Dynamical Diffusion: Learning Temporal Dynamics with Diffusion Models

Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong performance across various tasks and modalities, their application to temporal predictive learning remains underexplored. Existing approaches treat predictive learning as a conditional generation problem, but often fail to fully exploit the temporal dynamics inherent in the data, leading to challenges in generating temporally coherent sequences. To address this, we introduce Dynamical Diffusion (DyDiff), a theoretically sound framework that incorporates temporally aware forward and reverse processes. Dynamical Diffusion explicitly models temporal transitions at each diffusion step, establishing dependencies on preceding states to better capture temporal dynamics. Through the reparameterization trick, Dynamical Diffusion achieves efficient training and inference similar to any standard diffusion model. Extensive experiments across scientific spatiotemporal forecasting, video prediction, and time series forecasting demonstrate that Dynamical Diffusion consistently improves performance in temporal predictive tasks, filling a crucial gap in existing methodologies. Code is available at this repository: https://github.com/thuml/dynamical-diffusion.

TimesBERT: A BERT-Style Foundation Model for Time Series Understanding

Time series analysis is crucial in diverse scenarios. Beyond forecasting, considerable real-world tasks are categorized into classification, imputation, and anomaly detection, underscoring different capabilities termed time series understanding in this paper. While GPT-style models have been positioned as foundation models for time series forecasting, the BERT-style architecture, which has made significant advances in natural language understanding, has not been fully unlocked for time series understanding, possibly attributed to the undesirable dropout of essential elements of BERT. In this paper, inspired by the shared multi-granularity structure between multivariate time series and multisentence documents, we design TimesBERT to learn generic representations of time series including temporal patterns and variate-centric characteristics. In addition to a natural adaptation of masked modeling, we propose a parallel task of functional token prediction to embody vital multi-granularity structures. Our model is pre-trained on 260 billion time points across diverse domains. Leveraging multi-granularity representations, TimesBERT achieves state-of-the-art performance across four typical downstream understanding tasks, outperforming task-specific models and language pre-trained backbones, positioning it as a versatile foundation model for time series understanding.

LEDD: Large Language Model-Empowered Data Discovery in Data Lakes

Data discovery in data lakes with ever increasing datasets has long been recognized as a big challenge in the realm of data management, especially for semantic search of and hierarchical global catalog generation of tables. While large language models (LLMs) facilitate the processing of data semantics, challenges remain in architecting an end-to-end system that comprehensively exploits LLMs for the two semantics-related tasks. In this demo, we propose LEDD, an end-to-end system with an extensible architecture that leverages LLMs to provide hierarchical global catalogs with semantic meanings and semantic table search for data lakes. Specifically, LEDD can return semantically related tables based on natural-language specification. These features make LEDD an ideal foundation for downstream tasks such as model training and schema linking for text-to-SQL tasks. LEDD also provides a simple Python interface to facilitate the extension and the replacement of data discovery algorithms.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Although deep models have been widely explored in solving partial differential equations (PDEs), previous works are primarily limited to data only with up to tens of thousands of mesh points, far from the million-point scale required by industrial simulations that involve complex geometries. In the spirit of advancing neural PDE solvers to real industrial applications, we present Transolver++, a highly parallel and efficient neural solver that can accurately solve PDEs on million-scale geometries. Building upon previous advancements in solving PDEs by learning physical states via Transolver, Transolver++ is further equipped with an extremely optimized parallelism framework and a local adaptive mechanism to efficiently capture eidetic physical states from massive mesh points, successfully tackling the thorny challenges in computation and physics learning when scaling up input mesh size. Transolver++ increases the single-GPU input capacity to million-scale points for the first time and is capable of continuously scaling input size in linear complexity by increasing GPUs. Experimentally, Transolver++ yields 13% relative promotion across six standard PDE benchmarks and achieves over 20% performance gain in million-scale high-fidelity industrial simulations, whose sizes are 100$\times$ larger than previous benchmarks, covering car and 3D aircraft designs.

ProPINN: Demystifying Propagation Failures in Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) have earned high expectations in solving partial differential equations (PDEs), but their optimization usually faces thorny challenges due to the unique derivative-dependent loss function. By analyzing the loss distribution, previous research observed the propagation failure phenomenon of PINNs, intuitively described as the correct supervision for model outputs cannot ``propagate'' from initial states or boundaries to the interior domain. Going beyond intuitive understanding, this paper provides the first formal and in-depth study of propagation failure and its root cause. Based on a detailed comparison with classical finite element methods, we ascribe the failure to the conventional single-point-processing architecture of PINNs and further prove that propagation failure is essentially caused by the lower gradient correlation of PINN models on nearby collocation points. Compared to superficial loss maps, this new perspective provides a more precise quantitative criterion to identify where and why PINN fails. The theoretical finding also inspires us to present a new PINN architecture, named ProPINN, which can effectively unite the gradient of region points for better propagation. ProPINN can reliably resolve PINN failure modes and significantly surpass advanced Transformer-based models with 46% relative promotion.

Sundial: A Family of Highly Capable Time Series Foundation Models

We introduce Sundial, a family of native, flexible, and scalable time series foundation models. To predict the next-patch's distribution, we propose a TimeFlow Loss based on flow-matching, which facilitates native pre-training of Transformers on time series without discrete tokenization. Conditioned on arbitrary-length time series, our model is pre-trained without specifying any prior distribution and can generate multiple probable predictions, achieving flexibility in representation learning beyond using parametric densities. Towards time series foundation models, we leverage minimal but crucial adaptations of Transformers and curate TimeBench with 1 trillion time points, comprising mostly real-world datasets and synthetic data. By mitigating mode collapse through TimeFlow Loss, we pre-train a family of Sundial models on TimeBench, which exhibit unprecedented model capacity and generalization performance on zero-shot forecasting. In addition to presenting good scaling behavior, Sundial achieves new state-of-the-art on both point forecasting and probabilistic forecasting benchmarks. We believe that Sundial's pioneering generative paradigm will facilitate a wide variety of forecasting scenarios.

Timer-XL: Long-Context Transformers for Unified Time Series Forecasting

We present Timer-XL, a generative Transformer for unified time series forecasting. To uniformly predict 1D and 2D time series, we generalize next token prediction, predominantly adopted for causal generation of 1D sequences, to multivariate next token prediction. The proposed paradigm uniformly formulates various forecasting scenarios as a long-context generation problem. We opt for the generative Transformer, which can capture global-range and causal dependencies while providing contextual flexibility, to implement unified forecasting on univariate series characterized by non-stationarity, multivariate time series with complicated dynamics and correlations, and covariate-informed contexts that include both endogenous and exogenous variables. Technically, we propose a universal TimeAttention to facilitate generative Transformers on time series, which can effectively capture fine-grained intra- and inter-series dependencies of flattened time series tokens (patches) and is further strengthened by position embeddings in both temporal and variable dimensions. Timer-XL achieves state-of-the-art performance across challenging forecasting benchmarks through a unified approach. As a large time series model, it demonstrates notable model transferability by large-scale pre-training, as well as contextual flexibility in token lengths, positioning it as a one-for-all forecaster.

Metadata Matters for Time Series: Informative Forecasting with Transformers

Time series forecasting is prevalent in extensive real-world applications, such as financial analysis and energy planning. Previous studies primarily focus on time series modality, endeavoring to capture the intricate variations and dependencies inherent in time series. Beyond numerical time series data, we notice that metadata (e.g.~dataset and variate descriptions) also carries valuable information essential for forecasting, which can be used to identify the application scenario and provide more interpretable knowledge than digit sequences. Inspired by this observation, we propose a Metadata-informed Time Series Transformer (MetaTST), which incorporates multiple levels of context-specific metadata into Transformer forecasting models to enable informative time series forecasting. To tackle the unstructured nature of metadata, MetaTST formalizes them into natural languages by pre-designed templates and leverages large language models (LLMs) to encode these texts into metadata tokens as a supplement to classic series tokens, resulting in an informative embedding. Further, a Transformer encoder is employed to communicate series and metadata tokens, which can extend series representations by metadata information for more accurate forecasting. This design also allows the model to adaptively learn context-specific patterns across various scenarios, which is particularly effective in handling large-scale, diverse-scenario forecasting tasks. Experimentally, MetaTST achieves state-of-the-art compared to advanced time series models and LLM-based methods on widely acknowledged short- and long-term forecasting benchmarks, covering both single-dataset individual and multi-dataset joint training settings.

Deep Time Series Models: A Comprehensive Survey and Benchmark

Time series, characterized by a sequence of data points arranged in a discrete-time order, are ubiquitous in real-world applications. Different from other modalities, time series present unique challenges due to their complex and dynamic nature, including the entanglement of nonlinear patterns and time-variant trends. Analyzing time series data is of great significance in real-world scenarios and has been widely studied over centuries. Recent years have witnessed remarkable breakthroughs in the time series community, with techniques shifting from traditional statistical methods to advanced deep learning models. In this paper, we delve into the design of deep time series models across various analysis tasks and review the existing literature from two perspectives: basic modules and model architectures. Further, we develop and release Time Series Library (TSLib) as a fair benchmark of deep time series models for diverse analysis tasks, which implements 24 mainstream models, covers 30 datasets from different domains, and supports five prevalent analysis tasks. Based on TSLib, we thoroughly evaluate 12 advanced deep time series models on different tasks. Empirical results indicate that models with specific structures are well-suited for distinct analytical tasks, which offers insights for research and adoption of deep time series models. Code is available at https://github.com/thuml/Time-Series-Library.

RoPINN: Region Optimized Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) have been widely applied to solve partial differential equations (PDEs) by enforcing outputs and gradients of deep models to satisfy target equations. Due to the limitation of numerical computation, PINNs are conventionally optimized on finite selected points. However, since PDEs are usually defined on continuous domains, solely optimizing models on scattered points may be insufficient to obtain an accurate solution for the whole domain. To mitigate this inherent deficiency of the default scatter-point optimization, this paper proposes and theoretically studies a new training paradigm as region optimization. Concretely, we propose to extend the optimization process of PINNs from isolated points to their continuous neighborhood regions, which can theoretically decrease the generalization error, especially for hidden high-order constraints of PDEs. A practical training algorithm, Region Optimized PINN (RoPINN), is seamlessly derived from this new paradigm, which is implemented by a straightforward but effective Monte Carlo sampling method. By calibrating the sampling process into trust regions, RoPINN finely balances sampling efficiency and generalization error. Experimentally, RoPINN consistently boosts the performance of diverse PINNs on a wide range of PDEs without extra backpropagation or gradient calculation.