abstract We present a dense visualization of vector fields on multi‐layered surfaces. The method is based on the illustration buffer, which provides a screen space representation of the surface, where each pixel stores a list of all surface layers. This representation is implemented on the GPU using shaders and leads to a fast output sensitive technique. In our approach, we first use procedural noise to create an initial spot pattern on the surface that has both an almost constant screen space frequency and is view independent. Then, we perform anisotropic diffusion simultaneously on all surface layers using a discretization scheme that maintains second order convergence while only accessing the four neighboring pixels. Finally, we enhance this result with illustrative techniques and composite the final image. Our method works with time‐evolving surfaces, time‐dependent vector fields, and moving cameras. We apply our method to CFD data sets from engineering and astronomy as well as synthetic velocity fields.

Room air flow and air exchange are important aspects for the design of energy-efficient buildings. As a result, simulations are increasingly used prior to construction to achieve an energy-efficient design. We present a visual analysis of air flow generated at building entrances, which uses a combination of revolving doors and air curtains. The resulting flow pattern is challenging because of two interacting flow patterns: On the one hand, the revolving door acts as a pump, on the other hand, the air curtain creates a layer of uniformly moving warm air between the interior of the building and the revolving door. Lagrangian coherent structures (LCS), which by definition are flow barriers, are the method of choice for visualizing the separation and recirculation behavior of warm and cold air flow. The extraction of LCS is based on the finite-time Lyapunov exponent (FTLE) and makes use of a ridge definition which is consistent with the concept of weak LCS. Both FTLE computation and ridge extraction are done in a robust and efficient way by making use of the fast Fourier transform for computing scale-space derivatives.

Abstract Vector fields are a common concept for the representation of many different kinds of flow phenomena in science and engineering. Methods based on vector field topology are known for their convenience for visualizing and analysing steady flows, but a counterpart for unsteady flows is still missing. However, a lot of good and relevant work aiming at such a solution is available. We give an overview of previous research leading towards topology‐based and topology‐inspired visualization of unsteady flow, pointing out the different approaches and methodologies involved as well as their relation to each other, taking classical (i.e. steady) vector field topology as our starting point. Particularly, we focus on Lagrangian methods, space–time domain approaches, local methods and stochastic and multifield approaches. Furthermore, we illustrate our review with practical examples for the different approaches.

Flood disasters are the most common natural risk and tremendous efforts are spent to improve their simulation and management. However, simulation-based investigation of actions that can be taken in case of flood emergencies is rarely done. This is in part due to the lack of a comprehensive framework which integrates and facilitates these efforts. In this paper, we tackle several problems which are related to steering a flood simulation. One issue is related to uncertainty. We need to account for uncertain knowledge about the environment, such as levee-breach locations. Furthermore, the steering process has to reveal how these uncertainties in the boundary conditions affect the confidence in the simulation outcome. Another important problem is that the simulation setup is often hidden in a black-box. We expose system internals and show that simulation steering can be comprehensible at the same time. This is important because the domain expert needs to be able to modify the simulation setup in order to include local knowledge and experience. In the proposed solution, users steer parameter studies through the World Lines interface to account for input uncertainties. The transport of steering information to the underlying data-flow components is handled by a novel meta-flow. The meta-flow is an extension to a standard data-flow network, comprising additional nodes and ropes to abstract parameter control. The meta-flow has a visual representation to inform the user about which control operations happen. Finally, we present the idea to use the data-flow diagram itself for visualizing steering information and simulation results. We discuss a case-study in collaboration with a domain expert who proposes different actions to protect a virtual city from imminent flooding. The key to choosing the best response strategy is the ability to compare different regions of the parameter space while retaining an understanding of what is happening inside the data-flow system.

Abstract In this paper we present an extended critical point concept which allows us to apply vector field topology in the case of unsteady flow. We propose a measure forunsteadinesswhich describes the rate of change of the velocities in a fluid element over time. This measure allows us to select particles for which topological properties remain intact inside a finite spatio‐temporal neighborhood. One benefit of this approach is that the classification of critical points based on the eigenvalues of the Jacobian remains meaningful. In the steady case the proposed criterion reduces to the classical definition of critical points. As a first step we show that finding an optimal Galilean frame of reference can be obtained implicitly by analyzing the acceleration field. In a second step we show that this can be extended by switching to the Lagrangian frame of reference. This way the criterion can detect critical points moving along intricate trajectories. We analyze the behavior of the proposed criterion based on two analytical vector fields for which a correct solution is defined by their inherent symmetries and present results for numerical vector fields.

In this paper we present World Lines as a novel interactive visualization that provides complete control over multiple heterogeneous simulation runs. In many application areas, decisions can only be made by exploring alternative scenarios. The goal of the suggested approach is to support users in this decision making process. In this setting, the data domain is extended to a set of alternative worlds where only one outcome will actually happen. World Lines integrate simulation, visualization and computational steering into a single unified system that is capable of dealing with the extended solution space. World Lines represent simulation runs as causally connected tracks that share a common time axis. This setup enables users to interfere and add new information quickly. A World Line is introduced as a visual combination of user events and their effects in order to present a possible future. To quickly find the most attractive outcome, we suggest World Lines as the governing component in a system of multiple linked views and a simulation component. World Lines employ linking and brushing to enable comparative visual analysis of multiple simulations in linked views. Analysis results can be mapped to various visual variables that World Lines provide in order to highlight the most compelling solutions. To demonstrate this technique we present a flooding scenario and show the usefulness of the integrated approach to support informed decision making.

In this paper we present a method for vortex core line extraction which operates directly on the smoothed particle hydrodynamics (SPH) representation and, by this, generates smoother and more (spatially and temporally) coherent results in an efficient way. The underlying predictor-corrector scheme is general enough to be applied to other line-type features and it is extendable to the extraction of surfaces such as isosurfaces or Lagrangian coherent structures. The proposed method exploits temporal coherence to speed up computation for subsequent time steps. We show how the predictor-corrector formulation can be specialized for several variants of vortex core line definitions including two recent unsteady extensions, and we contribute a theoretical and practical comparison of these. In particular, we reveal a close relation between unsteady extensions of Fuchs et al. and Weinkauf et al. and we give a proof of the Galilean invariance of the latter. When visualizing SPH data, there is the possibility to use the same interpolation method for visualization as has been used for the simulation. This is different from the case of finite volume simulation results, where it is not possible to recover from the results the spatial interpolation that was used during the simulation. Such data are typically interpolated using the basic trilinear interpolant, and if smoothness is required, some artificial processing is added. In SPH data, however, the smoothing kernels are specified from the simulation, and they provide an exact and smooth interpolation of data or gradients at arbitrary points in the domain.