ICLR 2024 Papers

Climate and weather prediction traditionally relies on complex numerical simulations of atmospheric physics. Deep learning approaches, such as transformers, have recently challenged the simulation paradigm with complex network forecasts. However, they often act as data-driven black-box models that neglect the underlying physics and lack uncertainty quantification. We address these limitations with ClimODE, a spatiotemporal continuous-time process that implements a key principle of advection from statistical mechanics, namely, weather changes due to a spatial movement of quantities over time. ClimODE models precise weather evolution with value-conserving dynamics, learning global weather transport as a neural flow, which also enables estimating the uncertainty in predictions. Our approach outperforms existing data-driven methods in global and regional forecasting with an order of magnitude smaller parameterization, establishing a new state of the art.

We introduce a new model for multivariate probabilistic time series prediction, designed to flexibly address a range of tasks including forecasting, interpolation, and their combinations. Building on copula theory, we propose a simplified objective for the recently-introduced transformer-based attentional copulas (TACTiS), wherein the number of distributional parameters now scales linearly with the number of variables instead of factorially. The new objective requires the introduction of a training curriculum, which goes hand-in-hand with necessary changes to the original architecture. We show that the resulting model has significantly better training dynamics and achieves state-of-the-art performance across diverse real-world forecasting tasks, while maintaining the flexibility of prior work, such as seamless handling of unaligned and unevenly-sampled time series. Code is made available at https://github.com/ServiceNow/TACTiS.

Transformers have gained widespread usage in multivariate time series (MTS) forecasting, delivering impressive performance. Nonetheless, these existing transformer-based methods often neglect an essential aspect: the incorporation of uncertainty into the predicted series, which holds significant value in decision-making. In this paper, we introduce a Transformer-Modulated Diffusion Model (TMDM), uniting conditional diffusion generative process with transformers into a unified framework to enable precise distribution forecasting for MTS. TMDM harnesses the power of transformers to extract essential insights from historical time series data. This information is then utilized as prior knowledge, capturing covariate-dependence in both the forward and reverse processes within the diffusion model. Furthermore, we seamlessly integrate well-designed transformer-based forecasting methods into TMDM to enhance its overall performance. Additionally, we introduce two novel metrics for evaluating uncertainty estimation performance. Through extensive experiments on six datasets using four evaluation metrics, we establish the effectiveness of TMDM in probabilistic MTS forecasting.

Long-term forecasting presents unique challenges due to the time and memory complexity of handling long sequences. Existing methods, which rely on sliding windows to process long sequences, struggle to effectively capture long-term variations that are partially caught within the short window (i.e., outer-window variations). In this paper, we introduce a novel approach that overcomes this limitation by employing contrastive learning and enhanced decomposition architecture, specifically designed to focus on long-term variations. To this end, our contrastive loss incorporates global autocorrelation held in the whole time series, which facilitates the construction of positive and negative pairs in a self-supervised manner. When combined with our decomposition networks, our constrative learning significantly improves long-term forecasting performance. Extensive experiments demonstrate that our approach outperforms 14 baseline models on well-established nine long-term benchmarks, especially in challenging scenarios that require a significantly long output for forecasting. This paper not only presents a novel direction for long-term forecasting but also offers a more reliable method for effectively integrating long-term variations into time-series representation learning.

The diffusion model has been successfully used in many computer vision applications, such as text-guided image generation and image-to-image translation. Recently, there have been attempts on extending the diffusion model for time series data. However, these extensions are fairly straightforward and do not utilize the unique properties of time series data. As different patterns are usually exhibited at multiple scales of a time series, we in this paper leverage this multi-resolution temporal structure and propose the multi-resolution diffusion model (mr-Diff). By using the seasonal-trend decomposition, we sequentially extract fine-to-coarse trends from the time series for forward diffusion. The denoising process then proceeds in an easy-to-hard non-autoregressive manner. The coarsest trend is generated first. Finer details are progressively added, using the predicted coarser trends as condition variables. Experimental results on nine real-world time series datasets demonstrate that mr-Diff outperforms state-of-the-art time series diffusion models. It is also better than or comparable across a wide variety of advanced time series prediction models.

Transformers for time series forecasting mainly model time series from limited or fixed scales, making it challenging to capture different characteristics spanning various scales. We propose Pathformer, a multi-scale Transformer with adaptive pathways. It integrates both temporal resolution and temporal distance for multi-scale modeling. Multi-scale division divides the time series into different temporal resolutions using patches of various sizes. Based on the division of each scale, dual attention is performed over these patches to capture global correlations and local details as temporal dependencies. We further enrich the multi-scale Transformer with adaptive pathways, which adaptively adjust the multi-scale modeling process based on the varying temporal dynamics of the input, improving the accuracy and generalization of Pathformer. Extensive experiments on eleven real-world datasets demonstrate that Pathformer not only achieves state-of-the-art performance by surpassing all current models but also exhibits stronger generalization abilities under various transfer scenarios. The code is made available at https://github.com/decisionintelligence/pathformer.

Convolutional neural network (CNN)-based and Transformer-based methods have recently made significant strides in time series forecasting, which excel at modeling local temporal variations or capturing long-term dependencies. However, real-world time series usually contain intricate temporal patterns, thus making it challenging for existing methods that mainly focus on temporal variations modeling from the 1D time series directly. Based on the intrinsic periodicity of time series, we propose a novel Periodicity Decoupling Framework (PDF) to capture 2D temporal variations of decoupled series for long-term series forecasting. Our PDF mainly consists of three components: multi-periodic decoupling block (MDB), dual variations modeling block (DVMB), and variations aggregation block (VAB). Unlike the previous methods that model 1D temporal variations, our PDF mainly models 2D temporal variations, decoupled from 1D time series by MDB. After that, DVMB attempts to further capture short-term and long-term variations, followed by VAB to make final predictions. Extensive experimental results across seven real-world long-term time series datasets demonstrate the superiority of our method over other state-of-the-art methods, in terms of both forecasting performance and computational efficiency. Code is available at https://github.com/Hank0626/PDF.

Transparent machine learning (ML) models are essential for ensuring interpretability and trustworthiness in decision-making systems, particularly in high-stakes domains such as healthcare, finance, and criminal justice. While transparent machine learning models have been proposed for classification and regression, time series forecasting presents some unique challenges for ensuring transparency. In particular, currently used bottom-up approaches that focus on the values of the time series at specific time points (usually regularly spaced) do not provide a holistic understanding of the entire time series. This limits the applicability of ML in many critical areas. To open up these domains for ML, we propose a top-down framework of bi-level transparency, which involves understanding the higher-level trends and the lower-level properties of the predicted time series. Applying this framework, we develop TIMEVIEW, a transparent ML model for time series forecasting based on static features, complemented with an interactive visualization tool. Through a series of experiments, we demonstrate the efficacy and interpretability of our approach, paving the way for more transparent and reliable applications of ML in various domains.

Multivariate time series forecasting plays an important role in various applications ranging from meteorology study, traffic management to economics planning. In the past decades, many efforts have been made toward accurate and reliable forecasting methods development under the assumption of intact input data. However, the time series data from real-world scenarios is often partially observed due to device malfunction or costly data acquisition, which can seriously impede the performance of the existing approaches. A naive employment of imputation methods unavoidably involves error accumulation and leads to suboptimal solutions. Motivated by this, we propose a Biased Temporal Convolution Graph Network that jointly captures the temporal dependencies and spatial structure. In particular, we inject bias into the two carefully developed modules, the Multi-Scale Instance PartialTCN and Biased GCN, to account for missing patterns. The experimental results show that our proposed model is able to achieve up to $9.93$\% improvements over the existing methods on five real-world benchmark datasets. Our code is available at: https://github.com/chenxiaodanhit/BiTGraph.

Recent studies have demonstrated the great power of Transformer models for time series forecasting. One of the key elements that lead to the transformer's success is the channel-independent (CI) strategy to improve the training robustness. However, the ignorance of the correlation among different channels in CI would limit the model's forecasting capacity. In this work, we design a special Transformer, i.e., **C**hannel **A**ligned **R**obust Blen**d** Transformer (CARD for short), that addresses key shortcomings of CI type Transformer in time series forecasting. First, CARD introduces a channel-aligned attention structure that allows it to capture both temporal correlations among signals and dynamical dependence among multiple variables over time. Second, in order to efficiently utilize the multi-scale knowledge, we design a token blend module to generate tokens with different resolutions. Third, we introduce a robust loss function for time series forecasting to alleviate the potential overfitting issue. This new loss function weights the importance of forecasting over a finite horizon based on prediction uncertainties. Our evaluation of multiple long-term and short-term forecasting datasets demonstrates that CARD significantly outperforms state-of-the-art time series forecasting methods. The code is available at the following repository: https://github.com/wxie9/CARD.

Recently, channel-independent methods have achieved state-of-the-art performance in multivariate time series (MTS) forecasting. Despite reducing overfitting risks, these methods miss potential opportunities in utilizing channel dependence for accurate predictions. We argue that there exist locally stationary lead-lag relationships between variates, i.e., some lagged variates may follow the leading indicators within a short time period. Exploiting such channel dependence is beneficial since leading indicators offer advance information that can be used to reduce the forecasting difficulty of the lagged variates. In this paper, we propose a new method named LIFT that first efficiently estimates leading indicators and their leading steps at each time step and then judiciously allows the lagged variates to utilize the advance information from leading indicators. LIFT plays as a plugin that can be seamlessly collaborated with arbitrary time series forecasting methods. Extensive experiments on six real-world datasets demonstrate that LIFT improves the state-of-the-art methods by 5.4% in average forecasting performance. Our code is available at https://github.com/SJTU-Quant/LIFT.

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. Code is available at this repository: https://github.com/thuml/iTransformer.

Long-term time series forecasting (LTSF) is important for various domains but is confronted by challenges in handling the complex temporal-contextual relationships. As multivariate input models underperforming some recent univariate counterparts, we posit that the issue lies in the inefficiency of existing multivariate LTSF Transformers to model series-wise relationships: the characteristic differences between series are often captured incorrectly. To address this, we introduce ARM: a multivariate temporal-contextual adaptive learning method, which is an enhanced architecture specifically designed for multivariate LTSF modelling. ARM employs Adaptive Univariate Effect Learning (**A**UEL), Random Dropping (**R**D) training strategy, and Multi-kernel Local Smoothing (**M**KLS), to better handle individual series temporal patterns and correctly learn inter-series dependencies. ARM demonstrates superior performance on multiple benchmarks without significantly increasing computational costs compared to vanilla Transformer, thereby advancing the state-of-the-art in LTSF. ARM is also generally applicable to other LTSF architecture beyond vanilla Transformer.

Time series forecasting is widely used in extensive applications, such as traffic planning and weather forecasting. However, real-world time series usually present intricate temporal variations, making forecasting extremely challenging. Going beyond the mainstream paradigms of plain decomposition and multiperiodicity analysis, we analyze temporal variations in a novel view of multiscale-mixing, where time series present distinct patterns in different sampling scales. Specifically, the microscopic and the macroscopic information are reflected in fine and coarse scales, respectively, and thereby complex variations are inherently disentangled. Based on this observation, we propose TimeMixer as a fully MLP-based architecture with Past-Decomposable-Mixing (PDM) and Future-Multipredictor-Mixing (FMM) blocks to take full advantage of disentangled multiscale series in both past extraction and future prediction phases. Concretely, PDM applies the decomposition to multiscale series and further mixes the decomposed seasonal and trend components in fine-to-coarse and coarse-to-fine directions separately, which successively aggregates the microscopic seasonal and macroscopic trend information. FMM further ensembles multiple predictors to utilize complementary forecasting capabilities in multiscale observations. Consequently, our proposed TimeMixer is able to achieve consistent state-of-the-art performances in both long-term and short-term forecasting tasks with favorable run-time efficiency.

It is challenging to scale time series forecasting models such that they forecast accurately for multiple distinct domains and datasets, all with potentially different underlying collection procedures (e.g., sample resolution), patterns (e.g., periodicity), and prediction requirements (e.g., reconstruction vs. forecasting). We call this general task universal forecasting. Existing methods usually assume that input data is regularly sampled, and they forecast to pre-determined horizons, resulting in failure to generalise outside of the scope of their training. We propose the DAM -- a neural model that takes randomly sampled histories and outputs an adjustable basis composition as a continuous function of time for forecasting to non-fixed horizons. It involves three key components: (1) a flexible approach for using randomly sampled histories from a long-tail distribution, that enables an efficient global perspective of the underlying temporal dynamics while retaining focus on the recent history; (2) a transformer backbone that is trained on these actively sampled histories to produce, as representational output, (3) the basis coefficients of a continuous function of time. We show that a single univariate DAM, trained on 25 time series datasets, either outperformed or closely matched existing SoTA models at multivariate long-term forecasting across 18 datasets, including 8 held-out for zero-shot transfer, even though these models were trained to specialise for each dataset-horizon combination. This single DAM excels at zero-shot transfer and very-long-term forecasting, performs well at imputation, is interpretable via basis function composition and attention, can be tuned for different inference-cost requirements, is robust to missing and irregularly sampled data by design.