Accurately downscaling precipitation from coarse to high spatial resolutions remains a critical challenge in climate and hydrometeorological modeling. A key limitation is the frequent misclassification of dry and wet regions, which compromises the realism and reliability of high-resolution outputs. To address this, we propose a deep learning-based downscaling framework that explicitly models dry/wet classification by transforming low-resolution 6×6 precipitation inputs into high-resolution 60 × 60 binary classification fields. We evaluate two architectures, a convolutional encoder-decoder and a conditional Wasserstein generative adversarial network (WGAN), utilizing three training strategies: (1) using binary wet/dry inputs, (2) using precipitation intensity inputs, and (3) using precipitation intensity inputs and adding physical constraints. Models are trained and validated on both synthetically generated precipitation fields and real radar-estimated hourly precipitation data over the contiguous United States. Performance is assessed using metrics including the overall probability of zero ($ {\mathrm{P}}_0 $) and spatial autocorrelations. Results show that incorporating intensity information improves dry/wet classification, while adding physical constraints further enhances accuracy, generalization, and physical consistency, especially for WGAN models. The convolutional encoder-decoder produces smoother outputs with stable performance regarding marginal statistics, whereas the WGAN generates sharper boundaries and more realistic dry/wet fields, improving on the spatial dependence structure. Furthermore, we demonstrate that the derived dry/wet classification fields can be used as binary masks to bias correct downscaled precipitation fields, enhancing both statistical fidelity and spatial realism. These findings highlight the value of a physically informed bias-correction strategy for improving the spatial realism of high-resolution precipitation fields from coarse-scale inputs.

Inference and prediction under partial knowledge of a physical system is challenging, particularly when multiple confounding sources influence the measured response. Explicitly accounting for these influences in physics-based models is often infeasible due to epistemic uncertainty, cost, or time constraints, resulting in models that fail to accurately describe the behavior of the system. On the other hand, data-driven machine learning models such as variational autoencoders are not guaranteed to identify a parsimonious representation. As a result, they can suffer from poor generalization performance and reconstruction accuracy in the regime of limited and noisy data. We propose a physics-informed variational autoencoder architecture that combines the interpretability of physics-based models with the flexibility of data-driven models. To promote disentanglement of the known physics and confounding influences, the latent space is partitioned into physically meaningful variables that parametrize a physics-based model, and data-driven variables that capture variability in the domain and class of the physical system. The encoder is coupled with a decoder that integrates physics-based and data-driven components, and constrained by an adversarial training objective that prevents the data-driven components from overriding the known physics, ensuring that the physics-grounded latent variables remain interpretable. We demonstrate that the model is able to disentangle features of the input signal and separate the known physics from confounding influences using supervision in the form of class and domain observables. The model is evaluated on a series of synthetic case studies relevant to engineering structures, demonstrating the feasibility of the proposed approach.

Large-scale atmospheric circulation patterns, so-called weather regimes, modulate the occurrence of extreme events such as heatwaves or extreme precipitation. In their role as mediators between long-range teleconnections and local impacts, weather regimes have demonstrated potential in improving long-term climate projections as well as sub-seasonal to seasonal forecasts. However, existing methods for identifying weather regimes are not specifically designed to capture the relevant physical processes responsible for variations in the impact variable in question. This paper introduces a novel probabilistic machine learning method, RMM-VAE, for identifying weather regimes targeted to a local-scale impact variable. Based on a variational autoencoder architecture, the method combines non-linear dimensionality reduction with a prediction task and probabilistic clustering in one coherent architecture. The new method is applied to identify circulation patterns over the Mediterranean region targeted to precipitation over Morocco and compared to three existing approaches: two established linear methods and another machine-learning approach. The RMM-VAE method identifies regimes that are more predictive of the target variable compared to the two linear methods, both in terms of terciles and extremes in precipitation, while also improving the reconstruction of the input space. Further, the regimes identified by the RMM-VAE method are also more robust and persistent compared to the alternative machine learning method. The results demonstrate the potential benefit of the new method for use in various climate applications such as sub-seasonal forecasting, and illustrate the trade-offs involved in targeted clustering.

A framework is proposed for generative models as a basis for digital twins or mirrors of structures. The proposal is based on the premise that deterministic models cannot account for the uncertainty present in most structural modeling applications. Two different types of generative models are considered here. The first is a physics-based model based on the stochastic finite element (SFE) method, which is widely used when modeling structures that have material and loading uncertainties imposed. Such models can be calibrated according to data from the structure and would be expected to outperform any other model if the modeling accurately captures the true underlying physics of the structure. The potential use of SFE models as digital mirrors is illustrated via application to a linear structure with stochastic material properties. For situations where the physical formulation of such models does not suffice, a data-driven framework is proposed, using machine learning and conditional generative adversarial networks (cGANs). The latter algorithm is used to learn the distribution of the quantity of interest in a structure with material nonlinearities and uncertainties. For the examples considered in this work, the data-driven cGANs model outperforms the physics-based approach. Finally, an example is shown where the two methods are coupled such that a hybrid model approach is demonstrated.

A principled approach to understand networks is to formulate generative models and infer their parameters from given network data. Due to the scarcity of data in the form of multiple networks that have evolved from the same process, generative models are typically formulated to learn parameters from a single network observation, hence ignoring the natural variability of the “true” process. In this paper, we highlight the importance of variability in evaluating generative models and present two ways of quantifying the variability for a finite set of networks. The first evaluation scheme compares the statistical properties of networks in a dissimilarity space, while the other relies on data-driven entropy measures to compute variability in network populations. Using these measures, we evaluate the ability of four generative models to synthesize networks that capture the variability of the “true” process. Our empirical analysis suggests that generative models fitted for a single network observation fail to capture the variability in the network population. Our work highlights the need for rethinking the way we evaluate the goodness-of-fit of new and existing network models and devising models that are capable of matching the variability of network populations when available.