Coupled partial differential equations (PDEs) are key tasks in modeling the complex dynamics of many physical processes. Recently, neural operators have shown the ability to solve PDEs by learning the integral kernel directly in Fourier/Wavelet space, so the difficulty for solving the coupled PDEs depends on dealing with the coupled mappings between the functions. Towards this end, we propose a coupled multiwavelets neural operator (CMWNO) learning scheme by decoupling the coupled integral kernels during the multiwavelet decomposition and reconstruction procedures in the Wavelet space. The proposed model achieves significantly higher accuracy compared to previous learning-based solvers in solving the coupled PDEs including Gray-Scott (GS) equations and the non-local mean field game (MFG) problem. According to our experimental results, the proposed model exhibits a 2ˆ 4ˆ improvement relative L2 error compared to the best results from the state-of-the-art models. Human perception relies on detecting and processing waves. While our eyes detect waves of electromagnetic radiation, our ears detect waves of compression in the surrounding air.

Graph Neural Networks (GNN) have recently gained popularity in the forecasting domain due to their ability to model complex spatial and temporal patterns in tasks such as traffic forecasting and region-based demand forecasting. Most of these methods require a predefined graph as input, whereas in real-life multivariate time series problems, a well-predefined dependency graph rarely exists. This requirement makes it harder for GNNs to be utilised widely for multivariate forecasting problems in other domains such as retail or energy. In this paper, we propose a hybrid approach combining neural networks and statistical structure learning models to self-learn the dependencies and construct a dynamically changing dependency graph from multivariate data aiming to enable the use of GNNs for multivariate forecasting even when a well-defined graph does not exist. The statistical structure modeling in conjunction with neural networks provides a well-principled and efficient approach by bringing in causal semantics to determine dependencies among the series. Finally, we demonstrate significantly improved performance using our proposed approach on real-world benchmark datasets without a pre-defined dependency graph.

Diabetes encompasses a complex landscape of glycemic control that varies widely among individuals. However, current methods do not faithfully capture this variability at the meal level. On the one hand, expert-crafted features lack the flexibility of data-driven methods; on the other hand, learned representations tend to be uninterpretable which hampers clinical adoption. In this paper, we propose a hybrid variational autoencoder to learn interpretable representations of CGM and meal data. Our method grounds the latent space to the inputs of a mechanistic differential equation, producing embeddings that reflect physiological quantities, such as insulin sensitivity, glucose effectiveness, and basal glucose levels. Moreover, we introduce a novel method to infer the glucose appearance rate, making the mechanistic model robust to unreliable meal logs. On a dataset of CGM and self-reported meals from individuals with type-2 diabetes and pre-diabetes, our unsupervised representation discovers a separation between individuals proportional to their disease severity. Our embeddings produce clusters that are up to 4x better than naive, expert, black-box, and pure mechanistic features. Our method provides a nuanced, yet interpretable, embedding space to compare glycemic control within and across individuals, directly learnable from in-the-wild data.

Urban Air Mobility (UAM) represents a promising solution for future transportation. In this study, we introduce VertiSim, an advanced event-driven simulator developed to evaluate e-VTOL transportation networks. Uniquely, VertiSim simultaneously models passenger, aircraft, and energy flows, reflecting the interrelated complexities of UAM systems. We utilized VertiSim to assess 19 operational scenarios serving a daily demand for 2,834 passengers with varying fleet sizes and vertiport distances. The study aims to support stakeholders in making informed decisions about fleet size, network design, and infrastructure development by understanding tradeoffs in passenger delay time, operational costs, and fleet utilization. Our simulations, guided by a heuristic dispatch and charge policy, indicate that fleet size significantly influences passenger delay and energy consumption within UAM networks. We find that increasing the fleet size can reduce average passenger delays, but this comes at the cost of higher operational expenses due to an increase in the number of repositioning flights. Additionally, our analysis highlights how vertiport distances impact fleet utilization: longer distances result in reduced total idle time and increased cruise and charge times, leading to more efficient fleet utilization but also longer passenger delays. These findings are important for UAM network planning, especially in balancing fleet size with vertiport capacity and operational costs. Simulator demo is available at: https://tinyurl.com/vertisim-vis

With the growing volume of diverse information, the demand for classifying arbitrary topics has become increasingly critical. To address this challenge, we introduce DRAFT, a simple framework designed to train a classifier for few-shot topic classification. DRAFT uses a few examples of a specific topic as queries to construct Customized dataset with a dense retriever model. Multi-query retrieval (MQR) algorithm, which effectively handles multiple queries related to a specific topic, is applied to construct the Customized dataset. Subsequently, we fine-tune a classifier using the Customized dataset to identify the topic. To demonstrate the efficacy of our proposed approach, we conduct evaluations on both widely used classification benchmark datasets and manually constructed datasets with 291 diverse topics, which simulate diverse contents encountered in real-world applications. DRAFT shows competitive or superior performance compared to baselines that use in-context learning, such as GPT-3 175B and InstructGPT 175B, on few-shot topic classification tasks despite having 177 times fewer parameters, demonstrating its effectiveness.

Over the past year, data-driven global weather forecasting has emerged as a new alternative to traditional numerical weather prediction. This innovative approach yields forecasts of comparable accuracy at a tiny fraction of computational costs. Regrettably, as far as I know, existing models exclusively rely on regression losses, producing forecasts with substantial blurring. Such blurring, although compromises practicality, enjoys an unfair advantage on evaluation metrics. In this paper, I present Kunyu, a global data-driven weather forecasting model which delivers accurate predictions across a comprehensive array of atmospheric variables at 0.35{\deg} resolution. With both regression and adversarial losses integrated in its training framework, Kunyu generates forecasts with enhanced clarity and realism. Its performance outpaces even ECMWF HRES in some aspects such as the estimation of anomaly extremes, while remaining competitive with ECMWF HRES on evaluation metrics such as RMSE and ACC. Kunyu is an important step forward in closing the utility gap between numerical and data-driven weather prediction.

We present a method that uses a text-to-image model to generate consistent content across multiple image scales, enabling extreme semantic zooms into a scene, e.g., ranging from a wide-angle landscape view of a forest to a macro shot of an insect sitting on one of the tree branches. We achieve this through a joint multi-scale diffusion sampling approach that encourages consistency across different scales while preserving the integrity of each individual sampling process. Since each generated scale is guided by a different text prompt, our method enables deeper levels of zoom than traditional super-resolution methods that may struggle to create new contextual structure at vastly different scales. We compare our method qualitatively with alternative techniques in image super-resolution and outpainting, and show that our method is most effective at generating consistent multi-scale content.

Predicting typhoon intensity accurately across space and time is crucial for issuing timely disaster warnings and facilitating emergency response. This has vast potential for minimizing life losses and property damages as well as reducing economic and environmental impacts. Leveraging satellite imagery for scenario analysis is effective but also introduces additional challenges due to the complex relations among clouds and the highly dynamic context. Existing deep learning methods in this domain rely on convolutional neural networks (CNNs), which suffer from limited per-layer receptive fields. This limitation hinders their ability to capture long-range dependencies and global contextual knowledge during inference. In response, we introduce a novel approach, namely "Typhoon Intensity Transformer" (Tint), which leverages self-attention mechanisms with global receptive fields per layer. Tint adopts a sequence-to-sequence feature representation learning perspective. It begins by cutting a given satellite image into a sequence of patches and recursively employs self-attention operations to extract both local and global contextual relations between all patch pairs simultaneously, thereby enhancing per-patch feature representation learning.

The recent boom of linear forecasting models questions the ongoing passion for architectural modifications of Transformer-based forecasters. These forecasters leverage Transformers to model the global dependencies over temporal tokens of time series, with each token formed by multiple variates of the same timestamp. However, Transformers are challenged in forecasting series with larger lookback windows due to performance degradation and computation explosion. Besides, the embedding for each temporal token fuses multiple variates that represent potential delayed events and distinct physical measurements, which may fail in learning variate-centric representations and result in meaningless attention maps. In this work, we reflect on the competent duties of Transformer components and repurpose the Transformer architecture without any modification to the basic components. We propose iTransformer that simply applies the attention and feed-forward network on the inverted dimensions. Specifically, the time points of individual series are embedded into variate tokens which are utilized by the attention mechanism to capture multivariate correlations; meanwhile, the feed-forward network is applied for each variate token to learn nonlinear representations. The iTransformer model achieves state-of-the-art on challenging real-world datasets, which further empowers the Transformer family with promoted performance, generalization ability across different variates, and better utilization of arbitrary lookback windows, making it a nice alternative as the fundamental backbone of time series forecasting.

Historical records of climate fields are often sparse due to missing measurements, especially before the introduction of large-scale satellite missions. Several statistical and model-based methods have been introduced to fill gaps and reconstruct historical records. Here, we employ a recently introduced deep-learning approach based on Fourier convolutions, trained on numerical climate model output, to reconstruct historical climate fields. Using this approach we are able to realistically reconstruct large and irregular areas of missing data, as well as reconstruct known historical events such as strong El Ni\~no and La Ni\~na with very little given information. Our method outperforms the widely used statistical kriging method as well as other recent machine learning approaches. The model generalizes to higher resolutions than the ones it was trained on and can be used on a variety of climate fields. Moreover, it allows inpainting of masks never seen before during the model training.