Maximizing the Impact of Deep Learning on Subseasonal-to-Seasonal Climate Forecasting: The Essential Role of Optimization

Weather and climate forecasting is vital for sectors such as agriculture and disaster management. Although numerical weather prediction (NWP) systems have advanced, forecasting at the subseasonal-to-seasonal (S2S) scale, spanning 2 to 6 weeks, remains challenging due to the chaotic and sparse atmospheric signals at this interval. Even state-of-the-art deep learning models struggle to outperform simple climatology models in this domain. This paper identifies that optimization, instead of network structure, could be the root cause of this performance gap, and then we develop a novel multi-stage optimization strategy to close the gap. Extensive empirical studies demonstrate that our multi-stage optimization approach significantly improves key skill metrics, PCC and TCC, while utilizing the same backbone structure, surpassing the state-of-the-art NWP systems (ECMWF-S2S) by over \textbf{19-91\%}. Our research contests the recent study that direct forecasting outperforms rolling forecasting for S2S tasks. Through theoretical analysis, we propose that the underperformance of rolling forecasting may arise from the accumulation of Jacobian matrix products during training. Our multi-stage framework can be viewed as a form of teacher forcing to address this issue. Code is available at \url{https://anonymous.4open.science/r/Baguan-S2S-23E7/}

Guided MRI Reconstruction via Schrödinger Bridge

Magnetic Resonance Imaging (MRI) is a multi-contrast imaging technique in which different contrast images share similar structural information. However, conventional diffusion models struggle to effectively leverage this structural similarity. Recently, the Schr\"odinger Bridge (SB), a nonlinear extension of the diffusion model, has been proposed to establish diffusion paths between any distributions, allowing the incorporation of guided priors. This study proposes an SB-based, multi-contrast image-guided reconstruction framework that establishes a diffusion bridge between the guiding and target image distributions. By using the guiding image along with data consistency during sampling, the target image is reconstructed more accurately. To better address structural differences between images, we introduce an inversion strategy from the field of image editing, termed $\mathbf{I}^2$SB-inversion. Experiments on a paried T1 and T2-FLAIR datasets demonstrate that $\mathbf{I}^2$SB-inversion achieve a high acceleration up to 14.4 and outperforms existing methods in terms of both reconstruction accuracy and stability.

Mitigating Time Discretization Challenges with WeatherODE: A Sandwich Physics-Driven Neural ODE for Weather Forecasting

In the field of weather forecasting, traditional models often grapple with discretization errors and time-dependent source discrepancies, which limit their predictive performance. In this paper, we present WeatherODE, a novel one-stage, physics-driven ordinary differential equation (ODE) model designed to enhance weather forecasting accuracy. By leveraging wave equation theory and integrating a time-dependent source model, WeatherODE effectively addresses the challenges associated with time-discretization error and dynamic atmospheric processes. Moreover, we design a CNN-ViT-CNN sandwich structure, facilitating efficient learning dynamics tailored for distinct yet interrelated tasks with varying optimization biases in advection equation estimation. Through rigorous experiments, WeatherODE demonstrates superior performance in both global and regional weather forecasting tasks, outperforming recent state-of-the-art approaches by significant margins of over 40.0\% and 31.8\% in root mean square error (RMSE), respectively. The source code is available at \url{https://github.com/DAMO-DI-ML/WeatherODE}.

Less is more: Embracing sparsity and interpolation with Esiformer for time series forecasting

Time series forecasting has played a significant role in many practical fields. But time series data generated from real-world applications always exhibits high variance and lots of noise, which makes it difficult to capture the inherent periodic patterns of the data, hurting the prediction accuracy significantly. To address this issue, we propose the Esiformer, which apply interpolation on the original data, decreasing the overall variance of the data and alleviating the influence of noise. What's more, we enhanced the vanilla transformer with a robust Sparse FFN. It can enhance the representation ability of the model effectively, and maintain the excellent robustness, avoiding the risk of overfitting compared with the vanilla implementation. Through evaluations on challenging real-world datasets, our method outperforms leading model PatchTST, reducing MSE by 6.5% and MAE by 5.8% in multivariate time series forecasting. Code is available at: https://github.com/yyg1282142265/Esiformer/tree/main.

Unlocking the Power of LSTM for Long Term Time Series Forecasting

Traditional recurrent neural network architectures, such as long short-term memory neural networks (LSTM), have historically held a prominent role in time series forecasting (TSF) tasks. While the recently introduced sLSTM for Natural Language Processing (NLP) introduces exponential gating and memory mixing that are beneficial for long term sequential learning, its potential short memory issue is a barrier to applying sLSTM directly in TSF. To address this, we propose a simple yet efficient algorithm named P-sLSTM, which is built upon sLSTM by incorporating patching and channel independence. These modifications substantially enhance sLSTM's performance in TSF, achieving state-of-the-art results. Furthermore, we provide theoretical justifications for our design, and conduct extensive comparative and analytical experiments to fully validate the efficiency and superior performance of our model.

S$^3$Attention: Improving Long Sequence Attention with Smoothed Skeleton Sketching

Attention based models have achieved many remarkable breakthroughs in numerous applications. However, the quadratic complexity of Attention makes the vanilla Attention based models hard to apply to long sequence tasks. Various improved Attention structures are proposed to reduce the computation cost by inducing low rankness and approximating the whole sequence by sub-sequences. The most challenging part of those approaches is maintaining the proper balance between information preservation and computation reduction: the longer sub-sequences used, the better information is preserved, but at the price of introducing more noise and computational costs. In this paper, we propose a smoothed skeleton sketching based Attention structure, coined S$^3$Attention, which significantly improves upon the previous attempts to negotiate this trade-off. S$^3$Attention has two mechanisms to effectively minimize the impact of noise while keeping the linear complexity to the sequence length: a smoothing block to mix information over long sequences and a matrix sketching method that simultaneously selects columns and rows from the input matrix. We verify the effectiveness of S$^3$Attention both theoretically and empirically. Extensive studies over Long Range Arena (LRA) datasets and six time-series forecasting show that S$^3$Attention significantly outperforms both vanilla Attention and other state-of-the-art variants of Attention structures.

Sparse-VQ Transformer: An FFN-Free Framework with Vector Quantization for Enhanced Time Series Forecasting

Time series analysis is vital for numerous applications, and transformers have become increasingly prominent in this domain. Leading methods customize the transformer architecture from NLP and CV, utilizing a patching technique to convert continuous signals into segments. Yet, time series data are uniquely challenging due to significant distribution shifts and intrinsic noise levels. To address these two challenges,we introduce the Sparse Vector Quantized FFN-Free Transformer (Sparse-VQ). Our methodology capitalizes on a sparse vector quantization technique coupled with Reverse Instance Normalization (RevIN) to reduce noise impact and capture sufficient statistics for forecasting, serving as an alternative to the Feed-Forward layer (FFN) in the transformer architecture. Our FFN-free approach trims the parameter count, enhancing computational efficiency and reducing overfitting. Through evaluations across ten benchmark datasets, including the newly introduced CAISO dataset, Sparse-VQ surpasses leading models with a 7.84% and 4.17% decrease in MAE for univariate and multivariate time series forecasting, respectively. Moreover, it can be seamlessly integrated with existing transformer-based models to elevate their performance.

FusionSF: Fuse Heterogeneous Modalities in a Vector Quantized Framework for Robust Solar Power Forecasting

Accurate solar power forecasting is crucial to integrate photovoltaic plants into the electric grid, schedule and secure the power grid safety. This problem becomes more demanding for those newly installed solar plants which lack sufficient data. Current research predominantly relies on historical solar power data or numerical weather prediction in a single-modality format, ignoring the complementary information provided in different modalities. In this paper, we propose a multi-modality fusion framework to integrate historical power data, numerical weather prediction, and satellite images, significantly improving forecast performance. We introduce a vector quantized framework that aligns modalities with varying information densities, striking a balance between integrating sufficient information and averting model overfitting. Our framework demonstrates strong zero-shot forecasting capability, which is especially useful for those newly installed plants. Moreover, we collect and release a multi-modal solar power (MMSP) dataset from real-world plants to further promote the research of multi-modal solar forecasting algorithms. Our extensive experiments show that our model not only operates with robustness but also boosts accuracy in both zero-shot forecasting and scenarios rich with training data, surpassing leading models. We have incorporated it into our eForecaster platform and deployed it for more than 300 solar plants with a capacity of over 15GW.

Attention as Robust Representation for Time Series Forecasting

Time series forecasting is essential for many practical applications, with the adoption of transformer-based models on the rise due to their impressive performance in NLP and CV. Transformers' key feature, the attention mechanism, dynamically fusing embeddings to enhance data representation, often relegating attention weights to a byproduct role. Yet, time series data, characterized by noise and non-stationarity, poses significant forecasting challenges. Our approach elevates attention weights as the primary representation for time series, capitalizing on the temporal relationships among data points to improve forecasting accuracy. Our study shows that an attention map, structured using global landmarks and local windows, acts as a robust kernel representation for data points, withstanding noise and shifts in distribution. Our method outperforms state-of-the-art models, reducing mean squared error (MSE) in multivariate time series forecasting by a notable 3.6% without altering the core neural network architecture. It serves as a versatile component that can readily replace recent patching based embedding schemes in transformer-based models, boosting their performance.

SVQ: Sparse Vector Quantization for Spatiotemporal Forecasting

Spatiotemporal forecasting tasks, such as weather forecasting and traffic prediction, offer significant societal benefits. These tasks can be effectively approached as image forecasting problems using computer vision models. Vector quantization (VQ) is a well-known method for discrete representation that improves the latent space, leading to enhanced generalization and transfer learning capabilities. One of the main challenges in using VQ for spatiotemporal forecasting is how to balance between keeping enough details and removing noises from the original patterns for better generalization. We address this challenge by developing sparse vector quantization, or {\bf SVQ} for short, that leverages sparse regression to make better trade-off between the two objectives. The main innovation of this work is to approximate sparse regression by a two-layer MLP and a randomly fixed or learnable matrix, dramatically improving its computational efficiency. Through experiments conducted on diverse datasets in multiple fields including weather forecasting, traffic flow prediction, and video forecasting, we unequivocally demonstrate that our proposed method consistently enhances the performance of base models and achieves state-of-the-art results across all benchmarks.