Accurate forecasting of energy demand and supply is critical for optimizing sustainable energy systems, yet it is challenged by the variability of renewable sources and dynamic consumption patterns. This paper introduces a neural framework that integrates continuous-time Neural Ordinary Differential Equations (Neural ODEs), graph attention, multi-resolution wavelet transformations, and adaptive learning of frequencies to address the issues of time series prediction. The model employs a robust ODE solver, using the Runge-Kutta method, paired with graph-based attention and residual connections to better understand both structural and temporal patterns. Through wavelet-based feature extraction and adaptive frequency modulation, it adeptly captures and models diverse, multi-scale temporal dynamics. When evaluated across seven diverse datasets: ETTh1, ETTh2, ETTm1, ETTm2 (electricity transformer temperature), and Waste, Solar, and Hydro (renewable energy), this architecture consistently outperforms state-of-the-art baselines in various forecasting metrics, proving its robustness in capturing complex temporal dependencies. Furthermore, the model enhances interpretability through SHAP analysis, making it suitable for sustainable energy applications.
Many dynamic processes such as telecommunication and transport networks can be described through discrete time series of graphs. Modelling the dynamics of such time series enables prediction of graph structure at future time steps, which can be used in applications such as detection of anomalies. Existing approaches for graph prediction have limitations such as assuming that the vertices do not to change between consecutive graphs. To address this, we propose to exploit time series prediction methods in combination with an adapted form of flux balance analysis (FBA), a linear programming method originating from biochemistry. FBA is adapted to incorporate various constraints applicable to the scenario of growing graphs. Empirical evaluations on synthetic datasets (constructed via Preferential Attachment model) and real datasets (UCI Message, HePH, Facebook, Bitcoin) demonstrate the efficacy of the proposed approach.
Long-term time series prediction has predominantly relied on Transformer and MLP models, while the potential of convolutional networks in this domain remains underexplored. To address this gap, we introduce a novel multi-scale time series reshape module, which effectively captures the relationships among multi-period patches and variable dependencies. Building upon this module, we propose MS-TVNet, a multi-scale 3D dynamic convolutional neural network. Through comprehensive evaluations on diverse datasets, MS-TVNet demonstrates superior performance compared to baseline models, achieving state-of-the-art (SOTA) results in long-term time series prediction. Our findings highlight the effectiveness of leveraging convolutional networks for capturing complex temporal patterns, suggesting a promising direction for future research in this field.The code is realsed on https://github.com/Curyyfaust/TVNet.
Multivariate time series forecasting requires models to simultaneously capture variable-wise structural dependencies and generalize across diverse tasks. While structural encoders are effective in modeling feature interactions, they lack the capacity to support semantic-level reasoning or task adaptation. Conversely, large language models (LLMs) possess strong generalization capabilities but remain incompatible with raw time series inputs. This gap limits the development of unified, transferable prediction systems. Therefore, we introduce SEED, a structural encoder for embedding-driven decoding, which integrates four stages: a token-aware encoder for patch extraction, a projection module that aligns patches with language model embeddings, a semantic reprogramming mechanism that maps patches to task-aware prototypes, and a frozen language model for prediction. This modular architecture decouples representation learning from inference, enabling efficient alignment between numerical patterns and semantic reasoning. Empirical results demonstrate that the proposed method achieves consistent improvements over strong baselines, and comparative studies on various datasets confirm SEED's role in addressing the structural-semantic modeling gap.
Stock price prediction is vital for investment decisions and risk management, yet remains challenging due to markets' nonlinear dynamics and time-varying inter-stock correlations. Traditional static-correlation models fail to capture evolving stock relationships. To address this, we propose a Differential Graph Transformer (DGT) framework for dynamic relationship modeling and price prediction. Our DGT integrates sequential graph structure changes into multi-head self-attention via a differential graph mechanism, adaptively preserving high-value connections while suppressing noise. Causal temporal attention captures global/local dependencies in price sequences. We further evaluate correlation metrics (Pearson, Mutual Information, Spearman, Kendall's Tau) across global/local/dual scopes as spatial-attention priors. Using 10 years of S&P 500 closing prices (z-score normalized; 64-day sliding windows), DGT with spatial priors outperformed GRU baselines (RMSE: 0.24 vs. 0.87). Kendall's Tau global matrices yielded optimal results (MAE: 0.11). K-means clustering revealed "high-volatility growth" and "defensive blue-chip" stocks, with the latter showing lower errors (RMSE: 0.13) due to stable correlations. Kendall's Tau and Mutual Information excelled in volatile sectors. This study innovatively combines differential graph structures with Transformers, validating dynamic relationship modeling and identifying optimal correlation metrics/scopes. Clustering analysis supports tailored quantitative strategies. Our framework advances financial time-series prediction through dynamic modeling and cross-asset interaction analysis.
The continuous development of new adaptive filters (AFs) based on novel cost functions (CFs) is driven by the demands of various application scenarios and noise environments. However, these algorithms typically demonstrate optimal performance only in specific conditions. In the event of the noise change, the performance of these AFs often declines, rendering simple parameter adjustments ineffective. Instead, a modification of the CF is necessary. To address this issue, the robust generalized adaptive AF (RGA-AF) with strong adaptability and flexibility is proposed in this paper. The flexibility of the RGA-AF's CF allows for smooth adaptation to varying noise environments through parameter adjustments, ensuring optimal filtering performance in diverse scenarios. Moreover, we introduce several fundamental properties of negative RGA (NRGA) entropy and present the negative asymmetric RGA-AF (NAR-GA-AF) and kernel recursive NRGA-AF (KRNRGA-AF). These AFs address asymmetric noise distribution and nonlinear filtering issues, respectively. Simulations of linear system identification and time-series prediction for Chua's circuit under different noise environments demonstrate the superiority of the proposed algorithms in comparison to existing techniques.
While deep learning methods have achieved strong performance in time series prediction, their black-box nature and inability to explicitly model underlying stochastic processes often limit their generalization to non-stationary data, especially in the presence of abrupt changes. In this work, we introduce Neural MJD, a neural network based non-stationary Merton jump diffusion (MJD) model. Our model explicitly formulates forecasting as a stochastic differential equation (SDE) simulation problem, combining a time-inhomogeneous It\^o diffusion to capture non-stationary stochastic dynamics with a time-inhomogeneous compound Poisson process to model abrupt jumps. To enable tractable learning, we introduce a likelihood truncation mechanism that caps the number of jumps within small time intervals and provide a theoretical error bound for this approximation. Additionally, we propose an Euler-Maruyama with restart solver, which achieves a provably lower error bound in estimating expected states and reduced variance compared to the standard solver. Experiments on both synthetic and real-world datasets demonstrate that Neural MJD consistently outperforms state-of-the-art deep learning and statistical learning methods.
Irregular Multivariate Time Series (IMTS) forecasting is challenging due to the unaligned nature of multi-channel signals and the prevalence of extensive missing data. Existing methods struggle to capture reliable temporal patterns from such data due to significant missing values. While pre-trained foundation models show potential for addressing these challenges, they are typically designed for Regularly Sampled Time Series (RTS). Motivated by the visual Mask AutoEncoder's (MAE) powerful capability for modeling sparse multi-channel information and its success in RTS forecasting, we propose VIMTS, a framework adapting Visual MAE for IMTS forecasting. To mitigate the effect of missing values, VIMTS first processes IMTS along the timeline into feature patches at equal intervals. These patches are then complemented using learned cross-channel dependencies. Then it leverages visual MAE's capability in handling sparse multichannel data for patch reconstruction, followed by a coarse-to-fine technique to generate precise predictions from focused contexts. In addition, we integrate self-supervised learning for improved IMTS modeling by adapting the visual MAE to IMTS data. Extensive experiments demonstrate VIMTS's superior performance and few-shot capability, advancing the application of visual foundation models in more general time series tasks. Our code is available at https://github.com/WHU-HZY/VIMTS.
Recent advances in lightweight time series forecasting models suggest the inherent simplicity of time series forecasting tasks. In this paper, we present CMoS, a super-lightweight time series forecasting model. Instead of learning the embedding of the shapes, CMoS directly models the spatial correlations between different time series chunks. Additionally, we introduce a Correlation Mixing technique that enables the model to capture diverse spatial correlations with minimal parameters, and an optional Periodicity Injection technique to ensure faster convergence. Despite utilizing as low as 1% of the lightweight model DLinear's parameters count, experimental results demonstrate that CMoS outperforms existing state-of-the-art models across multiple datasets. Furthermore, the learned weights of CMoS exhibit great interpretability, providing practitioners with valuable insights into temporal structures within specific application scenarios.
Making accurate predictions of chaotic time series is a complex challenge. Reservoir computing, a neuromorphic-inspired approach, has emerged as a powerful tool for this task. It exploits the memory and nonlinearity of dynamical systems without requiring extensive parameter tuning. However, selecting and optimizing reservoir architectures remains an open problem. Next-generation reservoir computing simplifies this problem by employing nonlinear vector autoregression based on truncated Volterra series, thereby reducing hyperparameter complexity. Nevertheless, the latter suffers from exponential parameter growth in terms of the maximum monomial degree. Tensor networks offer a promising solution to this issue by decomposing multidimensional arrays into low-dimensional structures, thus mitigating the curse of dimensionality. This paper explores the application of a previously proposed tensor network model for predicting chaotic time series, demonstrating its advantages in terms of accuracy and computational efficiency compared to conventional echo state networks. Using a state-of-the-art tensor network approach enables us to bridge the gap between the tensor network and reservoir computing communities, fostering advances in both fields.
Reservoir Computing (RC) with physical systems requires an understanding of the underlying structure and internal dynamics of the specific physical reservoir. In this study, physical nano-electronic networks with neuromorphic dynamics are investigated for their use as physical reservoirs in an RC framework. These neuromorphic networks operate as dynamic reservoirs, with node activities in general coupled to the edge dynamics through nonlinear nano-electronic circuit elements, and the reservoir outputs influenced by the underlying network connectivity structure. This study finds that networks with varying degrees of sparsity generate more useful nonlinear temporal outputs for dynamic RC compared to dense networks. Dynamic RC is also tested on an autonomous multivariate chaotic time series prediction task with networks of varying densities, which revealed the importance of network sparsity in maintaining network activity and overall dynamics, that in turn enabled the learning of the chaotic Lorenz63 system's attractor behavior.
Multi-agents-based news-driven time series forecasting is considered as a potential paradigm shift in the era of large language models (LLMs). The challenge of this task lies in measuring the influences of different news events towards the fluctuations of time series. This requires agents to possess stronger abilities of innovative thinking and the identifying misleading logic. However, the existing multi-agent discussion framework has limited enhancement on time series prediction in terms of optimizing these two capabilities. Inspired by the role of competition in fostering innovation, this study embeds a competition mechanism within the multi-agent discussion to enhance agents' capability of generating innovative thoughts. Furthermore, to bolster the model's proficiency in identifying misleading information, we incorporate a fine-tuned small-scale LLM model within the reflective stage, offering auxiliary decision-making support. Experimental results confirm that the competition can boost agents' capacity for innovative thinking, which can significantly improve the performances of time series prediction. Similar to the findings of social science, the intensity of competition within this framework can influence the performances of agents, providing a new perspective for studying LLMs-based multi-agent systems.
Accurate channel prediction is essential in massive multiple-input multiple-output (m-MIMO) systems to improve precoding effectiveness and reduce the overhead of channel state information (CSI) feedback. However, existing methods often suffer from accumulated prediction errors and poor generalization to dynamic wireless environments. Large language models (LLMs) have demonstrated remarkable modeling and generalization capabilities in tasks such as time series prediction, making them a promising solution. Nevertheless, a significant modality gap exists between the linguistic knowledge embedded in pretrained LLMs and the intrinsic characteristics of CSI, posing substantial challenges for their direct application to channel prediction. Moreover, the large parameter size of LLMs hinders their practical deployment in real-world communication systems with stringent latency constraints. To address these challenges, we propose a novel channel prediction framework based on semantically aligned large models, referred to as CSI-ALM, which bridges the modality gap between natural language and channel information. Specifically, we design a cross-modal fusion module that aligns CSI representations . Additionally, we maximize the cosine similarity between word embeddings and CSI embeddings to construct semantic cues. To reduce complexity and enable practical implementation, we further introduce a lightweight version of the proposed approach, called CSI-ALM-Light. This variant is derived via a knowledge distillation strategy based on attention matrices. Extensive experimental results demonstrate that CSI-ALM achieves a 1 dB gain over state-of-the-art deep learning methods. Moreover, under limited training data conditions, CSI-ALM-Light, with only 0.34M parameters, attains performance comparable to CSI-ALM and significantly outperforms conventional deep learning approaches.
The rapid advancements in quantum computing (QC) and machine learning (ML) have led to the emergence of quantum machine learning (QML), which integrates the strengths of both fields. Among QML approaches, variational quantum circuits (VQCs), also known as quantum neural networks (QNNs), have shown promise both empirically and theoretically. However, their broader adoption is hindered by reliance on quantum hardware during inference. Hardware imperfections and limited access to quantum devices pose practical challenges. To address this, the Quantum-Train (QT) framework leverages the exponential scaling of quantum amplitudes to generate classical neural network parameters, enabling inference without quantum hardware and achieving significant parameter compression. Yet, designing effective quantum circuit architectures for such quantum-enhanced neural programmers remains non-trivial and often requires expertise in quantum information science. In this paper, we propose an automated solution using differentiable optimization. Our method jointly optimizes both conventional circuit parameters and architectural parameters in an end-to-end manner via automatic differentiation. We evaluate the proposed framework on classification, time-series prediction, and reinforcement learning tasks. Simulation results show that our method matches or outperforms manually designed QNN architectures. This work offers a scalable and automated pathway for designing QNNs that can generate classical neural network parameters across diverse applications.
Accurate blood glucose prediction can enable novel interventions for type 1 diabetes treatment, including personalized insulin and dietary adjustments. Although recent advances in transformer-based architectures have demonstrated the power of attention mechanisms in complex multivariate time series prediction, their potential for blood glucose (BG) prediction remains underexplored. We present a comparative analysis of transformer models for multi-horizon BG prediction, examining forecasts up to 4 hours and input history up to 1 week. The publicly available DCLP3 dataset (n=112) was split (80%-10%-10%) for training, validation, and testing, and the OhioT1DM dataset (n=12) served as an external test set. We trained networks with point-wise, patch-wise, series-wise, and hybrid embeddings, using CGM, insulin, and meal data. For short-term blood glucose prediction, Crossformer, a patch-wise transformer architecture, achieved a superior 30-minute prediction of RMSE (15.6 mg / dL on OhioT1DM). For longer-term predictions (1h, 2h, and 4h), PatchTST, another path-wise transformer, prevailed with the lowest RMSE (24.6 mg/dL, 36.1 mg/dL, and 46.5 mg/dL on OhioT1DM). In general, models that used tokenization through patches demonstrated improved accuracy with larger input sizes, with the best results obtained with a one-week history. These findings highlight the promise of transformer-based architectures for BG prediction by capturing and leveraging seasonal patterns in multivariate time-series data to improve accuracy.
Predicting the price that has the least error and can provide the best and highest accuracy has been one of the most challenging issues and one of the most critical concerns among capital market activists and researchers. Therefore, a model that can solve problems and provide results with high accuracy is one of the topics of interest among researchers. In this project, using time series prediction models such as ARIMA to estimate the price, variables, and indicators related to technical analysis show the behavior of traders involved in involving psychological factors for the model. By linking all of these variables to stepwise regression, we identify the best variables influencing the prediction of the variable. Finally, we enter the selected variables as inputs to the artificial neural network. In other words, we want to call this whole prediction process the "ARIMA_Stepwise Regression_Neural Network" model and try to predict the price of gold in international financial markets. This approach is expected to be able to be used to predict the types of stocks, commodities, currency pairs, financial market indicators, and other items used in local and international financial markets. Moreover, a comparison between the results of this method and time series methods is also expressed. Finally, based on the results, it can be seen that the resulting hybrid model has the highest accuracy compared to the time series method, regression, and stepwise regression.
Predicting financial time series presents significant challenges due to inherent low signal-to-noise ratios and intricate temporal patterns. Traditional machine learning models exhibit limitations in this forecasting task constrained by their restricted model capacity. Recent advances in large language models (LLMs), with their greatly expanded parameter spaces, demonstrate promising potential for modeling complex dependencies in temporal sequences. However, existing LLM-based approaches typically focus on fixed-length patch analysis due to the Transformer architecture, ignoring market data's multi-scale pattern characteristics. In this study, we propose $LLM4FTS$, a novel framework that enhances LLM capabilities for temporal sequence modeling through learnable patch segmentation and dynamic wavelet convolution modules. Specifically,we first employ K-means++ clustering based on DTW distance to identify scale-invariant patterns in market data. Building upon pattern recognition results, we introduce adaptive patch segmentation that partitions temporal sequences while preserving maximal pattern integrity. To accommodate time-varying frequency characteristics, we devise a dynamic wavelet convolution module that emulates discrete wavelet transformation with enhanced flexibility in capturing time-frequency features. These three modules work together to improve large language model's ability to handle scale-invariant patterns in financial time series. Extensive experiments on real-world financial datasets substantiate the framework's efficacy, demonstrating superior performance in capturing complex market patterns and achieving state-of-the-art results in stock return prediction. The successful deployment in practical trading systems confirms its real-world applicability, representing a significant advancement in LLM applications for financial forecasting.
With the intensification of global climate change, accurate prediction of weather indicators is of great significance in disaster prevention and mitigation, agricultural production, and transportation. Precipitation, as one of the key meteorological indicators, plays a crucial role in water resource management, agricultural production, and urban flood control. This study proposes a multidimensional precipitation index prediction model based on a CNN- LSTM hybrid framework, aiming to improve the accuracy of precipitation forecasts. The dataset is sourced from Pune, Maharashtra, India, covering monthly mean precipitation data from 1972 to 2002. This dataset includes nearly 31 years (1972-2002) of monthly average precipitation, reflecting the long-term fluctuations and seasonal variations of precipitation in the region. By analyzing these time series data, the CNN-LSTM model effectively captures local features and long-term dependencies. Experimental results show that the model achieves a root mean square error (RMSE) of 6.752, which demonstrates a significant advantage over traditional time series prediction methods in terms of prediction accuracy and generalization ability. Furthermore, this study provides new research ideas for precipitation prediction. However, the model requires high computational resources when dealing with large-scale datasets, and its predictive ability for multidimensional precipitation data still needs improvement. Future research could extend the model to support and predict multidimensional precipitation data, thereby promoting the development of more accurate and efficient meteorological prediction technologies.
Environmental crisis remains a global challenge that affects public health and environmental quality. Despite extensive research, accurately forecasting environmental change trends to inform targeted policies and assess prediction efficiency remains elusive. Conventional methods for multivariate time series (MTS) analysis often fail to capture the complex dynamics of environmental change. To address this, we introduce an innovative meta-learning MTS model, MMformer with Adaptive Transferable Multi-head Attention (ATMA), which combines self-attention and meta-learning for enhanced MTS forecasting. Specifically, MMformer is used to model and predict the time series of seven air quality indicators across 331 cities in China from January 2018 to June 2021 and the time series of precipitation and temperature at 2415 monitoring sites during the summer (276 days) from 2012 to 2014, validating the network's ability to perform and forecast MTS data successfully. Experimental results demonstrate that in these datasets, the MMformer model reaching SOTA outperforms iTransformer, Transformer, and the widely used traditional time series prediction algorithm SARIMAX in the prediction of MTS, reducing by 50\% in MSE, 20\% in MAE as compared to others in air quality datasets, reducing by 20\% in MAPE except SARIMAX. Compared with Transformer and SARIMAX in the climate datasets, MSE, MAE, and MAPE are decreased by 30\%, and there is an improvement compared to iTransformer. This approach represents a significant advance in our ability to forecast and respond to dynamic environmental quality challenges in diverse urban and rural environments. Its predictive capabilities provide valuable public health and environmental quality information, informing targeted interventions.
Reservoir computing (RC) represents a class of state-space models (SSMs) characterized by a fixed state transition mechanism (the reservoir) and a flexible readout layer that maps from the state space. It is a paradigm of computational dynamical systems that harnesses the transient dynamics of high-dimensional state spaces for efficient processing of temporal data. Rooted in concepts from recurrent neural networks, RC achieves exceptional computational power by decoupling the training of the dynamic reservoir from the linear readout layer, thereby circumventing the complexities of gradient-based optimization. This work presents a systematic exploration of RC, addressing its foundational properties such as the echo state property, fading memory, and reservoir capacity through the lens of dynamical systems theory. We formalize the interplay between input signals and reservoir states, demonstrating the conditions under which reservoirs exhibit stability and expressive power. Further, we delve into the computational trade-offs and robustness characteristics of RC architectures, extending the discussion to their applications in signal processing, time-series prediction, and control systems. The analysis is complemented by theoretical insights into optimization, training methodologies, and scalability, highlighting open challenges and potential directions for advancing the theoretical underpinnings of RC.