Conditional Invertible Generative Models for Supervised Problems

Invertible neural networks (INNs), in the setting of normalizing flows, are a type of unconditional generative likelihood model. Despite various attractive properties compared to other common generative model types, they are rarely useful for supervised tasks or real applications due to their unguided outputs. In this work, we therefore present three new methods that extend the standard INN setting, falling under a broader category we term generative invertible models. These new methods allow leveraging the theoretical and practical benefits of INNs to solve supervised problems in new ways, including real-world applications from different branches of science. The key finding is that our approaches enhance many aspects of trustworthiness in comparison to conventional feed-forward networks, such as uncertainty estimation and quantification, explainability, and proper handling of outlier data

ProDAS: Probabilistic Dataset of Abstract Shapes

We introduce a novel and comprehensive dataset, named ProDAS, which enables the generation of diverse objects with varying shape, size, rotation, and texture/color through a latent factor model. ProDAS offers complete access and control over the data generation process, serving as an ideal environment for investigating disentanglement, causal discovery, out-of-distribution detection, and numerous other research questions. We provide pre-defined functions for the important cases of creating distinct and interconnected distributions, allowing the investigation of distribution shifts and other intriguing applications. The library can be found at https://github.com/XarwinM/ProDAS

Model updating of wind turbine blade cross sections with invertible neural networks

Fabricated wind turbine blades have unavoidable deviations from their designs due to imperfections in the manufacturing processes. Model updating is a common approach to enhance model predictions and therefore improve the numerical blade design accuracy compared to the built blade. An updated model can provide a basis for a digital twin of the rotor blade including the manufacturing deviations. Classical optimization algorithms, most often combined with reduced order or surrogate models, represent the state of the art in structural model updating. However, these deterministic methods suffer from high computational costs and a missing probabilistic evaluation. This feasibility study approaches the model updating task by inverting the model through the application of invertible neural networks, which allow for inferring a posterior distribution of the input parameters from given output parameters, without costly optimization or sampling algorithms. In our use case, rotor blade cross sections are updated to match given cross-sectional parameters. To this end, a sensitivity analysis of the input (material properties or layup locations) and output parameters (such as stiffness and mass matrix entries) first selects relevant features in advance to then set up and train the invertible neural network. The trained network predicts with outstanding accuracy most of the selected cross-sectional input parameters for different radial positions; that is, the posterior distribution of these parameters shows a narrow width. At the same time, it identifies some parameters that are hard to recover accurately or contain intrinsic ambiguities. Hence, we demonstrate that invertible neural networks are highly capable for structural model updating