Johannes Exenberger

Parsa Gooya, Reinel Sospedra-Alfonso, Johannes Exenberger

Accurately quantifying uncertainty in predictions and projections arising from irreducible internal climate variability is critical for informed decision making. Such uncertainty is typically assessed using ensembles produced with physics based climate models. However, computational constraints impose a trade off between generating the large ensembles required for robust uncertainty estimation and increasing model resolution to better capture fine scale dynamics. Generative machine learning offers a promising pathway to alleviate these constraints. We develop a conditional Variational Autoencoder (cVAE) trained on a limited sample of climate simulations to generate arbitrary large ensembles. The approach is applied to output from monthly CMIP6 historical and future scenario experiments produced with the Canadian Centre for Climate Modelling and Analysis' (CCCma's) Earth system model CanESM5. We show that the cVAE model learns the underlying distribution of the data and generates physically consistent samples that reproduce realistic low and high moment statistics, including extremes. Compared with more sophisticated generative architectures, cVAEs offer a mathematically transparent, interpretable, and computationally efficient framework. Their simplicity lead to some limitations, such as overly smooth outputs, spectral bias, and underdispersion, that we discuss along with strategies to mitigate them. Specifically, we show that incorporating output noise improves the representation of climate relevant multiscale variability, and we propose a simple method to achieve this. Finally, we show that cVAE-enhanced ensembles capture realistic global teleconnection patterns, even under climate conditions absent from the training data.

Johannes Exenberger, Sascha Ranftl, Robert Peharz

Polynomial chaos expansion (PCE) is a classical and widely used surrogate modeling technique in physical simulation and uncertainty quantification. By taking a linear combination of a set of basis polynomials - orthonormal with respect to the distribution of uncertain input parameters - PCE enables tractable inference of key statistical quantities, such as (conditional) means, variances, covariances, and Sobol sensitivity indices, which are essential for understanding the modeled system and identifying influential parameters and their interactions. As the number of basis functions grows exponentially with the number of parameters, PCE does not scale well to high-dimensional problems. We address this challenge by combining PCE with ideas from probabilistic circuits, resulting in the deep polynomial chaos expansion (DeepPCE) - a deep generalization of PCE that scales effectively to high-dimensional input spaces. DeepPCE achieves predictive performance comparable to that of multi-layer perceptrons (MLPs), while retaining PCE's ability to compute exact statistical inferences via simple forward passes.

Johannes Exenberger, Matteo Di Salvo, Thomas Hirsch et al.

Machine learning plays an important role in the operation of current wind energy production systems. One central application is predictive maintenance to increase efficiency and lower electricity costs by reducing downtimes. Integrating physics-based knowledge in neural networks to enforce their physical plausibilty is a promising method to improve current approaches, but incomplete system information often impedes their application in real world scenarios. We describe a simple and efficient way for physics-constrained deep learning-based predictive maintenance for wind turbine gearbox bearings with partial system knowledge. The approach is based on temperature nowcasting constrained by physics, where unknown system coefficients are treated as learnable neural network parameters. Results show improved generalization performance to unseen environments compared to a baseline neural network, which is especially important in low data scenarios often encountered in real-world applications.