In this paper, we intent to handle this emerging issue.

While numerous forecasters have been proposed using different network architectures, the Transformer-based models have state-of-the-art performance in time series forecasting.

The vast majority of time-series forecasting approaches require a substantial training dataset. However, many real-life forecasting applications have very little initial observations, sometimes just 40 or fewer. Thus, the applicability of most forecasting methods is restricted in data-sparse commercial applications.

We introduce Moirai 2.0, a decoder-only time-series foundation model trained on a new corpus of 36M series. The model adopts quantile forecasting and multi-token prediction, improving both probabilistic accuracy and inference efficiency. On the Gift-Eval benchmark, it ranks among the top pretrained models while achieving a strong trade-off between accuracy, speed, and model size. Compared to Moirai 1.0, Moirai 2.0 replaces masked-encoder training, multi-patch inputs, and mixture-distribution outputs with a simpler decoder-only architecture, single patch, and quantile loss. Ablation studies isolate these changes -- showing that the decoder-only backbone along with recursive multi-quantile decoding contribute most to the gains. Additional experiments show that Moirai 2.0 outperforms larger models from the same family and exhibits robust domain-level results. In terms of efficiency and model size, Moirai 2.0 is twice as fast and thirty times smaller than its prior best version, Moirai 1.0-Large, while also performing better. Model performance plateaus with increasing parameter count and declines at longer horizons, motivating future work on data scaling and long-horizon modeling. We release code and evaluation details to support further research.

Then, we propose FreTS, a simple yet effective architecture built upon Fre quency-domain MLPs for T ime S eries forecasting.

Time series forecasting is essential across diverse domains. While MLP-based methods have gained attention for achieving Transformer-comparable performance with fewer parameters and better robustness, they face critical limitations including loss of weak seasonal signals, capacity constraints in weight-sharing MLPs, and insufficient channel fusion in channel-independent strategies. To address these challenges, we propose MDMLP-EIA (Multi-domain Dynamic MLPs with Energy Invariant Attention) with three key innovations. First, we develop an adaptive fused dual-domain seasonal MLP that categorizes seasonal signals into strong and weak components. It employs an adaptive zero-initialized channel fusion strategy to minimize noise interference while effectively integrating predictions. Second, we introduce an energy invariant attention mechanism that adaptively focuses on different feature channels within trend and seasonal predictions across time steps. This mechanism maintains constant total signal energy to align with the decomposition-prediction-reconstruction framework and enhance robustness against disturbances. Third, we propose a dynamic capacity adjustment mechanism for channel-independent MLPs. This mechanism scales neuron count with the square root of channel count, ensuring sufficient capacity as channels increase. Extensive experiments across nine benchmark datasets demonstrate that MDMLP-EIA achieves state-of-the-art performance in both prediction accuracy and computational efficiency.

Coastal flooding poses increasing threats to communities worldwide, necessitating accurate and hyper-local inundation forecasting for effective emergency response. However, real-world deployment of forecasting systems is often constrained by sparse sensor networks, where only a limited subset of locations may have sensors due to budget constraints. To approach this challenge, we present DIFF -SPARSE, a masked conditional diffusion model designed for probabilistic coastal inundation forecasting from sparse sensor observations. DIFF -SPARSE primarily utilizes the inundation history of a location and its neighboring locations from a context time window as spatiotemporal context. The fundamental challenge of spatiotemporal prediction based on sparse observations in the context window is addressed by introducing a novel masking strategy during training. Digital elevation data and temporal co-variates are utilized as additional spatial and temporal contexts, respectively. A convolutional neural network and a conditional UNet architecture with cross-attention mechanism are employed to capture the spatiotemporal dynamics in the data. We trained and tested DIFF -SPARSE on coastal inundation data from the Eastern Shore of Virginia and systematically assessed the performance of DIFF -SPARSE across different sparsity levels 0%, 50%, 95% missing observations. Our experiment results show that DIFF -SPARSE achieves upto 62% improvement in terms of two forecasting performance metrics compared to existing methods, at 95% sparsity level. Moreover, our ablation studies reveal that digital elevation data becomes more useful at high sparsity levels compared to temporal co-variates.

Time Series Forecasting (TSF) faces persistent challenges in modeling intricate temporal dependencies across different scales. Despite recent advances leveraging different decomposition operations and novel architectures based on CNN, MLP or Transformer, existing methods still struggle with static decomposition strategies, fragmented dependency modeling, and inflexible fusion mechanisms, limiting their ability to model intricate temporal dependencies. To explicitly solve the mentioned three problems respectively, we propose a novel Dynamic Multi-Scale Coordination Framework (DMSC) with Multi-Scale Patch Decomposition block (EMPD), Triad Interaction Block (TIB) and Adaptive Scale Routing MoE block (ASR-MoE). Specifically, EMPD is designed as a built-in component to dynamically segment sequences into hierarchical patches with exponentially scaled granularities, eliminating predefined scale constraints through input-adaptive patch adjustment. TIB then jointly models intra-patch, inter-patch, and cross-variable dependencies within each layer's decomposed representations. EMPD and TIB are jointly integrated into layers forming a multi-layer progressive cascade architecture, where coarse-grained representations from earlier layers adaptively guide fine-grained feature extraction in subsequent layers via gated pathways. And ASR-MoE dynamically fuses multi-scale predictions by leveraging specialized global and local experts with temporal-aware weighting. Comprehensive experiments on thirteen real-world benchmarks demonstrate that DMSC consistently maintains state-of-the-art (SOTA) performance and superior computational efficiency for TSF tasks. Code is available at https://github.com/1327679995/DMSC.

Spectral Attention preserves long-period trends through a low-pass filter and facilitates gradient to flow between samples. Spectral Attention can be seamlessly integrated into most sequence models, allowing models with fixed-sized look-back windows to capture long-range dependencies over thousands of steps.