Explainable Time Series Forecasting

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Overview

Explainable time series forecasting studies how to show which past observations, variables, contexts, or learned dynamics shape predictions across future horizons. Approaches include post-hoc methods such as SHAP and counterfactuals, interpretable decompositions and symbolic equations, causal or concept-based models, and language-model reasoning. Methods are tested on settings such as energy demand, health, traffic, and industrial forecasting, where temporal dependence, multiple variables, uncertainty, and changing regimes matter. A central challenge is ensuring explanations are faithful and stable—not merely plausible—while preserving forecast accuracy, especially when different horizons rely on different evidence.

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61 papers12 papers in the last four weeks, up 50% on the four weeks before. 0.1% of all new papers.

Jul 30, 2026

HealthCAT: An Interpretable Encoder-only Transformer Framework for Health Indicator Prediction and Temporal Interpretation of Wearable Sensor Data

Wearable sensors continuously capture fine-grained multivariate time-series data, providing opportunities to model behavioural patterns associated with health outcomes. However, existing deep learning methods prioritise predictive accuracy over interpretability, limiting their application in health research. In this study, we present HealthCAT, a flexible framework that integrates an Encoder-only Transformer with an Attentive Class Activation Token (AttentiveCAT) to generate class-specific, time-step-level interpretations. These interpretations can be mapped back onto behavioural cycles that are relevant to the domain (e.g., time-of-day), supporting individual-level analysis of wearable sensor data. We evaluated HealthCAT using two real-world wearable sensor datasets (306 participants in total). HealthCAT outperformed deep learning baselines by up to 17% in F1-score and 12% in accuracy on both datasets (p<0.05p<0.05). In masking experiments, the time steps identified by HealthCAT carried significantly more predictive value than random selection across all masking conditions (p<0.05p<0.05), indicating that the identified time steps are predictively informative. By coupling predictive performance with validated time-step-level interpretability, HealthCAT moves wearable sensor analysis beyond aggregated metrics towards temporal patterns that support health monitoring, behavioural pattern analysis, and intervention design in health research. The significance of this work is that it enables accurate prediction of health indicators from wearable sensor data while providing insights into when and how physical activity patterns occur, rather than relying solely on aggregated summary measures.

Xiaotong Yu, Joshua Y. Kim, HaeJin Lee +1

Transformer InterpretabilityExplainable Time Series ForecastingExplainable Artificial IntelligenceTime Series ClassificationWearable Health MonitoringTime Series Transformers
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Jul 2, 2026

Autorelevance function and other feature relevance measures for univariate time series

We propose a model agnostic methodology to measure lag relevance in machine learning forecasting models applied to univariate time series. Particularly, we are working in the context of time series using the frameworks of Ghost variables and Shapley values, together with additive importance measures, to introduce the auto-relevance and partial auto-relevance functions as the lag importance values. Additionally, we propose a novel method to replace absent features in coalition based methods with a one step forecast from the same model. We evaluate these proposals under different simulations and real data cases. This combined framework perspective is particularly suitable for time series. In addition, to show our discoveries we use a pull of models from the seasonal ARMA family and recurrent neural networks. We found that the calculated relevance measures successfully demonstrate the expected lag structure in almost all cases.

Julian Cardenas, Jamie Arjona, Pedro Delicado

Departament d’Estad´ıstica i Investigaci´o Operativa, Universitat Polit`ecnica de Catalunya - BarcelonaTech, C/ Jordi Girona 1-3, Barcelona, 08034, Catalunya, Spain.

Explainable Time Series ForecastingFeature AttributionTime Series ForecastingShapley Value Attribution
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Jun 25, 2026

Global Explanations for Multivariate Time Series Forecasting Models via KK-Order Markov Approximations

While many explainable AI (XAI) methods have been proposed, most are not designed for time-series forecasting models and often rely on the implicit assumption that timestamp features are independent. This assumption ignores the fundamental property of temporal dependence and can lead to explanations that violate the sequential and causal structure of the data. We introduce KARMA, a method for explaining time-series predictors by constructing a Markov surrogate model that captures the temporal dependencies learned by the predictor. Our approach revolves around three main aspects: identifying the minimal history length KK that is predictively sufficient for the model, estimating the best-fitting KK-order Markov transition kernel from the discretized history space, and a five-level global explanation hierarchy that can be derived from the Markov transition kernel, which we illustrate using real-world weather data (Beijing PM 2.5). We also certify using complex synthetic data with known true causal edges that KARMA (i) recovers the data causal structure as learned by the model via a controlled experiment and (ii) identifies temporal dependencies better than established attribution methods such as TimeSHAP.

Amadeo Tunyi

XITASO GmbH Austraße 35, 86153 Augsburg, Germany

Markov ModelsSurrogate ModelingExplainable Time Series ForecastingMultivariate Time Series ForecastingCausal InterpretabilityTime Series Forecasting+1
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Jun 23, 2026

FDN: Interpretable Spatiotemporal Forecasting with Future Decomposition Networks

Spatiotemporal systems comprise a collection of spatially distributed yet interdependent entities each generating unique dynamic signals. Highly sophisticated methods have been proposed in recent years delivering state-of-the-art (SOTA) forecasts but few have focused on interpretability. To address this, we propose the Future Decomposition Network (FDN), a novel forecast model capable of (a) providing interpretable predictions through classification (b) revealing latent activity patterns in the target time-series and (c) delivering forecasts competitive with SOTA methods at a fraction of their memory and runtime cost. We conduct comprehensive analyses on FDN for multiple datasets from hydrologic, traffic, and energy systems, demonstrating its improved accuracy and interpretability.

Nicholas Majeske, Ariful Azad

Department of Intelligent Systems Engineering, Indiana University Bloomington, USA · Department of Computer Science and Engineering, Texas A&M University, USA

Explainable Time Series ForecastingTime Series ForecastingTime Series DecompositionSpatiotemporal Forecasting
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Jun 16, 2026

ConTex: Reformulating Counterfactual Generation For Time Series Forecasting

Decision-making with deep learning-based time series forecasting requires not only accurate predictions but also actionable insights. However, current architectures do not inherently provide such information. Specifically, guidance is needed on how current conditions must be modified to shift from a predicted outcome to a desired future scenario. Counterfactual explanations provide a natural framework for this task, as they represent minimal input changes that alter the model's prediction, indicating when and how intervention is required. Existing approaches rely on instance-wise optimization, leading to inconsistency across instances, high computational costs, and limited applicability in real-time settings. To address these limitations, we reformulate counterfactual generation for time series forecasting as the problem of learning a globally consistent intervention strategy, allowing counterfactuals to be generated through a single shared function. We propose Counterfactual Time Series Explanations (ConTex), a model-agnostic, decomposed architecture comprising a temporal context encoder and a conditional encoder, followed by two heads that capture interventions in terms of temporal relevance and modification strength. This structure overcomes the instability and inconsistency of instance-based approaches by producing targeted, interpretable interventions across time and feature dimensions in a single forward pass, making it suitable for real-time applications. Across multiple forecasting architectures and benchmark datasets, ConTex achieves state-of-the-art validity while generating sparse counterfactuals that minimize the number of necessary interventions. Additionally, our approach reduces computational cost by at least 12-36x compared to instance-wise generation and supports real-time inference at approximately 0.007 seconds.

Jan Voets, Hasan Tercan, Tobias Meisen +1

Institute for Technologies and Management of Digital Transformation University of Wuppertal

Explainable Time Series ForecastingCounterfactual ExplanationsCausal Counterfactual GenerationTime Series ForecastingGraph Counterfactual ExplanationsCounterfactual Learning
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Jun 2, 2026

AnchorMoE: Interpretable Time Series Classification via Anchor-Routed MoE

Multivariate time series classification (MTSC) is pivotal in high-stakes domains, such as clinical diagnosis and industrial fault detection, where safe deployment necessitates transparent decision-making. However, isolating the temporal segments that drive model predictions is challenging because discriminative signals in real-world time series are typically sparse, heterogeneous, and heavily obscured by background noise. This paper, therefore, proposes AnchorMoE, an interpretable-by-construction classification framework. Built upon a Mixture-of-Experts (MoE) architecture, AnchorMoE encodes multi-view representations of local patches and routes them to specialized experts, ensuring that the final prediction is formulated as an exact additive decomposition over the input segments, facilitating ante-hoc transparency rather than relying on post-hoc estimations. To maintain the reliability of this decomposition under sparse signal distributions, we introduce a geometric orthogonality constraint that penalizes representational redundancy, compelling distinct experts to specialize in heterogeneous predictive patterns. Furthermore, an uncertainty-aware reliability gate is designed to dynamically calibrate the contribution of each segment, effectively suppressing residual background noise. Extensive experiments on real-world and synthetic benchmarks demonstrate that AnchorMoE achieves highly competitive classification performance while faithfully grounding its decisions in the raw time series.

Tao Xie, Zexi Tan, Haoyi Xiao +5

Guangdong University of Technology · Guangzhou, China · Shenzhen University +7

Explainable Time Series ForecastingMultivariate Time Series ClassificationTime Series ClassificationMixture of ExpertsInterpretable Time-Series Classification
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May 15, 2026

Peak-Detector: Explainable Peak Detection via Instruction-Tuned Large Language Models in Physiological Sign

Accurate peak detection across diverse cardiac physiological signals, including the Electrocardiogram (ECG), Photoplethysmogram (PPG), Ballistocardiogram (BCG), and Bodyseismography (BSG), is fundamental for cardiovascular monitoring but is often hindered by artifacts and signal variability. Conventional algorithms are typically engineered with expert knowledge for a single signal modality, limiting their generalizability. Conversely, deep learning-based methods often lack interpretability, limiting transparency for expert verification and hindering expert-computer interaction. To address these limitations, we introduce Peak-Detector, a novel framework that leverages instruction-tuned Large Language Models (LLMs) for robust, cross-modal, and explainable peak detection. A core innovation of our framework is a "peak-representation" technique that transforms time-series data into a condensed format, preserving critical event information while significantly reducing signal length. This representation provides a crucial inductive bias, guiding the LLM to reason over physiologically meaningful events rather than raw, noisy data. The model is optimized through a two-stage process: supervised fine-tuning (SFT) followed by reinforcement learning (RL) with a multi-objective reward function. The model's self-explanation capabilities are cultivated by fine-tuning on a custom-built Peak-Explanation dataset. Across four modalities-ECG, PPG, BCG, and BSG-spanning seven datasets (six public benchmarks plus one real-world cohort), Peak-Detector demonstrates strong cross-modal performance, achieving best or tied-best detection under clinically relevant temporal tolerance. Beyond accuracy, the generated rationales surface failure modes and support verification and error analysis.

Jiahui Li, Yida Zhang, Zixuan Zeng +10

University of Georgia, Athens, Georgia, USA · Yixing People’s Hospital, Yixing, Jiangsu Province, China · University of Washington, Seattle, Washington, USA +1

Explainable Time Series Forecasting
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May 13, 2026

INSIGHTS: Demonstration-Based Summaries of Time Series Predictors

Explainability methods have progressed rapidly, but global explanations for time-series models remain underdeveloped, with most approaches focusing on local, instance-level attributions. We introduce INSIGHTS, a model-agnostic, user-centric approach for providing global explanations of time series models. Our approach prioritizes simplicity, efficiency, and transparency in its design, ensuring that stakeholders can readily adopt its outputs. While current methods focus on local explanations, INSIGHTS generates sample summaries that offer a comprehensive overview of model behavior. It balances the importance and diversity of time series samples to create informative subsets using utility functions that capture domain-specific aspects of time series behavior, such as exceeding domain norms. We evaluate INSIGHTS through experiments, interviews, and a user study. Our results indicate INSIGHTS effectively constructs comprehensive, diverse time series subsets, producing summaries manageable for individual evaluation. It is preferred by domain experts for its ability to provide a stable understanding of model behavior and the quality of the samples identified. Moreover, user study participants presented with INSIGHTS-based summaries exhibit an enhanced understanding of the model's overall behavior.

Bar Eini Porat, Rom Gutman, Uri Shalit +1

Technion Israel Institute of Technology · Tel-Aviv University

Explainable Time Series ForecastingExplainable Artificial IntelligenceInterpretable ML
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May 7, 2026

Temporal Functional Circuits: From Spline Plots to Faithful Explanations in KAN Forecasting

Unlike MLPs, Kolmogorov-Arnold Networks (KANs) expose explicit learnable edge functions on every connection, enabling mechanistic explanation in time-series forecasting. This paper introduces Temporal Functional Circuits, a framework that transforms KAN edge functions from latent visualizations into faithful, temporally grounded explanations. Built on a gated residual KAN that decomposes forecasts into a linear base and a sparsely activated KAN correction, the framework (i) maps each edge to input lags via output-aware attribution, (ii) ranks edges by learned activation range, and (iii) validates faithfulness through edge-level interventions including zeroing and spline removal. Removing the learned B-spline component while retaining the base SiLU term degrades forecasts, providing evidence that the spline shape itself carries predictive value beyond the base activation. On four synthetic regimes of increasing complexity, the learned gate opens progressively wider as signal complexity grows. On regime-switching signals, gated KAN achieves 59% lower MSE than linear-only models. Across eight benchmarks, the gated architecture is competitive with linear, attention, and MLP alternatives, while providing interpretable edge functions that MLP-based corrections cannot offer.

Naveen Mysore

University of California, Santa Barbara

Explainable Time Series ForecastingExplainable Artificial IntelligenceTime Series ForecastingNeural Network InterpretabilityKolmogorov-Arnold Networks
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Apr 30, 2026

Explainable Load Forecasting with Covariate-Informed Time Series Foundation Models

Time Series Foundation Models (TSFMs) have recently emerged as general-purpose forecasting models and show considerable potential for applications in energy systems. However, applications in critical infrastructure like power grids require transparency to ensure trust and reliability and cannot rely on pure black-box models. To enhance the transparency of TSFMs, we propose an efficient algorithm for computing Shapley Additive Explanations (SHAP) tailored to these models. The proposed approach leverages the flexibility of TSFMs with respect to input context length and provided covariates. This property enables efficient temporal and covariate masking (selectively withholding inputs), allowing for a scalable explanation of model predictions using SHAP. We evaluate two TSFMs - Chronos-2 and TabPFN-TS - on a day-ahead load forecasting task for a transmission system operator (TSO). In a zero-shot setting, both models achieve predictive performance competitive with a Transformer model trained specifically on multiple years of TSO data. The explanations obtained through our proposed approach align with established domain knowledge, particularly as the TSFMs appropriately use weather and calendar information for load prediction. Overall, we demonstrate that TSFMs can serve as transparent and reliable tools for operational energy forecasting.

Matthias Hertel, Alexandra Nikoltchovska, Sebastian Pütz +3

Karlsruhe Institute of Technology, Karlsruhe, Germany

Explainable Time Series ForecastingTime Series ForecastingShapley Value AttributionElectricity Load ForecastingTime-Series Foundation Models
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Apr 27, 2026

DecompKAN: Decomposed Patch-KAN for Long-Term Time Series Forecasting

Accurate time series forecasting in scientific domains such as climate modeling, physiological monitoring, and energy systems benefits from both competitive predictions and model transparency. This work proposes DecompKAN, a lightweight attention-free architecture that combines trend-residual decomposition, channel-wise patching, learned instance normalization, and B-spline Kolmogorov-Arnold Network (KAN) edge functions. Each KAN edge learns an explicit, inspectable 1D scalar function over learned patch-embedding coordinates that can be directly visualized. On standard benchmarks, DecompKAN achieves best or tied-best MSE on 15 of 32 dataset-horizon combinations among selected published baselines, and achieves best or tied-best MSE on 20 of 36 comparisons under a controlled same-recipe evaluation across 9 datasets including the physiological PPG-DaLiA benchmark. The architecture shows particular strength on datasets with smooth temporal dynamics (Solar -17%, ECL -10% vs. iTransformer, Weather) and physiological time series. Visualization of learned edge functions reveals qualitatively different latent nonlinearities across domains. Ablation analysis shows that the architectural pipeline (decomposition, patching, normalization) drives performance more than the choice of nonlinear layer, while the KAN formulation enables inspection of learned latent transformations.

Naveen Mysore

Long-Term Time Series ForecastingExplainable Time Series ForecastingTime Series ForecastingKolmogorov-Arnold Networks
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Apr 20, 2026

CAARL: In-Context Learning for Interpretable Co-Evolving Time Series Forecasting

In this paper we investigate forecasting coevolving time series that feature intricate dependencies and nonstationary dynamics by using an LLM Large Language Models approach We propose a novel modeling approach named ContextAware ARLLM CAARL that provides an interpretable framework to decode the contextual dynamics influencing changes in coevolving series CAARL decomposes time series into autoregressive segments constructs a temporal dependency graph and serializes this graph into a narrative to allow processing by LLM This design yields a chainofthoughtlike reasoning path where intermediate steps capture contextual dynamics and guide forecasts in a transparent manner By linking prediction to explicit reasoning traces CAARL enhances interpretability while maintaining accuracy Experiments on realworld datasets validate its effectiveness positioning CAARL as a competitive and interpretable alternative to stateoftheart forecasting methods

Etienne Tajeuna, Patrick Asante Owusu, Armelle Brun +1

Explainable Time Series ForecastingTime Series ForecastingLLM-Based Time Series ForecastingNon-Stationary Time Series ForecastingIn-Context Learning
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Apr 14, 2026

CycloneMAE: A Scalable Multi-Task Learning Model for Global Tropical Cyclone Probabilistic Forecasting

Tropical cyclones (TCs) rank among the most destructive natural hazards, yet their forecasting faces fundamental trade-offs: numerical weather prediction (NWP) models are computationally prohibitive and struggle to leverage historical data, while existing deep learning (DL)-based intelligent models are variable-specific and deterministic, which fail to generalize across different forecasting variables. Here we present CycloneMAE, a scalable multi-task forecasting model that learns transferable TC representations from multi-modal data using a TC structure-aware masked autoencoder. By coupling a discrete probabilistic gridding mechanism with a pre-train/fine-tune paradigm, CycloneMAE simultaneously delivers deterministic forecasts and probability distributions. Evaluated across five global ocean basins, CycloneMAE outperforms leading NWP systems in pressure and wind forecasting up to 120 hours and in track forecasting up to 24 hours. Attribution analysis via integrated gradients reveals physically interpretable learning dynamics: short-term forecasts rely predominantly on the internal core convective structure from satellite imagery, whereas longer-term forecasts progressively shift attention to external environmental factors. Our framework establishes a scalable, probabilistic, and interpretable pathway for operational TC forecasting.

Renlong Hang, Zihao Xu, Jiuwei Zhao +3

School of Computer Science, School of Software, Nanjing University of Information Science and Technology, Nanjing, 210044, China. · School of Atmospheric Sciences, Nanjing University of Information Science and Technology, Nanjing, 210044, China. · Shanghai Typhoon Institute, China Meteorological Administration, Shanghai, 200030, China. +1

Tropical Cyclone Intensity ForecastingWeather ForecastingProbabilistic ForecastingMulti-Task LearningMasked AutoencodersExplainable Time Series Forecasting
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Apr 8, 2026

DSPR: Dual-Stream Physics-Residual Networks for Trustworthy Industrial Time Series Forecasting

Accurate forecasting of industrial time series requires balancing predictive accuracy with physical plausibility under non-stationary operating conditions. Existing data-driven models often achieve strong statistical performance but struggle to respect regime-dependent interaction structures and transport delays inherent in real-world systems. To address this challenge, we propose DSPR (Dual-Stream Physics-Residual Networks), a forecasting framework that explicitly decouples stable temporal patterns from regime-dependent residual dynamics. The first stream models the statistical temporal evolution of individual variables. The second stream focuses on residual dynamics through two key mechanisms: an Adaptive Window module that estimates flow-dependent transport delays, and a Physics-Guided Dynamic Graph that incorporates physical priors to learn time-varying interaction structures while suppressing spurious correlations. Experiments on four industrial benchmarks spanning heterogeneous regimes demonstrate that DSPR consistently improves forecasting accuracy and robustness under regime shifts while maintaining strong physical plausibility. It achieves state-of-the-art predictive performance, with Mean Conservation Accuracy exceeding 99% and Total Variation Ratio reaching up to 97.2%. Beyond forecasting, the learned interaction structures and adaptive lags provide interpretable insights that are consistent with known domain mechanisms, such as flow-dependent transport delays and wind-to-power scaling behaviors. These results suggest that architectural decoupling with physics-consistent inductive biases offers an effective path toward trustworthy industrial time-series forecasting. Furthermore, DSPR's demonstrated robust performance in long-term industrial deployment bridges the gap between advanced forecasting models and trustworthy autonomous control systems.

Yeran Zhang, Pengwei Yang, Guoqing Wang +1

School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, China · Research Center, East Hope Group Co., Ltd, Shanghai, China

Time Series ForecastingMultivariate Time Series ForecastingNon-Stationary Time Series ForecastingPhysics-Informed MLExplainable Time Series ForecastingDynamic Graph Learning
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Apr 7, 2026

TFRBench: A Reasoning Benchmark for Evaluating Forecasting Systems

We introduce TFRBench, the first benchmark designed to evaluate the reasoning capabilities of forecasting systems. Traditionally, time-series forecasting has been evaluated solely on numerical accuracy, treating foundation models as ``black boxes.'' Unlike existing benchmarks, TFRBench provides a protocol for evaluating the reasoning generated by forecasting systems--specifically their analysis of cross-channel dependencies, trends, and external events. To enable this, we propose a systematic multi-agent framework that utilizes an iterative verification loop to synthesize numerically grounded reasoning traces. Spanning ten datasets across five domains, our evaluation confirms that this reasoning is causally effective; useful for evaluation; and prompting LLMs with our generated traces significantly improves forecasting accuracy compared to direct numerical prediction (e.g., avg. ∼40.2%→56.6%)\sim40.2\%\to56.6\%), validating the quality of our reasoning. Conversely, benchmarking experiments reveal that off-the-shelf LLMs consistently struggle with both reasoning (lower LLM-as-a-Judge scores) and numerical forecasting, frequently failing to capture domain-specific dynamics. TFRBench thus establishes a new standard for interpretable, reasoning-based evaluation in time-series forecasting. Our benchmark is available at: https://tfrbench.github.io

Md Atik Ahamed, Mihir Parmar, Palash Goyal +7

Google · University of Kentucky

Forecasting BenchmarksTime Series ReasoningExplainable Time Series ForecastingLLM-Based Time Series Forecasting
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Mar 26, 2026

Interpretable PM2.5 Forecasting for Urban Air Quality: A Comparative Study of Adaptive Time-Series Models

Accurate short-term air-quality forecasting is essential for public health protection and urban management, yet many recent forecasting frameworks rely on complex, data-intensive, and computationally demanding models. This study investigates whether lightweight and interpretable forecasting approaches can provide competitive performance for hourly PM2.5 prediction in Beijing, China. Using multi-year pollutant and meteorological time-series data, we developed a leakage-aware forecasting workflow that combined chronological data partitioning, preprocessing, feature selection, and exogenous-driver modeling under the Perfect Prognosis setting. Three forecasting families were evaluated: SARIMAX, Facebook Prophet, and NeuralProphet. To assess practical deployment behavior, the models were tested under two adaptive regimes: weekly walk-forward refitting and frozen forecasting with online residual correction. Results showed clear differences in both predictive accuracy and computational efficiency. Under walk-forward refitting, Facebook Prophet achieved the strongest completed performance, with an MAE of 37.6137.61 and an RMSE of 50.1050.10, while also requiring substantially less execution time than NeuralProphet. In the frozen-model regime, online residual correction improved Facebook Prophet and SARIMAX, with corrected SARIMAX yielding the lowest overall error (MAE 32.5032.50; RMSE 46.8546.85). NeuralProphet remained less accurate and less stable across both regimes, and residual correction did not improve its forecasts. Notably, corrected Facebook Prophet reached nearly the same error as its walk-forward counterpart while reducing runtime from 1515 min 21.9121.91 sec to 46.6046.60 sec. These findings show that lightweight additive forecasting strategies can remain highly competitive for urban air-quality prediction, offering a practical balance between accuracy, interpretability, ...

Moazzam Umer Gondal, Hamad ul Qudous, Asma Ahmad Farhan +1

School of Computing, National University of Computer & Emerging Sciences (FAST), Lahore 54000, Pakistan · College of Computing and Informatics, Saudi Electronic University, Riyadh, 11673, Saudi Arabia

Air Quality PredictionTime Series ForecastingExplainable Time Series Forecasting
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Mar 25, 2026

A Practical Guide Towards Interpreting Time-Series Deep Clinical Predictive Models: A Reproducibility Study

Clinical decisions are high-stakes and require explicit justification, making model interpretability essential for auditing deep clinical models prior to deployment. As the ecosystem of model architectures and explainability methods expands, critical questions remain: Do architectural features like attention improve explainability? Do interpretability approaches generalize across clinical tasks? While prior benchmarking efforts exist, they often lack extensibility and reproducibility, and critically, fail to systematically examine how interpretability varies across the interplay of clinical tasks and model architectures. To address these gaps, we present a comprehensive benchmark evaluating interpretability methods across diverse clinical prediction tasks and model architectures. Our analysis reveals that: (1) attention when leveraged properly is a highly efficient approach for faithfully interpreting model predictions; (2) black-box interpreters like KernelSHAP and LIME are computationally infeasible for time-series clinical prediction tasks; and (3) several interpretability approaches are too unreliable to be trustworthy. From our findings, we discuss several guidelines on improving interpretability within clinical predictive pipelines. To support reproducibility and extensibility, we provide our implementations via PyHealth, a well-documented open-source framework: https://github.com/sunlabuiuc/PyHealth.

Yongda Fan, John Wu, Andrea Fitzpatrick +3

University of Illinois Urbana-Champaign, Champaign, IL 61801, USA · PyHealth · University of Illinois College of Medicine, Chicago, IL 60612, USA

Explainable Time Series ForecastingNeural Network InterpretabilityExplainability EvaluationClinical Prediction
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Mar 19, 2026

MLOW: Interpretable Low-Rank Frequency Magnitude Decomposition of Multiple Effects for Time Series Forecasting

Separating multiple effects in time series is fundamental yet challenging for time-series forecasting (TSF). However, existing TSF models cannot effectively learn interpretable multi-effect decomposition by their smoothing-based temporal techniques. Here, a new interpretable frequency-based decomposition pipeline MLOW captures the insight: a time series can be represented as a magnitude spectrum multiplied by the corresponding phase-aware basis functions, and the magnitude spectrum distribution of a time series always exhibits observable patterns for different effects. MLOW learns a low-rank representation of the magnitude spectrum to capture dominant trending and seasonal effects. We explore low-rank methods, including PCA, NMF, and Semi-NMF, and find that none can simultaneously achieve interpretable, efficient and generalizable decomposition. Thus, we propose hyperplane-nonnegative matrix factorization (Hyperplane-NMF). Further, to address the frequency (spectral) leakage restricting high-quality low-rank decomposition, MLOW enables a flexible selection of input horizons and frequency levels via a mathematical mechanism. Visual analysis demonstrates that MLOW enables interpretable and hierarchical multiple-effect decomposition, robust to noises. It can also enable plug-and-play in existing TSF backbones with remarkable performance improvement but minimal architectural modifications.

Runze Yang, Longbing Cao, Xiaoming Wu +4

1Macquarie University · 2Shanghai Jiao Tong University · 3Nanyang Technological University +1

Frequency-Domain Time Series ModelingTime Series ForecastingTime Series DecompositionExplainable Time Series ForecastingLow-Rank Matrix Decomposition
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Mar 14, 2026

Locally Linear Continual Learning for Time Series based on VC-Theoretical Generalization Bounds

Most machine learning methods assume fixed probability distributions, limiting their applicability in nonstationary real-world scenarios. While continual learning methods address this issue, current approaches often rely on black-box models or require extensive user intervention for interpretability. We propose SyMPLER (Systems Modeling through Piecewise Linear Evolving Regression), an explainable model for time series forecasting in nonstationary environments based on dynamic piecewise-linear approximations. Unlike other locally linear models, SyMPLER uses generalization bounds from Statistical Learning Theory to automatically determine when to add new local models based on prediction errors, eliminating the need for explicit clustering of the data. Experiments show that SyMPLER can achieve comparable performance to both black-box and existing explainable models while maintaining a human-interpretable structure that reveals insights about the system's behavior. In this sense, our approach conciliates accuracy and interpretability, offering a transparent and adaptive solution for forecasting nonstationary time series.

Yan V. G. Ferreira, Igor B. Lima, Pedro H. G. Mapa S. +2

Department of Electronic Engineering, Universidade Federal de Minas Gerais, UFMG, Belo Horizonte 31270-901, Brazil · Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada · Graduate Program in Electrical Engineering, Universidade Federal de Minas Gerais, UFMG, Belo Horizonte 31270-901, Brazil

Explainable Time Series ForecastingNon-Stationary Time Series ForecastingOnline Continual LearningLinear Regression
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Mar 13, 2026

Explainable AI Using Inherently Interpretable Components for Wearable-based Health Monitoring

The use of wearables in medicine and wellness, enabled by AI-based models, offers tremendous potential for real-time monitoring and interpretable event detection. Explainable AI (XAI) is required to assess what models have learned and build trust in model outputs, for patients, healthcare professionals, model developers, and domain experts alike. Explaining AI decisions made on time-series data recorded by wearables is especially challenging due to the data's complex nature and temporal dependencies. Too often, explainability using interpretable features leads to performance loss. We propose a novel XAI method that combines explanation spaces and concept-based explanations to explain AI predictions on time-series data. By using Inherently Interpretable Components (IICs), which encapsulate domain-specific, interpretable concepts within a custom explanation space, we preserve the performance of models trained on time series while achieving the interpretability of concept-based explanations based on extracted features. Furthermore, we define a domain-specific set of IICs for wearable-based health monitoring and demonstrate their usability in real applications, including state assessment and epileptic seizure detection.

Maurice Kuschel, Solveig Vieluf, Claus Reinsberger +2

Signal and System Theory Group, Paderborn University, Paderborn, Germany · Department of Medicine I, Ludwig Maximilian University, Munich, Germany · Konrad Zuse School of Excellence in Reliable AI, Munich, Germany +3

Explainable Time Series ForecastingExplainable Artificial IntelligenceInterpretable MLConcept-Based ExplanationsWearable Health Monitoring
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Mar 11, 2026

Data-Driven Integration Kernels for Interpretable Nonlocal Operator Learning

Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it makes learned relationships difficult to interpret and prone to overfitting as the extent of nonlocal information grows. We address this challenge by introducing data-driven integration kernels, a framework that adds structure to nonlocal operator learning by explicitly separating nonlocal information aggregation from local nonlinear prediction. Each spatiotemporal predictor field is first integrated using learnable kernels (defined as continuous weighting functions over horizontal space, height, and/or time), after which a local nonlinear mapping is applied only to the resulting kernel-integrated features and optional local inputs. This design confines nonlinear interactions to a small set of integrated features and makes each kernel directly interpretable as a weighting pattern that reveals which horizontal locations, vertical levels, and/or past timesteps contribute most to the prediction. We demonstrate the framework for South Asian monsoon precipitation using a hierarchy of neural network models with increasing structure, including baseline, nonparametric kernel, and parametric kernel models. Across this hierarchy, kernel models achieve near-baseline performance with far fewer trainable parameters, indicating that much of the relevant nonlocal information can be captured through a small set of interpretable integrations when appropriate structural constraints are imposed.

Savannah L. Ferretti, Jerry Lin, Sara Shamekh +3

Department of Earth System Science, University of California Irvine, Irvine, USA · Department of Computing and Data Science, Boston University, Boston, USA · The Center for Atmosphere Ocean Science, New York University, New York, USA +4

Operator LearningSpatiotemporal ForecastingExplainable Time Series ForecastingClimate Modeling
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Mar 7, 2026

Turning Time Series into Algebraic Equations: Symbolic Machine Learning for Interpretable Modeling of Chaotic Time Series

Chaotic time series are notoriously difficult to forecast. Small uncertainties in initial conditions amplify rapidly, while strong nonlinearities and regime dependent variability constrain predictability. Although modern deep learning often delivers strong short horizon accuracy, its black box nature limits scientific insight and practical trust in settings where understanding the underlying dynamics matters. To address this gap, we propose two complementary symbolic forecasters that learn explicit, interpretable algebraic equations from chaotic time series data. Symbolic Neural Forecaster (SyNF) adapts a neural network based equation learning architecture to the forecasting setting, enabling fully differentiable discovery of compact and interpretable algebraic relations. The Symbolic Tree Forecaster (SyTF) builds on evolutionary symbolic regression to search directly over equation structures under a principled accuracy complexity trade off. We evaluate both approaches in a rolling window nowcasting setting with one step ahead forecasting using several accuracy metrics and compare against a broad suite of baselines spanning classical statistical models, tree ensembles, and modern deep learning architectures. Numerical experiments cover a benchmark of 132 low dimensional chaotic attractors and two real world chaotic time series, namely weekly dengue incidence in San Juan and the Nino 3.4 sea surface temperature index. Across datasets, symbolic forecasters achieve competitive one step ahead accuracy while providing transparent equations that reveal salient aspects of the underlying dynamics.

Madhurima Panja, Grace Younes, Tanujit Chakraborty

SAFIR, Sorbonne University Abu Dhabi, UAE · Sorbonne Center for Artificial Intelligence, Sorbonne University, Paris, France

Time Series ForecastingChaotic Time-Series PredictionExplainable Time Series ForecastingSymbolic Regression
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Mar 6, 2026

Hierarchical Industrial Demand Forecasting with Temporal and Uncertainty Explanations

Hierarchical time-series forecasting is essential for demand prediction across various industries. While machine learning models have obtained significant accuracy and scalability on such forecasting tasks, the interpretability of their predictions, informed by application, is still largely unexplored. To bridge this gap, we introduce a novel interpretability method for large hierarchical probabilistic time-series forecasting, adapting generic interpretability techniques while addressing challenges associated with hierarchical structures and uncertainty. Our approach offers valuable interpretative insights in response to real-world industrial supply chain scenarios, including 1) the significance of various time-series within the hierarchy and external variables at specific time points, 2) the impact of different variables on forecast uncertainty, and 3) explanations for forecast changes in response to modifications in the training dataset. To evaluate the explainability method, we generate semi-synthetic datasets based on real-world scenarios of explaining hierarchical demands for over ten thousand products at a large chemical company. The experiments showed that our explainability method successfully explained state-of-the-art industrial forecasting methods with significantly higher explainability accuracy. Furthermore, we provide multiple real-world case studies that show the efficacy of our approach in identifying important patterns and explanations that help stakeholders better understand the forecasts. Additionally, our method facilitates the identification of key drivers behind forecasted demand, enabling more informed decision-making and strategic planning. Our approach helps build trust and confidence among users, ultimately leading to better adoption and utilization of hierarchical forecasting models in practice.

Harshavardhan Kamarthi, Shangqing Xu, Xinjie Tong +4

Georgia Institute of Technology Atlanta, USA · Aspen Technology Houston, USA · The Dow Chemical Company Houston, USA +1

Explainable Time Series ForecastingTime Series Forecasting
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Mar 4, 2026

SELDON: Supernova Explosions Learned by Deep ODE Networks

The discovery rate of optical transients will explode to 10 million public alerts per night once the Vera C. Rubin Observatory's Legacy Survey of Space and Time comes online, overwhelming the traditional physics-based inference pipelines. A continuous-time forecasting AI model is of interest because it can deliver millisecond-scale inference for thousands of objects per day, whereas legacy MCMC codes need hours per object. In this paper, we propose SELDON, a new continuous-time variational autoencoder for panels of sparse and irregularly time-sampled (gappy) astrophysical light curves that are nonstationary, heteroscedastic, and inherently dependent. SELDON combines a masked GRU-ODE encoder with a latent neural ODE propagator and an interpretable Gaussian-basis decoder. The encoder learns to summarize panels of imbalanced and correlated data even when only a handful of points are observed. The neural ODE then integrates this hidden state forward in continuous time, extrapolating to future unseen epochs. This extrapolated time series is further encoded by deep sets to a latent distribution that is decoded to a weighted sum of Gaussian basis functions, the parameters of which are physically meaningful. Such parameters (e.g., rise time, decay rate, peak flux) directly drive downstream prioritization of spectroscopic follow-up for astrophysical surveys. Beyond astronomy, the architecture of SELDON offers a generic recipe for interpretable and continuous-time sequence modeling in any time domain where data are multivariate, sparse, heteroscedastic, and irregularly spaced.

Jiezhong Wu, Jack O'Brien, Jennifer Li +6

NSF-Simons AI Institute for the Sky (SkAI), Chicago, IL, USA · Department of Industrial Engineering and Management Sciences, Northwestern University · Department of Astronomy, University of Illinois Urbana-Champaign +4

AstrophysicsIrregular Time-Series ModelingTime Series ForecastingExplainable Time Series ForecastingNeural ODEs
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Mar 4, 2026

PatchDecomp: Interpretable Patch-Based Time Series Forecasting

Time series forecasting, which predicts future values from past observations, plays a central role in many domains and has driven the development of highly accurate neural network models. However, the complexity of these models often limits human understanding of the rationale behind their predictions. We propose PatchDecomp, a neural network-based time series forecasting method that achieves both high accuracy and interpretability. PatchDecomp divides input time series into subsequences (patches) and generates predictions by aggregating the contributions of each patch. This enables clear attribution of each patch, including those from exogenous variables, to the final prediction. Experiments on multiple benchmark datasets demonstrate that PatchDecomp provides predictive performance comparable to recent forecasting methods. Furthermore, we show that the model's explanations not only influence predicted values quantitatively but also offer qualitative interpretability through visualization of patch-wise contributions.

Hiroki Tomioka, Genta Yoshimura

Mitsubishi Electric Corporation, Japan

Time Series ForecastingExplainable Time Series Forecasting
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Mar 3, 2026

Towards Accurate and Interpretable Time-series Forecasting: A Polynomial Learning Approach

Time series forecasting enables early warning and has driven asset performance management from traditional planned maintenance to predictive maintenance. However, the lack of interpretability in forecasting methods undermines users' trust and complicates debugging for developers. Consequently, interpretable time-series forecasting has attracted increasing research attention. Nevertheless, existing methods suffer from several limitations, including insufficient modeling of temporal dependencies, lack of feature-level interpretability to support early warning, and difficulty in simultaneously achieving the accuracy and interpretability. This paper proposes the interpretable polynomial learning (IPL) method, which integrates interpretability into the model structure by explicitly modeling original features and their interactions of arbitrary order through polynomial representations. This design preserves temporal dependencies, provides feature-level interpretability, and offers a flexible trade-off between prediction accuracy and interpretability by adjusting the polynomial degree. We evaluate IPL on simulated and Bitcoin price data, showing that it achieves high prediction accuracy with superior interpretability compared with widely used explainability methods. Experiments on field-collected antenna data further demonstrate that IPL yields simpler and more efficient early warning mechanisms.

Bo Liu, Shao-Bo Lin, Changmiao Wang +1

Center for Intelligent Decision-Making and Machine Learning, School of Management, Xi’an Jiaotong University, Xi’an, China · The 39th Research Institute of China Electronics Technology Group Corporation, Xi’an, China · Shenzhen Research Institute of Big Data, ShenZhen, China

Time Series ForecastingExplainable Time Series Forecasting
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Feb 26, 2026

Forecasting Bacterial Antimicrobial Resistance Trends Using Machine Learning on WHO GLASS Surveillance Data: A Retrieval-Augmented Generation Approach for Policy Decision Support

Background: Antimicrobial resistance (AMR) is a global health threat. While the WHO Global Antimicrobial Resistance and Use Surveillance System (GLASS) provides standardized data, population-level machine learning forecasting of resistance trends remains limited. Translating forecasts into policy also requires transparent interpretation. Methods: Surveillance data (2021-2023) comprising 5,909 observations across 44 countries and five WHO regions were processed. Six models (Naive, Linear, Ridge, XGBoost, LightGBM, LSTM) were benchmarked to forecast one-year-ahead resistance rates using prior-year resistance, antibiotic consumption, and related features. MAE, RMSE, and sMAPE were computed with 95% bootstrap confidence intervals for MAE. A local Retrieval-Augmented Generation (RAG) system (Gemma 4) translated forecast findings into policy guidance grounded in WHO documents. Results: XGBoost achieved the best predictive performance (test MAE = 6.13% [95% CI: 5.83-6.44]), an 85.3% error reduction versus the naive baseline (MAE = 41.79%). SHAP analysis identified prior-year resistance as the dominant predictor (50.5% gain). Regional forecast error tracked surveillance coverage, from 3.65% in the European Region to 8.61% in South-East Asia. The RAG pipeline generated source-attributed policy responses without fabricated citations. Conclusion: Short-term AMR resistance rates exhibit strong temporal autocorrelation that can be accurately forecasted using gradient boosting. Coupling these forecasts with a hallucination-resistant RAG system provides a scalable, evidence-based decision-support framework for AMR governance. v3 correction: a leakage audit found feature-construction defects; on the corrected panel a persistence forecast (MAE 5.79) significantly outperforms XGBoost (6.55), and the 85.3% claim is withdrawn (see Correction).

Md Tanvir Hasan Turja

Independent Researcher, London, United Kingdom

Time Series ForecastingExplainable Time Series Forecasting
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Feb 19, 2026

AdaptStress: Online Adaptive Learning for Interpretable and Personalized Stress Prediction Using Multivariate and Sparse Physiological Signals

Continuous stress forecasting could potentially contribute to lifestyle interventions. This paper presents a novel, explainable, and individualized approach for stress prediction using physiological data from consumer-grade smartwatches. We develop a time series forecasting model that leverages multivariate features, including heart rate variability, activity patterns, and sleep metrics, to predict stress levels across 16 temporal horizons (History window: 3, 5, 7, 9 days; forecasting window: 1, 3, 5, 7 days). Our evaluation involves 16 participants monitored for 10-15 weeks. We evaluate our approach across 16 participants, comparing against state-of-the-art time series models (Informer, TimesNet, PatchTST) and traditional baselines (CNN, LSTM, CNN-LSTM) across multiple temporal horizons. Our model achieved performance with an MSE of 0.053, MAE of 0.190, and RMSE of 0.226 in optimal settings (5-day input, 1-day prediction). A comparison with the baseline models shows that our model outperforms TimesNet, PatchTST, CNN-LSTM, LSTM, and CNN under all conditions, representing improvements of 36.9%, 25.5%, and 21.5% over the best baseline. According to the explanability analysis, sleep metrics are the most dominant and consistent stress predictors (importance: 1.1, consistency: 0.9-1.0), while activity features exhibit high inter-participant variability (0.1-0.2). Most notably, the model captures individual-specific patterns where identical features can have opposing effects across users, validating its personalization capabilities. These findings establish that consumer wearables, combined with adaptive and interpretable deep learning, can deliver relevant stress assessment adapted to individual physiological responses, providing a foundation for scalable, continuous, explainable mental health monitoring in real-world settings.

Xueyi Wang, Claudine J. C. Lamoth, Elisabeth Wilhelm

Engineering and Technology institute Groningen (ENTEG), University of Groningen, Groningen, 9742AG, the Netherlands · Department of Human Movement Sciences, University Medical Center Groningen, Groningen, Netherlands

Wearable Health MonitoringExplainable Time Series ForecastingTime Series ForecastingOnline LearningMultivariate Time Series Forecasting
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Nov 28, 2025

Auditable Context-Aware HFMD Forecasting with Structured LLM Agents

Effective HFMD surveillance requires forecasts capturing both time-series patterns and contextual drivers such as school calendars, weather, and policy or surveillance reports. In clinical settings, forecasts must be trusted and actionable; thus, beyond point accuracy, decision-makers require concise, auditable explanations of why risk is expected to rise or fall. Classical models (e.g., ARIMA and Prophet) and foundation models (e.g., Chronos, Moirai, and TimesFM) treat external covariates as numerical inputs, lacking semantic reasoning to reflect epidemiological mechanisms or resolve conflicting signals. We propose a two-agent neuro-symbolic framework that decouples contextual interpretation from probabilistic forecasting. An LLM-based Event Interpreter ingests heterogeneous signals -- school schedules, weather summaries, government reports, and clinical guidelines -- and outputs a scalar transmission-impact signal. A Forecast Generator combines this signal with historical case counts to produce point forecasts that are mapped to probabilistic predictions through Poisson/negative-binomial moment matching. We focus on one-week-ahead rolling forecasts, aligning with weekly hospital-capacity planning and the rapid, context-driven inflections typical of HFMD. We evaluate on two datasets: Hong Kong surveillance (90 target weeks in 2023--2024) and Lishui hospital visits (33 target weeks in 2024). Against traditional and foundation-model baselines, our approach achieves competitive point accuracy while providing robust 90% intervals (coverage approximately 0.85--1.00) and concise rationales. This demonstrates that integrating domain knowledge through LLM-based agents can match strong numerical forecasters while yielding interpretable, context-aware forecasts aligned with public-health decision-making.

Joongwon Chae, Runming Wang, Chen Xiong +5

Institute of Biomedicine and Health Engineering, Tsinghua Shenzhen International Graduate School (SIGS), Tsinghua University, Shenzhen, China · The First Hospital of Hebei Medical University, Shijiazhuang, China · The Fifth Affiliated Hospital of Wenzhou Medical University, Lishui 323000, China +1

Epidemic ForecastingExplainable Time Series ForecastingHealthcareTime Series ForecastingLLM-Based Time Series ForecastingMulti-Agent LLMs+1
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Nov 12, 2025

AlphaCast: A Human Wisdom-LLM Intelligence Co-Reasoning Framework for Time Series Forecasting

Time series forecasting is typically treated as a single-pass numerical prediction task based on historical observations. However, real-world forecasting often requires expert-like reasoning, where temporal patterns, contextual cues, case-based references, and domain knowledge are jointly considered and iteratively revised. Existing statistical, deep learning, foundation, and LLM-based forecasting models mainly rely on pattern fitting, direct prompting, or static context augmentation, leaving interactive and reflective forecasting insufficiently explored. In this work, we propose AlphaCast, a human wisdom-LLM intelligence co-reasoning framework for interactive time series forecasting. AlphaCast does not require real-time human intervention; instead, it operationalizes human wisdom as structured forecasting support, including time-series features, contextual cues, case-based references, and domain knowledge. Built upon an expert-like think-forecast-reflect workflow, AlphaCast comprises three agents: an Investigator that constructs forecasting context from available evidence, a Generator that produces context-grounded forecasts, and a Reflector that evaluates plausibility and provides feedback for refinement. Extensive experiments demonstrate that AlphaCast improves forecasting accuracy and produces interpretable forecast explanations, offering a promising step toward interactive and context-aware time series forecasting.

Xiaohan Zhang, Tian Gao, Mingyue Cheng +5

State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei, China.

Time Series ForecastingLLM-Based Time Series ForecastingExplainable Time Series Forecasting
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