Multivariate Time Series Forecasting

Multivariate time-series analysis involves extracting informative representations from sequences of multiple interdependent variables, supporting tasks such as forecasting, imputation, and anomaly detection. In real-world scenarios, these variables are typically collected from a shared context or underlying phenomenon, suggesting the presence of latent dependencies across time and channels that can be leveraged to improve performance. However, recent findings show that channel-independent (CI) models, which assume no inter-variable dependencies, often outperform channel-dependent (CD) models that explicitly model such relationships. This surprising result indicates that current CD models may not fully exploit their potential due to limitations in how dependencies are captured. Recent studies have revisited channel dependence modeling with various approaches; however, these methods often employ indirect modeling strategies, which can lead to meaningful dependencies being overlooked. To address this issue, we introduce XCTFormer, a transformer-based channel-dependent (CD) model that explicitly captures cross-temporal and cross-channel dependencies via an enhanced attention mechanism. The model operates in a token-to-token fashion, modeling pairwise dependencies between every pair of tokens across time and channels. The architecture comprises (i) a data processing module, (ii) a novel Cross-Relational Attention Block (CRAB) that increases capacity and expressiveness, and (iii) an optional Dependency Compression Plugin (DeCoP) that improves scalability. Through extensive experiments on three time-series benchmarks, we show that XCTFormer achieves strong results compared to widely recognized baselines; in particular, it attains state-of-the-art performance on the imputation task, outperforming the second-best method by an average of 20.8% in MSE and 15.3% in MAE.

Accurate and efficient time-series forecasting remains a challenging problem for both classical and quantum neural architectures, particularly in multivariate environmental settings. This work adapts the Quantum Leaky Integrate-and-Fire (QLIF) spiking neural network for time-series regression tasks, specifically short-term multivariate weather forecasting. We extend QLIF beyond classification and demonstrate its applicability to continuous-valued prediction problems. The QLIF-CAST model encodes neuron excitation states as single-qubit quantum superpositions, driven by R_x rotation gates and T1 relaxation decay, and is embedded within a hybrid quantum-classical recurrent architecture. We conduct two distinct evaluations. First, a controlled comparison against a parameter-matched classical LIF baseline on a multivariate weather dataset shows that QLIF-CAST achieves 15.4% lower MSE and 4.4% lower MAE, demonstrating that quantum neuronal dynamics reduce prediction error over classical equivalents. Second, a cross-domain comparative analysis with state-of-the-art quantum LSTM (QLSTM) and quantum neural network (QNN) models on air quality and wind speed benchmarks reveals that QLIF-CAST converges in up to 94% less training time, occupying a distinct position in the speed-error trade-off space. Hardware verification on IBM Marrakesh (156-qubit QPU) confirms reliable circuit execution with only 1.2% average deviation from simulation.

Anomaly detection in batch processes is hindered by transient dynamics, scarce fault labels, and reliance on single-modality sensor data. This work introduces UTOPYA (Unified Temporal Observation for Physics-Informed Anomaly Detection and Time-Series Prediction), a 15.2M-parameter multimodal framework that jointly addresses anomaly detection, time-series prediction, and phase classification in batch distillation by fusing eight data modalities through Feature-wise Linear Modulation (FiLM) conditioned cross-modal attention and gated fusion. A physics-informed regularisation scheme introduced in this work enforces temporal smoothness and thermodynamic monotonicity, while curriculum learning introduces training samples in order of physical difficulty. On the 119-experiment multimodal batch distillation dataset of Arweiler et al. (2026), UTOPYA achieves a window-level test AUROC of 0.832 and 0.874 under multi-signal experiment-level scoring, substantially outperforming four external baselines (PCA, autoencoder, Isolation Forest, and LSTM autoencoder) evaluated under identical conditions (+0.147 window-level AUROC over the best baseline). A multimodal ablation over 15~architectural configurations shows that static context via FiLM conditioning is the key enabler, lifting experiment-level multi-signal AUROC by +0.145 over the unimodal baseline (0.729 to 0.874). Separately, a training ablation across 14 design choices reveals that several widely-adopted techniques, including instance normalisation, Mixup, ensembling, test-time augmentation, and stochastic weight averaging, fail to improve or actively degrade generalisation in this data-scarce setting. These negative results expose a fundamental tension between smoothing-based regularisation and anomaly detection, providing practical guidance for multimodal process monitoring deployment.

Mainstream methods for multivariate time-series forecasting largely follow the Direct-Mapping paradigm. They learn a unified mapping from history to the future in the observation space to fit value-level dependencies. However, real-world systems often undergo distribution shifts and regime changes. In such cases, a unified mapping can exhibit response lag around turning points, causing error accumulation within the switching window and reducing forecasting reliability. To address this issue, we propose L-Drive, a change-aware forecasting framework. L-Drive introduces a Latent-Context, to explicitly characterize high-level dynamics evolving over time, and uses gating to modulate increment representations. This provides more timely change cues and improves adaptation to changing segments. In addition, it incorporates patch-shared relative positional basis functions to strengthen intra-segment structural modeling and reduce overfitting caused by absolute-position memorization. Extensive experiments validate the effectiveness of L-Drive and show a better overall trade-off between forecasting accuracy and computational efficiency.

Accurate and efficient long-term multivariate time series forecasting requires capturing recurring temporal structure while keeping inference cheap across many variables and horizons. Frequency-space models represent long-range and periodic variation compactly, but they typically process the real and imaginary spectral components as weakly coupled streams and treat periodic cues as ordinary input features, even when such cues are unreliable. This paper proposes FRWKV-Plus, a lightweight periodic-aware frequency-space forecasting model built on the efficient FRWKV backbone. FRWKV-Plus introduces a cross-branch spectral gate that reweights each spectral branch using a summary of its sibling branch, and a trust-gated residual correction that converts compact within-period context into a bounded, sign-flexible adjustment of these gates under a learned, data-dependent trust score. By construction, the correction is identity-preserving at initialization and strictly bounded, so periodic evidence can refine but never dominate or invert the base interaction. On seven standard benchmarks, FRWKV-Plus is consistently competitive with strong linear, frequency-domain, recurrent-style, and Transformer-based forecasters while preserving the lightweight profile of the backbone. Controlled three-seed ablations show that each component contributes, that the benefit is modest on strongly periodic data and pronounced on the harder Exchange and ILI datasets, and that the within-period context is the most influential single component. The implementation is publicly available at https://github.com/yangqingyuan-byte/FRWKV-plus.

Deep forecasting models often suffer from attenuated periodic perception and entangled trend-noise representations as network depth increases. Moreover, the widely adopted channel-independent paradigm, while improving training stability, disrupts intrinsic dynamic coordination among variables, hindering the modeling of cross-variable consistency in multivariate time series. To address these issues, we propose PESD-TSF, a physics-inspired structured decomposition framework for long-term time series forecasting that jointly emphasizes interpretability and predictive accuracy. PESD-TSF introduces three key designs. First, a Multiplicative Periodic Gating mechanism incorporates continuous-time priors to dynamically modulate signal amplitudes, preserving periodic structures across deep layers. Second, a multi-scale structured encoder integrates detrended attention with hierarchical sampling to explicitly decouple long-term trends from high-frequency variations while retaining fine-grained temporal semantics. Third, to recover disrupted inter-variable dependencies, we propose Cross-Scale Collaborative Attention (CSCA) together with an RLC regularization scheme, which reconstructs global inter-variable topology in deep feature spaces and enforces physically consistent collaboration through orthogonality and consistency constraints. Extensive experiments on benchmark datasets from multiple domains demonstrate that PESD-TSF consistently achieves state-of-the-art performance, with particularly strong gains on multivariate forecasting tasks involving complex inter-variable coupling, highlighting its superior structural modeling capability and generalization.

Physiological time series signals reflect complex, multi-scale dynamical processes of the human body. Existing modeling studies focus on static tasks such as classification, event forecasting, or short-horizon next step prediction, while long-horizon signal-level forecasting and predictive nature of physiological signals remain underexplored. We introduce NormWear-2, a world model that encodes both multivariate physiological signals and clinical intervention variables into a shared latent space and models their joint temporal evolution as a dynamical system. Our approach combines inference from prior pre-trained knowledge (intuition) with instant non-parametric latent state transition adaptation (insight), enabling coherent forecasting across multiple temporal scales, conditioned on heterogeneous clinical interventions. During the pretraining phase, we find that chaos-theoretic balancing of dynamical regime diversity yields more robust representations, with a smaller balanced corpus outperforming one twice its size and capturing bifurcation regimes. We evaluate the world model performance across diverse real-world physiological datasets spanning heterogeneous temporal resolutions and intervention regimes, covering daily life, point-of-care, and clinical settings, including fitness planning, hemodialysis, diabetes management, and surgical monitoring. These evaluation datasets comprise records from 8,026 subjects, spanning study durations from 3.2 hours for high-resolution signal data to 2.3 years for longitudinal clinical biomarker tracking. NormWear-2 achieves the best overall forecasting performance across time, frequency, and latent representation domains, with significant improvements over state-of-the-art time series foundation models, while maintaining competitive downstream representation quality, providing a step toward general-purpose world models for physiological signals.

Accurate forecasting of residual Physical Resource Blocks (PRBs) is critical for proactive network slice provisioning, energy-efficient operation, and spectrum-aware decision making in cellular systems, where residual PRBs serve as a practical proxy for short- and medium-term spectrum availability. Existing PRB prediction methods typically rely only on historical PRB values and are trained independently per carrier or sector, limiting their ability to capture cross-carrier dependencies and providing no measure of forecast uncertainty. Moreover, point forecasts alone are insufficient for robust spectrum-aware control under highly variable traffic conditions. This paper proposes PRB-RUPFormer, a recursive unified probabilistic Transformer for residual PRB forecasting. The proposed model jointly processes multivariate KPI time series using temporal, seasonal, and carrier-aware embeddings, preserving inter-metric temporal coupling during recursive rollout and stabilizing long-horizon forecasting. A single shared model is trained across all carriers and sectors of an eNB, enabling efficient learning of joint traffic dynamics with low computational overhead. Forecast uncertainty is captured through quantile-based prediction intervals, providing confidence-aware estimates of future PRB availability. Evaluations on six months of commercial LTE network data from multiple U.S. locations demonstrate median MAE below 0.05 and hit probabilities above 0.80 for both one-day and seven-day recursive forecasts. These probabilistic predictions directly support spectrum-aware RAN functions such as dynamic carrier activation, congestion avoidance, and proactive spectrum sharing, making the proposed framework well-suited for dynamic spectrum access scenarios.

Forecasting multivariate hidden Markov processes is challenging due to nonlinear and nonstationary observations, latent state transitions, and cross-sequence dependencies. While deep learning methods achieve strong predictive accuracy, they typically lack explicit state modeling, whereas Hidden Markov Models (HMMs) provide interpretable latent states but struggle with complex nonlinear emissions and scalability. To address these limitations, we propose DRL-STAF, a Deep Reinforcement Learning based STate-Aware Forecasting framework that jointly predicts next-step observations and estimates the corresponding hidden states for complex multivariate hidden Markov processes. Specifically, DRL-STAF models complex nonlinear emissions using deep neural networks and estimates discrete hidden states using reinforcement learning, reducing the reliance on predefined transition structures and enabling flexible adaptation to diverse temporal dynamics. In particular, DRL-STAF mitigates the state-space explosion encountered by typical multivariate HMM-based methods. Extensive experiments demonstrate that DRL-STAF outperforms HMM variants, standalone deep learning models, and existing DL-HMM hybrids in most cases, while also providing reliable hidden-state estimates.

Instance normalization (IN) is widely used in non-stationary multivariate time series forecasting to reduce distribution shifts and highlight common patterns across samples. However, IN can over-smooth instance-specific structural information that is essential for modeling temporal and cross-channel heterogeneity. While prior methods further suppress distribution discrepancies or attempt to recover temporal specific dependencies, they often ignore a central tension: how to adaptively model common and instance-specific dependency based on each instance's non-stationary structures. To address this dilemma, we propose SeesawNet, a unified architecture that dynamically balances common and instance-specific dependency modeling in both temporal and channel dimensions. At its core is Adaptive Stationary-Nonstationary Attention (ASNA), which captures common dependencies from normalized sequences and specific dependencies from raw sequences, and adaptively fuses them according to instance-level non-stationarity. Built upon ASNA, SeesawNet alternates dedicated temporal and channel relationship modeling to jointly capture long-range and cross-variable dependencies. Extensive experiments on multiple real-world benchmarks demonstrate that SeesawNet consistently outperforms state-of-the-art methods.

Irregularly sampled multivariate event streams remain a difficult modality for generative modeling: tokenization-based approaches break down when inter-event intervals vary by orders of magnitude. We (i) propose \textbf{SurF}, a generative model that uses the Time Rescaling Theorem (TRT) as a learnable bijection between event sequences and i.i.d.\ unit-rate exponential noise, enabling a single model to be trained across heterogeneous event-stream datasets; (ii) three efficient parameterizations of the cumulative intensity that scale to long sequences; and (iii) a Transformer-based encoder for multi-dataset pretraining. On six real-world benchmarks, SurF achieves the best reported time RMSE on Earthquake, Retweet, and Taobao, and is within trial-level noise of the strongest specialist on the remaining three. Under a strict leave-one-out protocol, the held-out checkpoint beats every classical and neural-autoregressive baseline on $5/6$ datasets and beats every baseline on Amazon and Earthquake, an initial step toward foundation models over asynchronous event streams (Code is available at https://github.com/MrRezaeiUofT/SurF).

Recent studies on long-term time series forecasting have shown that simple linear models and MLP-based predictors can achieve strong performance without increasingly complex architectures. However, many competitive baselines still rely on structural priors such as frequency-domain modeling, explicit decomposition, multi-scale mixing, or sophisticated cross-variable interaction modules, while paying less attention to how simple temporal mappings should be trained and organized. In this paper, we propose STAIR, short for Stagewise Temporal Adaptation via Individualization and Residual Learning, a training paradigm for long-term time series forecasting that aims to unlock the capacity of simple temporal mapping models without introducing complex architectural modules. STAIR decomposes forecasting ability into three progressive stages: it first learns common temporal dynamics across variables through a shared temporal mapping, then adapts the shared model to each variable via channel-wise fine-tuning to capture variable-specific patterns, and finally complements the backbone with cross-variable information through residual learning. We further introduce Shared-to-Individual Fine-tuning and alpha-RevIN to mitigate the limitations of strict channel independence and the overly strong normalization prior induced by standard RevIN. This design gradually increases modeling flexibility while keeping the core temporal predictor as a shallow MLP in the main experiments, with linear variants analyzed separately. Experiments on nine long-term forecasting benchmarks show that STAIR matches or outperforms recent strong baselines while preserving a simple temporal backbone, providing a concise and effective modeling perspective for long-term time series forecasting.

Time Series Foundation Models (TSFMs) have recently achieved state-of-the-art performance, often outperforming supervised models in zero-shot settings. Recent TSFM architectures, such as Chronos-2 and TabPFN-TS, aim to integrate covariates. In this paper, we design controlled experiments based on simple target-covariate relationships to assess this integration capability. Our results show that TabPFN-TS captures these relationships more effectively than Chronos-2, especially for short horizons, suggesting that the strong benchmark performance of Chronos-2 does not automatically translate into optimal modeling of simple covariate-target dependencies.

The increasing adoption of data-driven decision-making in public health has established epidemic forecasting as a critical area of research. Recent advances in multivariate forecasting models better capture complex temporal dependencies than conventional univariate approaches, which model individual series independently. Despite this potential, the development of robust epidemic forecasting methods is constrained by the lack of high-quality benchmarks comprising diverse multivariate datasets across infectious diseases and geographical regions. To address this gap, we present EpiCastBench, a large-scale benchmarking framework featuring 40 curated (correlated) multivariate epidemic datasets. These publicly available datasets span a wide range of infectious diseases and exhibit diverse characteristics in terms of temporal granularity, series length, and sparsity. We analyze these datasets to identify their global features and structural patterns. To ensure reproducibility and fair comparison, we establish standardized evaluation settings, including a unified forecasting horizon, consistent preprocessing pipelines, diverse performance metrics, and statistical significance testing. By leveraging this framework, we conduct a comprehensive evaluation of 15 multivariate forecasting models spanning statistical baselines to state-of-the-art deep learning and foundation models. All datasets and code are publicly available on Kaggle (https://www.kaggle.com/datasets/aimltsf/epicastbench) and GitHub (https://github.com/aimltsf/EpiCastBench).

Using Chronos-2, an open-source time-series foundation model, we evaluate pretrained time-series models for economic and financial forecasting with an emphasis on whether multivariate (MV) inputs improve accuracy relative to univariate (UV) baselines. The study covers two panels -- the Magnificent-7 equities and U.S. Treasury interest rates -- as well as a combined panel, using rolling monthly evaluations from 2000--2025. We vary input window lengths and forecast horizons and report RMSE and MAPE. Across datasets, MV forecasts consistently outperform UV forecasts, with especially strong gains for interest rates and meaningful improvements for equities. Series-level comparisons show MV improvements in every case, and error dispersion is generally lower under MV inputs. We also provide parameter-heatmap and time-series visualizations. However, mixing time series across equity and interest rate markets reduces forecast accuracy, indicating that adding noisy context degrades model performance. Overall, the results indicate that foundation models can leverage cross-series information to improve forecast accuracy in finance, and that the benefits are strongest when related series are modeled jointly under disciplined rolling protocols. Other than using an open-source foundation model, this paper also showcases how AI may be used for financial research.

Multivariate time series forecasting remains a challenge due to the complexity of local temporal dynamics and global dependencies across multiple variables. In this paper, we propose \textbf{N}eighboring \textbf{P}atching \textbf{Mixer} (\textbf{NPMixer}), a hierarchical architecture featuring a Learnable Stationary Wavelet Transform that adaptively learns filter coefficients to decompose signals into trend and detail components in a data-dependent manner. Our framework introduces a Neighboring Mixer Block that captures local temporal dynamics through a series of hierarchical MLP layers operating on non-overlapping patches. Specifically, the mixer block utilizes MLPs to learn temporal patterns within and across these patches, expanding the receptive field to capture multi-scale dependencies. A Channel-Mixing Encoder is applied to high-frequency components to learn channel correlations while preserving the stability of the underlying global trend. Extensive experiments on seven benchmark datasets demonstrate that NPMixer consistently outperforms state-of-the-art models, achieving better performance in 20 out of 28 ($71.4\%$) evaluated experimental setups for MSE.

Multivariate time series forecasting is critical in many real-world systems, and thus modeling cross-channel dependencies is essential. Although existing methods improve overall accuracy by enhancing representations and cross-channel interactions, it remains challenging to reliably capture inter-variable dependencies under specific conditions. We observe that dependencies in real data are often state-dependent and noisy; in such cases, dense interactions can amplify spurious correlations and lead to representation over-smoothing, which may yield unreliable predictions in certain scenarios. Motivated by this, we propose MS-FLOW, a sparse-bottleneck framework that explicitly models inter-variable interaction as capacity-limited information flow. Specifically, MS-FLOW replaces fully connected communication with selective sparse routing, retaining only a few critical dependency paths and injecting cross-variable signals under a strict communication budget, thereby suppressing redundant connections and spurious-correlation propagation. Extensive experiments demonstrate that MS-FLOW learns more reliable multivariate correlations, achieving state-of-the-art forecasting accuracy on 12 real-world benchmarks while producing fewer yet more reliable dependencies, shifting multivariate forecasting from "more interaction" to "more effective interaction".

Accurate cloud workload forecasting is pivotal for efficient resource management but remains challenging as workloads are highly volatile and prone to sudden bursts. Although wavelets preserve temporal locality, rigid fixed bases struggle with complex patterns and isolated processing neglects critical spatial dependencies. To address this, we propose SWIFT, a pure convolutional framework designed for high-efficiency workload forecasting. We introduce a Learnable Cascaded Wavelet Path that reformulates the traditional fixed wavelet bases into adaptive convolutional operators, enabling precise, data-driven feature peeling. Complementing this, our Multivariate Interaction Module sequentially models inter-variable spatial and intra-variable feature interactions to stabilize and refine noisy workload states. Extensive experiments demonstrate that SWIFT achieves SOTA accuracy with linear O(L) complexity, reducing prediction error by up to 31.04% while cutting latency by 79.74%.

Point forecasting for graph-structured multivariate time series is a fundamental problem, but rigorous uncertainty quantification for such predictions is still underexplored. Conformal prediction (CP) offers uncertainty estimation with a solid coverage guarantee under the exchangeability assumption, which requires the joint data distribution to be unchanged under permutation. However, in graph-structured time series, inherent cross-node coupling can violate the exchangeability condition, making direct application of CP unreliable. Inspired by the spectral graph theory, such coupling resides in global trends and can be characterized by the low-frequency components, while high-frequency components are nearly exchangeable. Therefore, we propose a novel concept named Spectral Graph Conditional Exchangeability (SGCE), which conditions exchangeable high-frequency components on low-frequency ones to preserve global trends and enable effective CP in the spectral domain. Based on SGCE, we further propose Spectral Conformal prediction via wAveLEt transform (SCALE). SCALE uses graph wavelets to decompose low/high-frequency components and conformalizes high-frequency residuals via adaptive gating over a low-frequency embedding. Experimental results on real-world traffic datasets show that SCALE not only achieves valid coverage but also consistently improves the coverage-efficiency trade-off over the state-of-the-art CP methods.

Reliable periodic patterns serve as a fundamental basis for accurate multivariate time series forecasting. However, existing methods either implicitly extract periodicity through complex model architectures (e.g., Transformers) with high computational overhead or overlook the intrinsic phase-amplitude coupling when modeling periodic components explicitly. To address these issues, we propose a novel Cycle-aware Phase-Amplitude Modulation Network (PAMNet) that explicitly decomposes periodic patterns into complementary phase and amplitude components. The core innovation lies in its dual-branch modulator, featuring dedicated learnable embeddings for phase positioning and amplitude modulation. The phase branch employs cyclical embeddings to capture phase-dependent mean shifts, while the amplitude branch models intensity variations to adapt to changes in variance. A lightweight modulator with element-wise fusion efficiently combines these components, enabling explicit modeling of their interactions without complex attention mechanisms. Extensive experiments on twelve real-world datasets demonstrate that our method achieves state-of-the-art performance through its novel phase-amplitude decoupling mechanism, offering a new perspective for cyclical modeling in time series forecasting.

Accurate forecasting of bus ridership (passengers numbers) is crucial for efficient management and optimization of public transport systems. Traditional forecasting models often fail to capture the unique and localized dynamics of different urban areas by treating the entire city as a single, homogeneous region. This paper introduces a novel framework that enhances bus ridership prediction by integrating a spatial clustering methodology with multi-dimensional feature analysis. The proposed framework utilizes a diverse set of data, including bus ridership data (by route number, time, and bus stop) complemented by a variety of open source data, such as spatial features (e.g., attractive destinations), meteorological conditions (e.g., temperature, rainfall), and temporal patterns (e.g., time of day, day of week). By clustering the urban area into distinct regions, based on the principle that bus stops in close proximity share similar ridership characteristics, a separate local forecasting model is trained for each of these clusters. This localized approach demonstrates an accuracy comparable to that of global models. The findings suggest that a spatially-aware, localized modeling strategy is effective for public transport prediction, paving the way for more targeted and efficient service improvements.

Multivariate time series forecasting plays a pivotal role in numerous real-world applications, including financial analysis, energy management, and traffic planning. While Transformer-based architectures have gained popularity for this task, recent studies reveal that simpler MLP-based models can achieve competitive or superior performance with significantly reduced computational cost. In this paper, we propose ITS-Mina, a novel all-MLP framework for multivariate time series forecasting that integrates three key innovations: (1) an iterative refinement mechanism that progressively enhances temporal representations by repeatedly applying a shared-parameter residual mixer stack, effectively deepening the model's computational capacity without multiplying the number of distinct parameters; (2) an external attention module that replaces traditional self-attention with learnable memory units, capturing cross-sample global dependencies at linear computational complexity; and (3) a Harris Hawks Optimization (HHO) algorithm for automatic dropout rate tuning, enabling adaptive regularization tailored to each dataset. Extensive experiments on six widely-used benchmark datasets demonstrate that ITS-Mina achieves state-of-the-art or highly competitive performance compared to eleven baseline models across multiple forecasting horizons.

Understanding how human health changes over time, and why responses to interventions vary between individuals, remains a central challenge in medicine. Here we present HealthFormer, a decoder-only transformer that models the human physiological trajectory generatively, by training on data from the Human Phenotype Project, a multi-visit cohort of over 15,000 deeply phenotyped individuals. We tokenise each participant's health trajectory across 667 measurements spanning seven domains: blood biomarkers, body composition, sleep physiology, continuous glucose monitoring, gut microbiome, wearable-derived physiology, and behaviour and medication exposure. We train HealthFormer to forecast individual physiological trajectories across these domains, and from this single generative objective a range of clinically relevant tasks can be expressed as queries on the model. We show that, without task-specific training, HealthFormer transfers to four independent cohorts and improves prediction for 27 of 30 incident-disease and mortality endpoints, exceeding established clinical risk scores in every comparison. We further show that the model can simulate interventions in silico: in a held-out personalised-nutrition trial, intervention-conditioned predictions recover individual six-month biomarker changes (e.g., Pearson r = 0.78 for diastolic blood pressure). Across 41 randomised intervention-outcome comparisons drawn from published trials, our results show that the predicted direction of effect agrees in every case, and the predicted mean falls within the reported 95% confidence interval in 30 cases. We position HealthFormer as an initial health world model, from which forecasting, risk stratification, and intervention-conditioned simulation arise as queries, providing a basis for clinical digital twins.

Joint probabilistic modeling is essential for forecasting irregular multivariate time series (IMTS) to accurately quantify uncertainty. Existing approaches often struggle to balance model expressivity with consistent marginalization, frequently leading to unreliable or contradictory forecasts. To address this, we propose CircuITS, a novel architecture for probabilistic IMTS forecasting based on probabilistic circuits. Our model is flexible in capturing intricate dependencies between time series channels while structurally guaranteeing valid joint distributions. Experiments on four real world datasets demonstrate that CircuITS achieves superior joint and marginal density estimation compared to state of the art baselines.

Accurate forecasting of solar power output is essential for efficient integration of renewable energy into the grid. In this study, an attention-based deep learning model, inspired by transformer architecture, is used for short-term solar power forecasting. Our proposed model, "SolarTformer", is designed to predict solar power output from meteorological data. Unlike traditional models, SolarTformer leverages self-attention mechanisms to effectively capture temporal dependencies and spatial variability in solar irradiance. In addition, the proposed methodology includes feeding power station-specific metadata into the model, which helps to generalize between power stations located at different locations and with different panel configurations and in different seasons. Our experiments demonstrate that SolarTformer significantly outperforms previous models on the same data set. In particular, the model exhibits strong performance on both clear and cloudy days, indicating high robustness and generalizability. These findings highlight the potential of attention-based architectures in enhancing the accuracy of solar forecasting, contributing to a more reliable management of renewable energy.

Accurate long-term time series forecasting (LTSF) requires the capture of complex long-range dependencies and dynamic periodic patterns. Recent advances in frequency-domain analysis offer a global perspective for uncovering temporal characteristics. However, real-world time series often exhibit pronounced cross-domain heterogeneity where variables that appear synchronized in the time domain can differ substantially in the frequency domain. Existing frequency-based LTSF methods often rely on implicit assumptions of cross-domain homogeneity, which limits their ability to adapt to such intricate variability. To effectively integrate frequency-domain analysis with temporal dependency learning, we propose AdaMamba, a novel framework that endogenizes adaptive and context-aware frequency analysis within the Mamba state-space update process. Specifically, AdaMamba introduces an interactive patch encoding module to capture inter-variable interaction dynamics. Then, we develop an adaptive frequency-gated state-space module that generates input-dependent frequency bases, and generalizes the conventional temporal forgetting gate into a unified time-frequency forgetting gate. This allows dynamic calibration of state transitions based on learned frequency-domain importance, while preserving Mamba's capability in modeling long-range dependencies. Extensive experiments on seven public LTSF benchmarks and two domain-specific datasets demonstrate that AdaMamba consistently outperforms state-of-the-art methods in forecasting accu racy while maintaining competitive computational efficiency. The code of AdaMamba is available at https://github.com/XDjiang25/AdaMamba.

Shanghai Composite Index prediction has become a hot issue for many investors and academic researchers. Deep learning models are widely applied in multivariate time series forecasting, including recurrent neural networks (RNN), convolutional neural networks (CNN), and transformers. Specifically, the Transformer encoder, with its unique attention mechanism and parallel processing capabilities, has become an important tool in time series prediction, and has an advantage in dealing with long sequence dependencies and multivariate data correlations. Drawing on the strengths of various models, we propose the CNN-Transformer-LSTM Networks (CTLNet). This paper explores the application of CTLNet for Shanghai Composite Index prediction and the comparative experiments show that the proposed model outperforms state-of-the-art baselines.

Oil and gas drilling operations generate extensive time-series data from surface sensors, yet accurate real-time prediction of critical downhole metrics remains challenging due to the scarcity of labelled downhole measurements. This systematic mapping study reviews thirteen papers published between 2015 and 2025 to assess the potential of Masked Autoencoder Foundation Models (MAEFMs) for predicting downhole metrics from surface drilling data. The review identifies eight commonly collected surface metrics and seven target downhole metrics. Current approaches predominantly employ neural network architectures such as artificial neural networks (ANNs) and long short-term memory (LSTM) networks, yet no studies have explored MAEFMs despite their demonstrated effectiveness in time-series modeling. MAEFMs offer distinct advantages through self-supervised pre-training on abundant unlabeled data, enabling multi-task prediction and improved generalization across wells. This research establishes that MAEFMs represent a technically feasible but unexplored opportunity for drilling analytics, recommending future empirical validation of their performance against existing models and exploration of their broader applicability in oil and gas operations.

Consumer wearables enable continuous measurement of physiological data related to stress and recovery, but turning these streams into actionable, personalized stress-management recommendations remains a challenge. In practice, users often do not know how a given intervention, defined as an activity intended to reduce stress, will affect heart rate (HR), heart rate variability (HRV), or inter-beat intervals (BBI) over the next 15 to 120 minutes. We present a framework that predicts post-intervention trajectories and the direction of change for these physiological indicators across time windows. Our methodology combines a Transformer model for multi-horizon trajectories of percent change relative to a pre-intervention baseline, direction-of-change calls (positive, negative, or neutral) at each horizon, and an empirical study using wearable sensor data overlaid with user-tagged events and interventions. This proof of concept shows that personalized post-intervention prediction is feasible. We encourage future integration into stress-management tools for personalized intervention recommendations tailored to each person's day following further validation in larger studies and, where applicable, appropriate regulatory review.

Augmentation has become a central technique for improving deep forecasting models, but classification-style transformations tend to break the coherence between the look-back window and its continuous future target. We describe a simple procedure that unfolds the joint input-target sequence into overlapping sliding windows, randomly reorders a controlled fraction of them-prioritized by a lightweight variance criterion-and reconstructs the sequence by averaging across the overlaps, producing synthetic samples with controlled variation while limiting temporal distortion. The procedure is model-agnostic, introduces only three interpretable hyperparameters, and achieves strong improvements over a comprehensive set of competing augmentations across nine long-term forecasting benchmarks with five backbone families (TSMixer, DLinear, PatchTST, TiDE, LightTS) and four short-term traffic benchmarks with PatchTST. Component-wise ablations, hyperparameter sensitivity studies, distributional-alignment diagnostics, probabilistic forecasting evaluation, and a transfer experiment to univariate and multivariate time series classification clarify the contribution of each design choice.