Neural operators have emerged as powerful surrogates for modeling complex physical problems. However, they suffer from spectral bias making them oblivious to high-frequency modes, which are present in multiscale physical systems. Therefore, they tend to produce over-smoothed solutions, which is particularly problematic in modeling turbulence and for systems with intricate patterns and sharp gradients such as multi-phase flow systems. In this work, we introduce a new approach named high-frequency scaling (HFS) to mitigate spectral bias in convolutional-based neural operators. By integrating HFS with proper variants of UNet neural operators, we demonstrate a higher prediction accuracy by mitigating spectral bias in single and two-phase flow problems. Unlike Fourier-based techniques, HFS is directly applied to the latent space, thus eliminating the computational cost associated with the Fourier transform. Additionally, we investigate alternative spectral bias mitigation through diffusion models conditioned on neural operators. While the diffusion model integrated with the standard neural operator may still suffer from significant errors, these errors are substantially reduced when the diffusion model is integrated with a HFS-enhanced neural operator.

Extreme weather events are increasing in frequency and intensity due to climate change. This, in turn, is exacting a significant toll in communities worldwide. While prediction skills are increasing with advances in numerical weather prediction and artificial intelligence tools, extreme weather still present challenges. More specifically, identifying the precursors of such extreme weather events and how these precursors may evolve under climate change remain unclear. In this paper, we propose to use post-hoc interpretability methods to construct relevance weather maps that show the key extreme-weather precursors identified by deep learning models. We then compare this machine view with existing domain knowledge to understand whether deep learning models identified patterns in data that may enrich our understanding of extreme-weather precursors. We finally bin these relevant maps into different multi-year time periods to understand the role that climate change is having on these precursors. The experiments are carried out on Indochina heatwaves, but the methodology can be readily extended to other extreme weather events worldwide.

Dynamic graph embedding has emerged as a very effective technique for addressing diverse temporal graph analytic tasks (i.e., link prediction, node classification, recommender systems, anomaly detection, and graph generation) in various applications. Such temporal graphs exhibit heterogeneous transient dynamics, varying time intervals, and highly evolving node features throughout their evolution. Hence, incorporating long-range dependencies from the historical graph context plays a crucial role in accurately learning their temporal dynamics. In this paper, we develop a graph embedding model with uncertainty quantification, TransformerG2G, by exploiting the advanced transformer encoder to first learn intermediate node representations from its current state ($t$) and previous context (over timestamps [$t-1, t-l$], $l$ is the length of context). Moreover, we employ two projection layers to generate lower-dimensional multivariate Gaussian distributions as each node's latent embedding at timestamp $t$. We consider diverse benchmarks with varying levels of ``novelty" as measured by the TEA (Temporal Edge Appearance) plots. Our experiments demonstrate that the proposed TransformerG2G model outperforms conventional multi-step methods and our prior work (DynG2G) in terms of both link prediction accuracy and computational efficiency, especially for high degree of novelty. Furthermore, the learned time-dependent attention weights across multiple graph snapshots reveal the development of an automatic adaptive time stepping enabled by the transformer. Importantly, by examining the attention weights, we can uncover temporal dependencies, identify influential elements, and gain insights into the complex interactions within the graph structure. For example, we identified a strong correlation between attention weights and node degree at the various stages of the graph topology evolution.

Numerical simulation for climate modeling resolving all important scales is a computationally taxing process. Therefore, to circumvent this issue a low resolution simulation is performed, which is subsequently corrected for bias using reanalyzed data (ERA5), known as nudging correction. The existing implementation for nudging correction uses a relaxation based method for the algebraic difference between low resolution and ERA5 data. In this study, we replace the bias correction process with a surrogate model based on the Deep Operator Network (DeepONet). DeepONet (Deep Operator Neural Network) learns the mapping from the state before nudging (a functional) to the nudging tendency (another functional). The nudging tendency is a very high dimensional data albeit having many low energy modes. Therefore, the DeepoNet is combined with a convolution based auto-encoder-decoder (AED) architecture in order to learn the nudging tendency in a lower dimensional latent space efficiently. The accuracy of the DeepONet model is tested against the nudging tendency obtained from the E3SMv2 (Energy Exascale Earth System Model) and shows good agreement. The overarching goal of this work is to deploy the DeepONet model in an online setting and replace the nudging module in the E3SM loop for better efficiency and accuracy.