Multivariate Time Series Forecasting

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46 papers in the last four weeks, up 39% on the four weeks before. 0.3% of all new papers.

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Latest papers 223

Jun 3, 2026cs.LG

An Empirical Audit of Input Encoders for Multi-Channel Signal Transformers

Transformers consuming multi-channel scalar signals must embed

C

simultaneous values into one

d_{\text{model}}

-dimensional vector per time step. We audit eight input encoders -- a shared-scalar baseline, per-channel linear projections, an orthogonality regulariser, a nonlinear MLP, block-partitioned concatenation, channel-independent and channel-as-token architectures, and a projected positional encoding -- on a synthetic benchmark where channel identity is informative and on ETTh1, scored by next-step negative log-likelihood. The headline is practical near-equivalence within a wide "top tier": the standard per-channel linear projection matches every alternative up to small, statistically real but practically modest differences. A direct geometric probe attributes this to a spontaneous orthogonalisation of the per-channel projections: they end up near-orthogonal with no explicit regulariser, letting the standard linear recover channel identity from the summed embedding. Two encoders lose decisively: the shared-scalar baseline collapses for information-theoretic reasons we make explicit, and the channel-independent PatchTST-spirit baseline overfits universally on the synthetic benchmark and underperforms on both. Paired tests resolve two small gaps: projecting the sinusoidal positional encoding through a learned linear layer edges the rest at small

C

by extending this orthogonality to the positional subspace; a nonlinear MLP stem edges them at the largest

C

, with the gap shrinking under more training data. The practical recommendation: use the standard per-channel linear projection by default; reach for something more elaborate only when the task calls for it.

Ossi Lehtinen

Ocon Oy

Multivariate Time Series Forecasting Time Series Transformers

Jun 3, 2026stat.ML

REGAIN: REconciliation GAIN-driven Auxiliary Direction Learning

Forecast reconciliation usually starts from a fixed measurement system and asks how forecasts should be projected onto a coherent space. We ask a different question: which additional linear measurements should be forecast and included in the reconciliation system? We propose REGAIN, a reconciliation-gain framework that learns normalized auxiliary directions, forecasts the induced series with a frozen forecasting oracle, and selects directions by their target-weighted loss reduction after augmented generalized least-squares reconciliation. Unlike variance-based components or predictability-based auxiliary selection, REGAIN optimizes the downstream effect of an auxiliary measurement on the final reconciled forecasts. We provide a statistical characterization showing that useful auxiliary directions must provide complementary information about unresolved target uncertainty, rather than merely being easy to forecast. The analysis also clarifies the covariance-risk reduction mechanism, the role of bias changes in realized quadratic risk, and the stability of estimated gain signals. A stagewise learning algorithm with held-out gain screening is developed, together with an optional joint refinement step. Experiments on Beijing PM2.5 and Australian Tourism data show that gain-selected measurements can improve both ordinary multivariate and hierarchical forecasts, especially when they reveal residual uncertainty not captured by the original measurement system.

Weijia Li, Shun Hu, Yanfei Kang

School of Mathematical Sciences, Beihang University, Beijing, China · School of Economics and Management, Beihang University, Beijing, China

Multivariate Time Series Forecasting Time Series Forecasting

Jun 2, 2026cs.LG

TiWeaver: Unified Temporal Dynamics Modeling via Contextual Patching

Multivariate time series forecasting plays a critical role in real-world applications, including weather prediction, stock analysis, and health monitoring. Due to the diversity of data sources, time series exhibit diverse temporal dynamics, often accompanied by various irregularities such as missing values and non-uniform sampling frequencies. Such irregularities lead to complex and asynchronous temporal dependencies across channels. Thus, a single model with a fixed patching scheme often fails to adapt well to diverse multivariate time series, hindering accurate forecasting. In this paper, we propose TiWeaver, a unified framework designed to handle temporal dynamics and fine-grained inter-channel dependencies adaptively. Specifically, we introduce a Graph-Guided Adaptive Tokenizer (G

^2

AT) that divides time series into high contextually coherent patches by jointly considering temporal density and representation consistency. In addition, we propose a Fine-grained Asynchronous Dependency Extractor (FADE), which is designed to model fine-grained asynchronous inter-channel dependencies while incorporating long-term historical dependencies. We evaluate TiWeaver on 12 real-world time series datasets, where it achieves state-of-the-art performance, outperforming existing methods up to 25%. These results demonstrate its robustness and effectiveness across diverse domains and data characteristics.

Zhe Li, Jindong Tian, Hao Miao +3

East China Normal University Shanghai, China · Hong Kong Polytechnic University Hong Kong, China · Aalborg University Aalborg, Denmark

Irregular Time-Series Modeling Multivariate Time Series Forecasting

Jun 1, 2026astro-ph.IM

Data-Driven Forecasting of three-Component Seismograms Using Transformer Architectures

Forecasting seismic waveforms beyond observed data remains challenging due to the nonlinear, dispersive, and multi-scale nature of seismic wave propagation. In this work, we introduce \textsc{SeismoGPT}, a transformer-based autoregressive model designed to forecast three-component seismic waveforms directly in the time domain. Forecasting is formulated as a physically constrained continuation problem in which the model receives waveform context beginning at the P-wave arrival and extending a defined time beyond the S-wave arrival, after which future motion is generated recursively without access to ground-truth samples. Evaluation is performed on synthetic seismograms spanning source depths of 5--100,km, epicentral distances of 10--90

^\circ

, and magnitudes

3 \leq M_w \leq 7

. To disentangle the effects of context length and prediction horizon, we define three evaluation configurations using a distance-normalized context ratio and fixed prediction horizons of 120 and 240,s. Across all configurations, the model achieves a median normalized cross correlation of 0.93 or higher. Analysis of representative forecasts shows that successful predictions preserve both phase coherence and spectral energy distribution. Where failure cases arise, this is primarily due to gradual phase drift during autoregressive rollout rather than unphysical signal generation. These results demonstrate that transformer-based sequence models can learn stable dynamical continuation of seismic wavefields, highlighting the potential of foundation-model approaches for physics-driven time-series forecasting. There are potential applications of this methodology in seismic warning and hazard mitigation, particularly for next-generation gravitational-wave observatories, such as the Einstein Telescope.

Waleed Esmail, Stuart Russell, Jana Klinge +2

Institut für Kernphysik, Universität Münster, Wilhelm-Klemm-Straße 9, 48149, Münster · Institut für Geophysik, Universität Münster, Corrensstraße 24, 48149, Münster · James Cook University, 1 James Cook Drive, Douglas, Queensland, 4814, Australia +1

Multivariate Time Series Forecasting Time Series Forecasting Seismology Time Series Transformers Autoregressive Modeling

Jun 1, 2026cs.LG

RESCAST-100K: A Comprehensive Dataset for Cross-Domain Residential Load and Indoor Temperature Forecasting

Accurate short-term forecasting of residential energy load and indoor temperature is essential for home energy management systems, grid-level demand response, and community energy efficiency efforts. Domain adaptation and transfer learning have shown promise for improving forecasting accuracy under data heterogeneity and scarcity commonly seen in residential settings. However, progress is limited by the lack of comprehensive residential datasets: existing benchmarks are narrow in target coverage and rarely support structured cross-domain evaluation. We introduce RESCAST-100K, a large-scale residential forecasting benchmark for studying cross-domain generalization. It provides a configuration-driven interface that instantiates source and target domains along interpretable axes, including geography, climate zone, wall construction, and heating equipment, enabling systematic evaluation of transfer learning, domain adaptation, and zero-shot generalization under controlled domain shifts. The benchmark covers approximately 100,000 EnergyPlus-simulated U.S. homes derived from ResStock, with 15-minute time series for three coupled targets per home: total load, HVAC load, and indoor temperature. These are paired with weather channels, HVAC setpoints, and over 40 static building covariates. RESCAST-100K also integrates five real-world residential datasets under a unified schema, supporting sim-to-real evaluation on the same tasks. We benchmark recurrent, attention-based, and MLP-mixer architectures for zero-shot performance across domains, missing-input conditions, and forecasting tasks. Cross-attention and MLP-mixer models consistently outperform recurrent and classical transformer baselines under domain shift. RESCAST-100K is intended to aid the machine learning and building analytics communities advance cross-domain residential forecasting at home, community, and grid scale.

Jainam Dhruva, Yousaf Raza, A. B. Siddique +1

Department of Computer Science University of Kentucky Lexington, KY 40506

Multivariate Time Series Forecasting Synthetic-to-Real Domain Adaptation Time Series Forecasting Forecasting Benchmarks Building Energy Management Cross-Domain Generalization+1

Jun 1, 2026cs.LG

VLBM: Variational Latent Basis Modeling for OOD Robust Multivariate Time Series Forecasting

Out of distribution (OOD) events in multivariate time series forecasting are rare but often dominate real world risk, making average case forecasting insufficient for reliable deployment. Under standard average risk training on mixed ID/OOD distributions, optimization signals from rare OOD events can be overwhelmed by frequent in distribution (ID) patterns, so strong benchmark accuracy may not translate into reliability under high impact shifts. To address this issue, we propose VLBM (Variational Latent Basis Model), a theory guided latent forecasting framework that separates stable dynamics from OOD induced deviations. VLBM learns a shared latent basis that defines a low rank subspace for stable ID dynamics, explicitly decomposes inputs into basis subspace components and orthogonal residual components, and aligns a future aware posterior with a future blind prior so that test time latent inference depends only on historical input. Across 12 benchmark tasks spanning transportation, weather, power systems, and other real world domains, including newly constructed real world OOD traffic datasets, VLBM achieves state of the art OOD robustness and ID accuracy, with average MAE and MSE gains of 15.08% and 7.74% over the strongest baseline. On a synthetic simulation dataset, VLBM also consistently achieves the best performance and better tracks OOD pulse recovery. These results support latent structured forecasting as a principled route to robust prediction under mixed ID and OOD conditions. The code is available at https://github.com/leijieruilq/VLBM_OOD_forecast.

Xudong Zhang, Jierui Lei, Jiacheng Li +3

School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 100049, China. · Center for Machine Learning Research, Peking University, Beijing, China. · Amap, Alibaba Group, China. +2

Multivariate Time Series Forecasting Latent Variable Models Time Series Forecasting OOD Generalization

May 31, 2026cs.LG

FAiT: Frequency-Aware Inverted Transformer for Multivariate Time Series Forecasting

While Transformer-based architectures have established themselves as a dominant paradigm in Multivariate Time Series Forecasting (MTSF), their core self-attention mechanism inherently functions as a low-pass filter, systematically smoothing out high-frequency signals vital for sharp local changes. Recent advancements have increasingly incorporated frequency-domain operations to address this bias, however, most existing designs rely on fixed spectral bases and apply sequence-wise (uniform) modulation, implicitly assuming a time-invariant frequency response. This overlooks a key property of real-world series that their spectral characteristics often evolve over time, making uniform modulation insufficient for capturing fine-grained temporal dynamics. To tackle these limitations, we propose FAiT, a Frequency-Aware inverted Transformer. Specifically, FAiT rectifies the spectral bias internally through Inverted Attention, which interprets the attention map as a learnable low-pass operator and constructs a dedicated complementary high-pass branch by inverting the attention matrix to recover attenuated transient signals. Furthermore, FAiT introduces Dynamic Temporal-Frequency Modulation (DTFM), which synthesizes instance-conditioned weights to adaptively re-calibrate the energy of spectral sub-bands, enabling fine-grained control over evolving multi-scale patterns. Extensive experiments on widely used benchmarks demonstrate that FAiT consistently outperforms state-of-the-art Transformer-based and frequency-enhanced baselines, while maintaining computational efficiency.

Peng He, Yao Liu, Yanglei Gan +3

University of Electronic Science and Technology of China · Chengdu, Sichuan, China

Multivariate Time Series Forecasting Frequency-Domain Feature Learning Transformer Attention Time Series Transformers Multiscale Time-Series Modeling

May 30, 2026cs.LG

Airport Terminal Passenger Queue Forecasting for Departure Gates and Security Checkpoints

Accurate passenger queue forecasting in airport terminals is essential for efficient departure operations, as it enables proactive congestion management. However, time-varying passenger demand and heterogeneous facility usage across multiple departure facilities make forecasting challenging. In this work, we propose a passenger queue forecasting framework that learns historical passenger flow patterns from operational data. The proposed model employs a Transformer-based architecture to capture temporal dependencies and inter-facility correlations using past queue length and waiting time at departure gates and security checkpoints, together with passenger throughput at check-in islands. The learned representations are mapped to two facility-specific prediction heads to predict queue length and waiting time at departure gates and security checkpoints. Experimental results demonstrate accurate forecasts up to two hours ahead. The proposed approach offers practical real-time decision support for proactive queue management and staff reallocation in airport terminal operations.

Juhwan Lee, Seokbin Yoon, Keumjin Lee +2

Department of Air Transport, Transportation, and Logistics, Korea Aerospace University, Goyang, South Korea · Airport Industry Technology Research Institute, Incheon International Airport Corporation, Incheon, South Korea

Multivariate Time Series Forecasting

May 29, 2026cs.LG

Giving Sensors a Voice: Multimodal JEPA for Semantic Time-Series Embeddings

Transformer-based architectures have advanced sequence modeling in language and vision, yet general-purpose representation learning for heterogeneous multivariate time series remains underexplored. We introduce CHARM (Channel-Aware Representation Model), which incorporates channel-level textual descriptions into a Transformer encoder equivariant to channel order. CHARM is trained with a Joint Embedding Predictive Architecture (JEPA) and a novel loss promoting informative, temporally stable embeddings; latent-space prediction encourages robustness to sensor noise while description-aware gating provides interpretability through learned inter-channel relationships. Across anomaly detection, classification, and short- and long-term forecasting, the learned embeddings achieve strong performance using only a linear probe. Performance is driven primarily by the JEPA objective and conditioning architecture, with text descriptions serving as channel identifiers for cross-dataset generalization.

Utsav Dutta, Gerardo Pastrana, Sina Khoshfetrat Pakazad +1

C3 AI, Redwood City, CA, USA

Multivariate Time Series Forecasting Joint-Embedding Predictive Architecture Multimodal Embedding Time Series Representation Learning Time-Series Anomaly Detection

May 28, 2026cs.AI

KairosAgent: Agentic Time Series Forecasting with Fused Semantic Reasoning

Cross-domain multimodal time series forecasting is a challenging task, requiring models to integrate precise numerical comprehension, cross-domain semantic understanding, and effective multimodal fusion. Existing approaches either build Time Series Foundation Models (TSFMs) from scratch or leverage pretrained Large Language Models (LLMs). However, TSFMs often overlook semantic understanding and lack the ability to perform future-oriented semantic reasoning, and LLMs struggle with numerical comprehension and accurate quantitative forecasting. To overcome these limitations, we propose KairosAgent, a novel agentic framework for multimodal time series forecasting, including an LLM-based reasoner and a TSFM-based forecaster. KairosAgent unifies textual reasoning and numerical forecasting by dynamically invoking analytical tools to enhance the numerical understanding and semantic reasoning capabilities of LLMs. The reasoning results are subsequently fused into the TSFM pipeline, enabling more accurate and reliable future predictions. To further improve the reasoning, we curate a large-scale corpus of high-quality trajectories, alongside a reinforcement learning from forecasting paradigm with multi-turn refinement and turn-level credit assignment. Experiments demonstrate that KairosAgent achieves superior zero-shot forecasting performance while maximizing the utility of pretrained LLMs and TSFMs, presenting a promising direction for efficient and interpretable time series agents. The project page is at https://foundation-model-research.github.io/KairosAgent .

Kun Feng, Ziwei Shan, Yuchen Fang +6

ShanghaiTech University · Ant Group

Multivariate Time Series Forecasting Zero-Shot Time Series Forecasting Time Series Reasoning Time Series Forecasting LLM-Based Time Series Forecasting

May 28, 2026cs.LG

Rethinking Post-Training Recipes for Multimodal Time-Series Forecasting

Time-Series Foundation Models (TSFMs) excel at zero-shot unimodal forecasting using numerical data, but unlike LLMs they cannot consume multimodal, non-numerical context that often shape real-world trajectories. In this work, we bridge this gap and argue for a multimodal time-series forecasting approach that post-trains LLMs to act as context-guided revisors over strong numerical TSFM priors. We introduce PostTime, a post-training recipe combining Supervised Fine-Tuning (SFT) and Reinforcement Learning with Verifiable Rewards (RLVR), along with a methodology to generate automated reasoning traces for forecast revisions. PostTime teaches an LLM to generate context-conditioned forecast interventions -- decisions to revise, preserve, or ignore the TSFM prior based on the multimodal context. We evaluate this approach on the TimesX multimodal forecasting benchmark using a Gemma-3-4B LLM and TimesFM-2.5 TSFM, and show that it significantly outperforms standalone TSFMs, LLM-only baselines, and existing multimodal forecasting approaches.

Haoxin Liu, Yichen Zhou, Rajat Sen +2

Georgia Institute of Technology · Google Research

Multivariate Time Series Forecasting LLM Post-Training Time-Series Foundation Models

May 27, 2026cs.LG

Online Irregular Multivariate Time Series Forecasting via Uncertainty-Driven Dual-Expert Calibration

Irregular multivariate time series forecasting is critical in many real-world applications, where time series are irregularly sampled and exhibit dynamically evolving missingness patterns. Although existing methods perform well in offline settings, they often suffer from significant performance degradation when deployed online due to dynamic shifts in data distribution. Maintaining forecasting capability in such dynamic scenarios typically necessitates online adaptation techniques. Since irregular sampling fundamentally undermines temporal continuity and periodicity, we cannot leverage these widely studied characteristics from regular MTS for online learning. To this end, we study the problem of online IMTS forecasting and propose Under-Cali, an uncertainty-driven dual-expert calibration framework consisting of three core components: an uncertainty estimator, a dual-expert calibration module, and an adaptive routing module. We design an uncertainty estimator that serves as the core control signal to jointly manage inference and adaptation processes. In our framework, the uncertainty estimator first assesses uncertainty for each incoming batch. The adaptive routing module then directs samples with high uncertainty to the unreliable expert for calibration, while low uncertainty samples remain with the reliable expert. Subsequently, the system updates the reliable expert and the uncertainty estimator using well-calibrated reliable samples, and updates the unreliable expert with challenging samples, enabling stable and efficient online learning. Under-Cali keeps the source forecasting model frozen and performs adaptation only through a lightweight, model-agnostic calibration module, enabling efficient adaptation. Extensive experiments on IMTS benchmarks demonstrate consistent improvements with low computational cost. Our code is available at https://github.com/HaonanWen/Under-Cali.

Haonan Wen, Hanyang Chen, Songhe Feng

Key Laboratory of Big Data & Artificial Intelligence in Transportation (Beijing Jiaotong University), Ministry of Education School of Computer Science and Technology, Beijing Jiaotong University Beijing, China · School of Computer Science and Technology, Beijing Jiaotong University Beijing, China · Tangshan Research Institute, Beijing Jiaotong University Tangshan, China

Irregular Time-Series Modeling Multivariate Time Series Forecasting Adaptive Inference Continual Test-Time Adaptation Time Series Forecasting Uncertainty Calibration

May 27, 2026cs.CV

Inpainting-Style Conditional Diffusion for Multivariable Time Series Forecasting

In this paper, we propose a novel conditional diffusion-based framework for multivariable time-series solar power forecasting. The proposed method reformulates temporal PV data as structured two-dimensional representations (images) using a sliding-window patch construction, enabling the application of Denoising Diffusion Probabilistic Models (DDPM) within a unified spatiotemporal learning paradigm. A key contribution of this work is the formulation of solar forecasting as an inpainting problem, where future time steps are treated as missing regions to be reconstructed. This is achieved through a mask-based conditional diffusion mechanism, in which historical observations are preserved as conditioning context while the target (future) region is progressively corrupted and subsequently recovered via reverse diffusion. The model learns to generate coherent future sequences conditioned on observed data, effectively performing time-series inpainting. To fully utilize all available features and ensure compatibility with U-Net architectural constraints, a zero-padding strategy is introduced to construct fixed-size inputs. The model is trained using a supervised denoising objective to predict injected noise, enabling accurate iterative reconstruction during the reverse process. Extensive experiments conducted on benchmark PV dataset, including GEFCom2014, demonstrate that the proposed approach achieves high forecasting accuracy, particularly for short-term horizons. The results highlight the effectiveness of integrating diffusion-based generative modeling with an inpainting formulation for robust, flexible, and high-fidelity solar power forecasting.

Kourosh Kiani, S. M. Muyeen

1Electrical and Computer Engineering, Semnan University, Semnan, Iran · Electrical Engineering Department, Qatar University, Doha, Qatar

Multivariate Time Series Forecasting Time Series Forecasting Solar Power Forecasting Conditional Diffusion Models

May 27, 2026cs.LG

QuITE: Query-Based Irregular Time Series Embedding

Irregular Multivariate Time Series (IMTS) are common in practice, yet their irregular sampling complicates effective modeling. Existing approaches typically either (i) design specialized architectures that limit the reuse of proven Multivariate Time Series (MTS) models, or (ii) map IMTS onto regular temporal grids through interpolation, which may distort temporal dynamics by introducing artificial values. To address these limitations, we propose a new input-embedding-based approach. We identify that the key bottleneck lies not in the backbone architecture, but in conventional embedding layers that assume uniform sampling. In this work, we introduce QuITE (Query-Based Irregular Time Series Embedding), a simple yet effective plug-and-play embedding module for IMTS. QuITE employs learnable query tokens to aggregate irregular observations through a single self-attention layer, directly producing backbone-compatible latent representations without artificial value generation or architectural modification. Extensive experiments on real-world benchmarks show that QuITE consistently improves MTS models, yielding average relative gains of up to

54.7\%

in forecasting and

15.8\%

in classification across diverse datasets and backbone architectures. Code is available at: https://github.com/Meaningfull9502/QuITE.

Junghoon Lim

SK Shieldus, Seongnam, Republic of Korea

Irregular Time-Series Modeling Multivariate Time Series Forecasting Time Series Classification Time Series Representation Learning

May 26, 2026cs.LG

Falcon-X: A Time Series Foundation Model for Heterogeneous Multivariate Modeling

Time series foundation models (TSFMs) are transforming the forecasting paradigm through large-scale cross-domain pretraining. However, most existing TSFMs remain univariate, and recent efforts to enable cross-variate modeling still operate directly within the raw variate space. This design introduces fundamental limitations in semantic alignment and relational expressivity. Specifically, raw-space group mixing lacks a dedicated mechanism to align heterogeneous physical quantities, while standard non-negative attention fails to capture the complex synergistic and antagonistic interactions ubiquitous in real-world systems. To address these challenges, we propose Falcon-X, decouples variates from the raw space and maps them into a unified latent prototype space. Falcon-X employs a Unified Prototype Diff-Attention mechanism that explicitly evaluates both positive and negative semantic affinities to explicitly align heterogeneous variates. Cross-variate interactions are then efficiently performed within this shared space via Latent Entity Attention, naturally facilitating zero-shot structural transfer. Finally, a Variate Reassembly Router robustly reconstructs variate-specific trajectories via a request-and-dispatch mechanism. Extensive evaluations on the GIFT-Eval and fev-bench benchmarks demonstrate that Falcon-X achieves excellent forecasting performance, offering a principled and scalable paradigm for complex multivariate environments. Falcon-X is publicly released to support future research.

Yiding Liu, Yifan Hu, Hongjie Xia +5

Multivariate Time Series Forecasting Zero-Shot Time Series Forecasting Time-Series Foundation Models

May 26, 2026cs.LG

Transfer Learning using 66 Diseases for Disease Forecasting Applications

Disease forecasting models typically rely on a single data stream, making models brittle when histories are short or noisy. Recent top-performing models have shown that synthesizing multiple reporting systems for the same disease improves performance. Other recent work takes this idea a step further, using transfer learning to train a forecasting model for one disease using data from a different disease. We expand upon each of these approaches greatly, training machine learning models on data that span 66 infectious diseases and several data streams. We investigate the value of incorporating different data streams for forecasting 20 different disease data streams. We find that incorporating other data streams improves forecasting in the vast majority (84.9%) of time series and model structures considered. However, our work highlights that the quality of the added data matters, where adding data extremely different from the target data stream can sometimes degrade forecast performance. A major contribution of this work is in compiling a publicly-available database of data for use by the infectious disease forecasting community.

Lauren J Beesley, Alexander C Murph, Dave Osthus +1

Statistics, Los Alamos National Laboratory · Computational Intelligence & Modeling, Los Alamos National Laboratory

Multivariate Time Series Forecasting Epidemic Forecasting Time Series Forecasting Forecasting Benchmarks Cross-Domain Transfer Learning Spatiotemporal Forecasting

May 26, 2026cs.AI

BatteryMFormer: Multi-level Learning for Battery Degradation Trajectory Forecasting

Early battery degradation trajectory forecasting (BDTF), which predicts the full-life state-of-health trajectory from early operational data, is critical for battery optimization, manufacturing, and deployment. Battery degradation data exhibit two key characteristics. First, degradation data present a multi-level structure, including regularities shared within aging conditions and trajectory patterns shared across batteries. Second, degradation-related variations in voltage-current profiles are often localized to specific state of charge (SOC) intervals. Existing approaches often fail to explicitly model these characteristics. To bridge this gap, we propose BatteryMFormer, a multi-level Transformer for early BDTF. BatteryMFormer integrates (1) an aging-condition-aware decoder that injects aging-condition priors via aging-condition-informed queries and aging-condition-aware attention, (2) a meta degradation pattern memory that learns and retrieves trajectory prototypes to guide long-horizon forecasting, and (3) a dual-view encoder that jointly captures temporal dynamics and SOC-localized variations from voltage and current time series. Extensive experiments on four battery domains show that BatteryMFormer consistently outperforms state-of-the-art baselines, marking a significant step toward reliable BDTF. Our code is available at https://github.com/Ruifeng-Tan/BatteryMFormer.

Ruifeng Tan, Jintao Dong, Weixiang Hong +3

School of Computer Science and Engineering, Central South University · Material Genome Institute, Shanghai University

Multivariate Time Series Forecasting RUL Estimation Time Series Transformers

May 26, 2026cs.LG

Unicorn: Scaling High-Dimensional Time Series Forecasting via Universal Correlation Modeling

Modern time series architectures face a fundamental trade-off: channel-independent models scale well with increasing data volume but ignore critical inter-channel dependencies, while channel-dependent models are expressive but remain ``dimension-bounded'', struggling to generalize across heterogeneous datasets.To bridge this gap, we introduce Unicorn (Universal Correlation Network), a framework for scalable, multi-dataset pretraining on high-dimensional time series. At the core of Unicorn is a latent prototype codebook that decouples correlation modeling from specific channel identities. By projecting heterogeneous channels into a shared latent space, UniCorN learns identity-agnostic, reusable interaction patterns that transfer across domains with diverse dimensionalities and semantics. Extensive experiments show that Unicorn significantly outperforms state-of-the-art forecasting architectures, particularly in few-shot transfer scenarios, offering a scalable path toward multivariate time series foundation models.

Haochen Yuan, Yichen Song, Yunbo Wang +1

MoE Key Lab of Artificial Intelligence, AI Institute, School of Computer Science Shanghai Jiao Tong University

Multivariate Time Series Forecasting Time-Series Foundation Models

May 26, 2026cs.LG

Beyond Holistic Models: Systematic Component-level Benchmarking of Deep Multivariate Time-Series Forecasting

While previous research in multivariate time series forecasting has focused on developing complex holistic models, this work advocates for a shift toward a granular, component-level understanding of their impacts. We propose TSCOMP, the first large-scale benchmark that systematically deconstructs deep forecasting methods into their core, fine-grained components--spanning series preprocessing, encoding strategies, network architectures including specific and large time-series models, and optimization methods. Using constrained orthogonal experimental design and extensive evaluations, we conduct multi-view analyses that reveal component effectiveness across different backbones, data characteristics, and their interactions. Beyond providing insights, this benchmark establishes a fine-grained performance corpus comprising over 20,000 model-dataset evaluations, which supports the learning of automated component selection, enabling zero-shot model construction on new datasets. Our experiments demonstrate that the corpus-driven approach, despite its simplicity, consistently outperforms state-of-the-art methods, validating the soundness of our evaluation design and confirming that systematic component selection surpasses manually designed complex architectures. All code and the performance corpus are publicly available at https://github.com/SUFE-AILAB/TSCOMP.

Shuang Liang, Chaochuan Hou, Xu Yao +4

Shanghai University of Finance and Economics Shanghai, China · Ant Group Shanghai, China · Key Laboratory of Interdisciplinary Research of Computation and Economics Shanghai University of Finance and Economics Shanghai, China

Multivariate Time Series Forecasting Forecasting Benchmarks Automated Machine Learning

May 25, 2026cs.LG

STARIXNet: Multivariate and Multi-attribute Deep Learning Approach to Real-Time Resource Allocation in Cloud Platforms

Intelligent scaling of microservices in cloud platforms is crucial for mitigating escalating compute costs while avoiding service disruptions. Current solutions are limited to the univariate space, typically focusing on CPU usage alone to drive scaling decisions. Moreover, they address the problem as a purely forecasting task, focusing on prediction precision while neglecting the greater risks of underestimation and delays in system responsiveness. Alternative solutions are computationally complex, making them impractical for large-scale, real-time deployments. To address these challenges, we present STARIXNet, a lightweight neural network that guides resource allocation decisions in the multivariate space by capturing spatio-temporal relationships among multiple system metrics. STARIXNet models multiple quasi-dependent attributes, in particular the (S)easonal, (T)emporal, (A)uto-(R)egressive (I)ntegrated, and e(X)ogenous patterns, then implements an aggregation policy to finalize scaling decisions, prioritizing service stability, followed by cost-efficiency, over raw forecast accuracy. We empirically demonstrate the performance of STARIXNet by benchmarking against existing solutions in real-world settings. STARIXNet is deployed for critical production microservices at Walmart achieving tangible savings ranging from 10% to 50%, in addition to intangible benefits through improved service stability and customer experience.

Ahmed Abdulaal, Maruf Aytekin, Thilaga kumaran Srinivasan +1

Walmart Global Tech Sunnyvale, California, USA

Multivariate Time Series Forecasting Cloud Computing Online Resource Allocation

May 25, 2026cs.LG

Electricity Consumption Forecasting: An Approach Using Cooperative Ensemble Learning with SHapley Additive exPlanations

Electricity expense management presents significant challenges, as this resource is susceptible to various influencing factors. In universities, the demand for this resource is rapidly growing with institutional expansion and has a significant environmental impact. In this study, the machine learning models long short-term memory (LSTM), random forest (RF), support vector regression (SVR), and extreme gradient boosting (XGBoost) were trained with historical consumption data from the Federal Institute of Paraná (IFPR) over the last seven years and climatic variables to forecast electricity consumption 12 months ahead. Datasets from two campuses were adopted. To improve model performance, feature selection was performed using Shapley additive explanations (SHAP), and hyperparameter optimization was carried out using genetic algorithm (GA) and particle swarm optimization (PSO). The results indicate that the proposed cooperative ensemble learning approach named Weaker Separator Booster (WSB) exhibited the best performance for datasets. Specifically, it achieved an sMAPE of 13.90% and MAE of 1990.87 kWh for the IFPR-Palmas Campus and an sMAPE of 18.72% and MAE of 465.02 kWh for the Coronel Vivida Campus. The SHAP analysis revealed distinct feature importance patterns across the two IFPR campuses. A commonality that emerged was the strong influence of lagged time-series values and a minimal influence of climatic variables.

Eduardo Luiz Alba, Gilson Adamczuk Oliveira, Matheus Henrique Dal Molin Ribeiro +1

Industrial & Systems Engineering Graduate Program (PPGEPS), Federal University of Technology-Parana (UTFPR), Via do Conhecimento, KM 0l—Fraron, Pato Branco 85503-390, PR, Brazil

Multivariate Time Series Forecasting Long-Term Time Series Forecasting Ensemble Learning Time Series Forecasting Electricity Load Forecasting

May 22, 2026cs.LG

Parametric Prior Mapping Framework for Non-stationary Probabilistic Time Series Forecasting

Effectively modeling non-stationary dynamics in probabilistic multivariate time series(MTS) forecasting requires balancing expressiveness with robustness. Existing parametric approaches benefit from strong inductive biases but lack flexibility, whereas deep generative models struggle to capture complex temporal dependencies without extensive data and computation. We introduce Parametric Prior Mapping (PPM), a framework that injects parametric structural priors into a generative modeling process. Specifically, PPM utilizes a parametric estimator to derive a dynamic, adaptive prior that guides the learning of a complex predictive distribution via a learnable mapping. This design allows the model to retain the efficiency of parametric methods while exploiting the expressive power of generative models. Trained with a hybrid objective, PPM yields precise forecasts with well-calibrated uncertainty estimates. Empirical results show that PPM outperforms existing baselines in handling non-stationary data, offering a superior trade-off between accuracy and computational efficiency. The code is available at https://github.com/ljl8336/PPM.

Jinglin Li, Jun Tan, QI Fang +1

School of Computer Science and Engineering, Central South University, Changsha, China.

Multivariate Time Series Forecasting Non-Stationary Time Series Forecasting Conditional Generative Modeling Probabilistic Time Series Forecasting

May 21, 2026cs.CE

Dynamic Hypergraph Representation Learning for Multivariate Time Series without Prior Knowledge

Hypergraphs have the capacity to capture higher-dimensional relationships among entities across various domains, making them a subject of growing interest within the research community for understanding the structure and dynamics of complex systems. However, a key challenge is the derivation of hypergraph representations from time series data in situations where the structure of the hypergraph is limited or absent. In this study, we propose a model that constructs a dynamic hypergraph representation for multivariate time series without relying on prior knowledge of the data. This is achieved by applying community detection to the time series and transforming the resulting communities, obtained through an attention mechanism, into a hypergraph using a clique-based technique. Hypergraph representations are derived from different time series datasets, and the resulting hypergraphs are then used by a Dynamic Hypergraph Attention Convolution Network (DHACN) for multivariate time series predictions. This research advances the field of hypergraph representation by introducing a novel approach that is better suited to uncover high-order relationships without prior knowledge.

Marco Gregnanin, Johannes De Smedt, Giorgio Gnecco +1

IMT School for Advanced Studies Lucca · KU Leuven · University of Chieti-Pescara

Multivariate Time Series Forecasting Graph Structure Learning Hypergraph Neural Networks Time Series Representation Learning Hypergraph Learning

May 20, 2026cs.SI

SURGE: An Event-Centric Social Media Sentiment Time Series Benchmark with Interaction Structure

Public events on social media generate large volumes of discussion whose collective dynamics carry direct value for opinion forecasting and crisis response. Capturing how these dynamics evolve across an event's lifecycle requires organizing fragmented posts into event-level time series. Existing datasets cover only a small number of events within a single category, and typically discard the interaction structure between posts when constructing time series, which restricts both transfer across event types and controlled study of how interactions shape the resulting collective dynamics. We present SURGE, a multi-event social media benchmark that pairs event-level time series with aligned text and interaction structure linking posts within an event. SURGE is built through an automated pipeline that produces calendar-aligned time series at three temporal granularities, covering 67 events and more than 800K posts across five event categories. Each time bin is paired with flat and structured textual views derived from the same selected posts, enabling controlled evaluation of whether social interaction structure affects forecasting behavior. On top of SURGE we define benchmark protocols for numerical-only forecasting, text-augmented forecasting, high-interaction evaluation, and leave-one-category-out generalization. Experiments with representative time-series and multimodal forecasting models reveal three properties of the benchmark: a strong local-persistence regime in which naive baselines remain hard to beat under absolute error, limited transfer of existing text-augmented forecasters to event-driven social-media data, and increased difficulty on reply-dense periods that aggregate metrics tend to obscure. We further include a lightweight structure-aware probe as a reference implementation, illustrating how SURGE can support interaction-aware forecasting research.

Chen Su, Pengsen Cheng, Yuanhe Tian +1

University of Science and Technology of China · Sichuan University · Zhongguancun Academy

Social Media Analysis Multivariate Time Series Forecasting Time Series Forecasting Forecasting Benchmarks

May 20, 2026cs.LG

Deep Learning Surrogates for Emulating Stochastic Climate Tipping Dynamics

This work explores a dynamics-informed Temporal Fusion Transformer (TFT) as a data-driven surrogate for computationally intensive Earth system simulations. Focusing on multivariate time series describing global ocean transport, we demonstrate the surrogate's ability to forecast tip events across thousands of time steps. The data involve up to 21 non-stationary time series in addition to static covariates describing free parameters and initial conditions. Modifications to the architecture and objective function yield a surrogate that anticipates the timing of Atlantic and Pacific collapses to high fidelity and captures the stochastic uncertainty in transition timing across ensemble predictions. The learned surrogate achieves a 465x computational speedup over the numerical simulator while maintaining differentiability with respect to parameters and initial conditions.

Adeline Hillier, Jennifer Sleeman, Jay Brett +3

Johns Hopkins Applied Physics Laboratory Hopkins University · Johns

Neural Surrogate Modeling Multivariate Time Series Forecasting Climate Science Probabilistic Forecasting Non-Stationary Time Series Forecasting Climate Modeling+1

May 19, 2026cs.LG

Latent Laplace Diffusion for Irregular Multivariate Time Series

Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift. To bridge this gap, we present Latent Laplace Diffusion (LLapDiff), a generative framework that models the target as a low-dimensional latent trajectory, enabling horizon-wide generation without step-by-step integration over physical time. We guide the reverse process utilizing a stable modal parameterization motivated by stochastic port-Hamiltonian dynamics, and parameterize its mean evolution in the Laplace domain via learnable complex-conjugate poles, enabling direct evaluation over irregular timestamps. We also link continuous dynamics to irregular observations through renewal-averaging analysis, which maps sampling gaps to effective event-domain poles and motivates a gap-aware history summarizer. Extensive experiments show that LLapDiff improves over baselines in long-horizon forecasting, and its continuous-time generative nature supports missing-value imputation by querying the same model at historical timestamps. Code is available at https://github.com/pixelhero98/LLapDiffusion.

Zinuo You, Jin Zheng, John Cartlidge

School of Computer Science, University of Bristol · School of Engineering Mathematics and Technology, University of Bristol

Irregular Time-Series Modeling Multivariate Time Series Forecasting Long-Term Time Series Forecasting Diffusion Models

May 19, 2026stat.ML

Probabilistic Multivariate Time Series Forecasting with Diffusion Copulas

Accurately assessing financial risk requires capturing both individual asset volatility and the complex, asymmetric dependence structures that emerge during extreme market events. While modern diffusion-based models have advanced multivariate forecasting, they often suffer from a "normality bias" when trained end-to-end, sacrificing marginal calibration for joint coherence and consistently underestimating tail risk. To address this, we propose a Diffusion-Copula framework that explicitly decouples the learning of marginal distributions from their dependence structure. We employ deep Mixture Density Networks to capture heavy-tailed asset dynamics, followed by a Classification-Diffusion Copula to model the joint dependence. Applied to cryptocurrency markets, our approach demonstrates superior performance over state-of-the-art baselines in forecasting systemic extremes of both marginal and joint events. Crucially, we demonstrate that while baseline models classify simultaneous market crashes as statistically impossible "Black Swans" (high surprise), our framework identifies them as "Expected Crashes" (low surprise), successfully preserving the correlation structure necessary for robust risk management during contagion events.

David Huk, Dongshan Wang, Miha Bresar

Department of Statistics The University of Warwick · School of Data Science The Chinese University of Hong Kong, Shenzhen

Multivariate Time Series Forecasting Copula Models Quantitative Finance Probabilistic Forecasting Probabilistic Time Series Forecasting Diffusion Models

May 19, 2026q-fin.PM

Do Better Volatility Forecasts Lead to Better Portfolios? Evidence from Graph Neural Networks

This paper tests whether graph neural networks improve realized volatility forecasts and whether those forecasts improve portfolio performance. Using weekly realized volatility for 465 S&P 500 equities from 2015-2025, Heterogeneous Autoregressive and Long Short-Term Memory baselines are compared against GraphSAGE models built on rolling correlation, sector, and Granger-causal graphs, with and without macro regime features. The empirical finding is that the model with the lowest forecast MSE, the model with the highest cross-sectional ranking accuracy, and the model with the highest portfolio Sharpe ratio are three different models. Forecast accuracy, ranking quality, and portfolio performance are related but not interchangeable objectives. Graph volatility models add value only when the portfolio rule can exploit the cross-sectional structure they encode.

Rylan Wade

University of Southern California

Multivariate Time Series Forecasting Graph Neural Networks Quantitative Finance Time Series Forecasting Portfolio Optimization

May 18, 2026cs.LG

Chronicle: A Multimodal Foundation Model for Joint Language and Time Series Understanding

Real-world time series come with text: metadata, descriptions, news, reports. Yet time series foundation models process numerical sequences in isolation, and the multimodal text-and-time-series models that attempt to bridge the two all adapt a pretrained language model post hoc, inheriting representations shaped without ever seeing temporal data. These models are also evaluated almost exclusively against other multimodal baselines, not against the strongest unimodal foundation models in either domain, leaving open whether joint training is needed at all. We present Chronicle, a compact 324M-parameter decoder-only transformer trained from scratch on natural language and time series within a single unified architecture. Both modalities share the same transformer blocks, attention mechanism, and residual stream; the bulk of pretraining uses unimodal batches so cross-modal capability emerges purely from shared parameters, with a short alignment stage that interleaves the two. To our knowledge, Chronicle is the first model jointly pretrained on text and time series from scratch, and the first multimodal model evaluated against dedicated foundation models in both domains. It matches Gemma-3-270M-PT on 19 NLU tasks, sets a new bar for frozen-embedding time series classification on 24 UCR/UEA datasets, and produces multimodal forecasts on Time-MMD that beat every supervised fusion baseline, all from a single backbone.

Paul Quinlan, Jeremy Levasseur, Qingguo Li +1

1InertialAI · Department of Electrical and Computer Engineering, Queen’s University · Department of Mechanical and Materials Engineering, Queen’s University

Cross-Modal Learning Multivariate Time Series Forecasting Time Series Classification Unified Multimodal Models Multimodal Pretraining Multimodal Foundation Models+2

May 18, 2026cs.CV

Learning Long-Term Temporal Dependencies in Photovoltaic Power Output Prediction Through Multi-Horizon Forecasting

The rapid global expansion of solar photovoltaic (PV) capacity-reaching a record 597 GW in 2024-highlights the urgent need for robust forecasting models to mitigate the grid instability caused by the intermittent nature of solar irradiance. While deep learning-based direct forecasting using ground-based sky images (GSI) has emerged as a dominant approach, existing literature is often constrained by single-architecture evaluations and an exclusive focus on single-horizon (point) prediction. This paper proposes a transition from traditional single-horizon estimation toward a multi-horizon forecasting framework, leading to an architecture-independent improvement in accuracy. We hypothesize and demonstrate experimentally that joint optimization over a sequence of future values allows deep neural networks to better capture latent inter-step temporal dependencies by avoiding precocious convergence of the network in terms of both weight gradients and filter diversity. Leveraging this architecture-independent improvement that integrates sequential sky imagery with historical PV generation data, we evaluate the models' abilities to predict power output across multiple discrete future time steps simultaneously. Our methodology is validated through a comparative analysis across diverse deep learning architectures. The results demonstrate that this multi-horizon approach significantly enhances predictive accuracy and robustness across the entire forecast horizon while maintaining computational parsimony. By achieving superior performance with negligible overhead compared to single-horizon models, this work provides a scalable and efficient solution to improve the resilience of modern power grids.

Sumit Laha, Ankit Sharma, Hassan Foroosh

Department of Computer Science University of Central Florida Orlando, Florida, United States.

Multivariate Time Series Forecasting Time Series Forecasting Solar Power Forecasting