However, it has several unique challenges.

To bridge the temporal granularity gap in energy network design and operation based on Energy System Models, resampling of time series is required. While conventional upsampling methods are computationally efficient, they often result in significant information loss or increased noise. Advanced models such as time series generation models, Super-Resolution models and imputation models show potential, but also face fundamental challenges. The goal of time series generative models is to learn the distribution of the original data to generate high-resolution series with similar statistical characteristics. This is not entirely consistent with the definition of upsampling. Time series Super-Resolution models or imputation models can degrade the accuracy of upsampling because the input low-resolution time series are sparse and may have insufficient context. Moreover, such models usually rely on supervised learning paradigms. This presents a fundamental application paradox: their training requires the high-resolution time series that is intrinsically absent in upsampling application scenarios. To address the mentioned upsampling issue, this paper introduces a new method utilizing Generative Adversarial Transformers (GATs), which can be trained without access to any ground-truth high-resolution data. Compared with conventional interpolation methods, the introduced method can reduce the root mean square error (RMSE) of upsampling tasks by 10%, and the accuracy of a model predictive control (MPC) application scenario is improved by 13%.

However, it has several unique challenges.

4D Flow Magnetic Resonance Imaging (4D Flow MRI) is a non-invasive technique for volumetric, time-resolved blood flow quantification. However, apparent trade-offs between acquisition time, image noise, and resolution limit clinical applicability. In particular, in regions of highly transient flow, coarse temporal resolution can hinder accurate capture of physiologically relevant flow variations. To overcome these issues, post-processing techniques using deep learning have shown promising results to enhance resolution post-scan using so-called super-resolution networks. However, while super-resolution has been focusing on spatial upsampling, temporal super-resolution remains largely unexplored. The aim of this study was therefore to implement and evaluate a residual network for temporal super-resolution 4D Flow MRI. To achieve this, an existing spatial network (4DFlowNet) was re-designed for temporal upsampling, adapting input dimensions, and optimizing internal layer structures. Training and testing were performed using synthetic 4D Flow MRI data originating from patient-specific in-silico models, as well as using in-vivo datasets. Overall, excellent performance was achieved with input velocities effectively denoised and temporally upsampled, with a mean absolute error (MAE) of 1.0 cm/s in an unseen in-silico setting, outperforming deterministic alternatives (linear interpolation MAE = 2.3 cm/s, sinc interpolation MAE = 2.6 cm/s). Further, the network synthesized high-resolution temporal information from unseen low-resolution in-vivo data, with strong correlation observed at peak flow frames. As such, our results highlight the potential of utilizing data-driven neural networks for temporal super-resolution 4D Flow MRI, enabling high-frame-rate flow quantification without extending acquisition times beyond clinically acceptable limits.

Downscaling techniques are one of the most prominent applications of Deep Learning (DL) in Earth System Modeling. A robust DL downscaling model can generate high-resolution fields from coarse-scale numerical model simulations, saving the timely and resourceful applications of regional/local models. Additionally, generative DL models have the potential to provide uncertainty information, by generating ensemble-like scenario pools, a task that is computationally prohibitive for traditional numerical simulations. In this study, we apply a Latent Diffusion Model (LDM) to downscale ERA5 data over Italy up to a resolution of 2 km. The high-resolution target data consists of results from a high-resolution dynamical downscaling performed with COSMO-CLM. Our goal is to demonstrate that recent advancements in generative modeling enable DL-based models to deliver results comparable to those of numerical dynamical downscaling models, given the same input data (i.e., ERA5 data), preserving the realism of fine-scale features and flow characteristics. The training and testing database consists of hourly data from 2000 to 2020. The target variables of this study are 2-m temperature and 10-m horizontal wind components. A selection of predictors from ERA5 is used as input to the LDM, and a residual approach against a reference UNET is leveraged in applying the LDM. The performance of the generative LDM is compared with reference baselines of increasing complexity: quadratic interpolation of ERA5, a UNET, and a Generative Adversarial Network (GAN) built on the same reference UNET. Results highlight the improvements introduced by the LDM architecture and the residual approach over these baselines. The models are evaluated on a yearly test dataset, assessing the models' performance through deterministic metrics, spatial distribution of errors, and reconstruction of frequency and power spectra distributions.

Modern deep learning techniques, which mimic traditional numerical weather prediction (NWP) models and are derived from global atmospheric reanalysis data, have caused a significant revolution within a few years. In this new paradigm, our research introduces a novel strategy that deviates from the common dependence on high-resolution data, which is often constrained by computational resources, and instead utilizes low-resolution data (2.5 degrees) for global weather prediction and climate data analysis. Our main focus is evaluating data-driven weather prediction (DDWP) frameworks, specifically addressing sample size adequacy, structural improvements to the model, and the ability of climate data to represent current climatic trends. By using the Adaptive Fourier Neural Operator (AFNO) model via FourCastNet and a proposed time-sliding method to inflate the dataset of the ECMWF Reanalysis v5 (ERA5), this paper improves on conventional approaches by adding more variables and a novel approach to data augmentation and processing. Our findings reveal that despite the lower resolution, the proposed approach demonstrates considerable accuracy in predicting atmospheric conditions, effectively rivaling higher-resolution models. Furthermore, the study confirms the model's proficiency in reflecting current climate trends and its potential in predicting future climatic events, underscoring its utility in climate change strategies. This research marks a pivotal step in the realm of meteorological forecasting, showcasing the feasibility of lower-resolution data in producing reliable predictions and opening avenues for more accessible and inclusive climate modeling. The insights gleaned from this study not only contribute to the advancement of climate science but also lay the groundwork for future innovations in the field.

As our planet is entering into the "global boiling" era, understanding regional climate change becomes imperative. Effective downscaling methods that provide localized insights are crucial for this target. Traditional approaches, including computationally-demanding regional dynamical models or statistical downscaling frameworks, are often susceptible to the influence of downscaling uncertainty. Here, we address these limitations by introducing a diffusion probabilistic downscaling model (DPDM) into the meteorological field. This model can efficiently transform data from 1{\deg} to 0.1{\deg} resolution. Compared with deterministic downscaling schemes, it not only has more accurate local details, but also can generate a large number of ensemble members based on probability distribution sampling to evaluate the uncertainty of downscaling. Additionally, we apply the model to generate a 180-year dataset of monthly surface variables in East Asia, offering a more detailed perspective for understanding local scale climate change over the past centuries.

In Computational Fluid Dynamics (CFD), coarse mesh simulations offer computational efficiency but often lack precision. Applying conventional super-resolution to these simulations poses a significant challenge due to the fundamental contrast between downsampling high-resolution images and authentically emulating low-resolution physics. The former method conserves more of the underlying physics, surpassing the usual constraints of real-world scenarios. We propose a novel definition of super-resolution tailored for PDE-based problems. Instead of simply downsampling from a high-resolution dataset, we use coarse-grid simulated data as our input and predict fine-grid simulated outcomes. Employing a physics-infused UNet upscaling method, we demonstrate its efficacy across various 2D-CFD problems such as discontinuity detection in Burger's equation, Methane combustion, and fouling in Industrial heat exchangers. Our method enables the generation of fine-mesh solutions bypassing traditional simulation, ensuring considerable computational saving and fidelity to the original ground truth outcomes. Through diverse boundary conditions during training, we further establish the robustness of our method, paving the way for its broad applications in engineering and scientific CFD solvers.

We introduce a two-stage probabilistic framework for statistical downscaling using unpaired data. Statistical downscaling seeks a probabilistic map to transform low-resolution data from a biased coarse-grained numerical scheme to high-resolution data that is consistent with a high-fidelity scheme. Our framework tackles the problem by composing two transformations: (i) a debiasing step via an optimal transport map, and (ii) an upsampling step achieved by a probabilistic diffusion model with a posteriori conditional sampling. This approach characterizes a conditional distribution without needing paired data, and faithfully recovers relevant physical statistics from biased samples. We demonstrate the utility of the proposed approach on one- and two-dimensional fluid flow problems, which are representative of the core difficulties present in numerical simulations of weather and climate. Our method produces realistic high-resolution outputs from low-resolution inputs, by upsampling resolutions of 8x and 16x. Moreover, our procedure correctly matches the statistics of physical quantities, even when the low-frequency content of the inputs and outputs do not match, a crucial but difficult-to-satisfy assumption needed by current state-of-the-art alternatives. Code for this work is available at: https://github.com/google-research/swirl-dynamics/tree/main/swirl_dynamics/projects/probabilistic_diffusion.

Although many deep-learning-based super-resolution approaches have been proposed in recent years, because no ground truth is available in the inference stage, few can quantify the errors and uncertainties of the super-resolved results. For scientific visualization applications, however, conveying uncertainties of the results to scientists is crucial to avoid generating misleading or incorrect information. In this paper, we propose PSRFlow, a novel normalizing flow-based generative model for scientific data super-resolution that incorporates uncertainty quantification into the super-resolution process. PSRFlow learns the conditional distribution of the high-resolution data based on the low-resolution counterpart. By sampling from a Gaussian latent space that captures the missing information in the high-resolution data, one can generate different plausible super-resolution outputs. The efficient sampling in the Gaussian latent space allows our model to perform uncertainty quantification for the super-resolved results. During model training, we augment the training data with samples across various scales to make the model adaptable to data of different scales, achieving flexible super-resolution for a given input. Our results demonstrate superior performance and robust uncertainty quantification compared with existing methods such as interpolation and GAN-based super-resolution networks.