train gnn-lstm surrogates

This work addresses the critical need for unified analysis of graph and time series data, an area currently lacking systematic organization in existing systems. It proposes the first comprehensive taxonomy that categorizes fusion architectures into four distinct classes. Through a multidimensional evaluation grounded in cross-model integration depth, maturity, and openness, the study establishes a clear classification framework via literature review, architectural analysis, and requirement mapping. This framework delineates the appropriate application scenarios and inherent design trade-offs for each architecture type, thereby offering researchers and practitioners a principled guide for system selection and identifying promising directions for future research.

To address the challenges of insufficient long-range temporal dependency modeling, excessive spatiotemporal coupling, and underutilization of auxiliary information in graph-structured time-series forecasting, this paper proposes the Graph Sequence Attention Network (GSAN). GSAN is the first framework to explicitly decouple spatial and temporal dependencies within a unified graph neural network architecture: it captures dynamic temporal patterns via a graph-structure-aware sequence attention mechanism, models spatial dependencies using topology-adaptive graph convolution, and integrates heterogeneous auxiliary information embeddings in an end-to-end manner. Extensive experiments on multiple real-world graph time-series datasets demonstrate that GSAN consistently outperforms state-of-the-art methods, achieving average prediction error reductions of 12.7%–23.4%. These results validate GSAN’s effectiveness and generalizability in jointly modeling spatiotemporal dynamics and heterogeneous auxiliary information.

Traditional time-series models neglect inter-firm value-chain dependencies, limiting their ability to accurately forecast stock returns. To address this, we propose LSTM-GCN, the first deep learning framework that explicitly incorporates real-world industry topology into stock price prediction—jointly modeling spatial dependencies among firms via Graph Convolutional Networks (GCN) and temporal dynamics of stock prices via Long Short-Term Memory (LSTM) in an end-to-end manner. The model integrates heterogeneous multi-source data, overcoming the limitations of univariate price-only modeling. Evaluated on EuroStoxx 600 and S&P 500 datasets, it significantly outperforms standard baselines—including ARIMA, vanilla LSTM, and GraphSAGE—demonstrating that value-chain structure encodes incremental predictive signals not fully captured by market prices. Our core contribution is the design of the first spatiotemporal neural architecture grounded in empirically derived industry graphs, establishing a novel fundamentals-driven paradigm for quantitative forecasting.

This work addresses the lack of theoretical characterization of expressive power and inefficiency in spectral-temporal graph neural networks (Spectral-Temporal GNNs) for time series forecasting. We establish, for the first time, a rigorous theoretical framework for their expressivity: proving universal approximation capability under linearity constraints and characterizing their discriminative capacity via dynamic graph 1-WL equivalence. Leveraging this insight, we propose the Temporal Gegenbauer Graph Convolution (TGGC), a linear spatiotemporal convolutional module based on Gegenbauer orthogonal polynomials—achieving strong expressivity while maintaining computational efficiency. On multiple benchmark datasets, TGGC attains state-of-the-art performance using only linear components, with 3–5× speedups in both training and inference. Our approach introduces an interpretable, scalable paradigm for spectral-domain spatiotemporal modeling.

Existing graph deep learning approaches for multivariate time series forecasting predominantly focus on architectural innovations, lacking systematic methodology studies on problem formalization, model design principles, and evaluation paradigms. This paper introduces the first unified methodology framework for graph-enhanced time series forecasting. It formally defines the forecasting problem by modeling dynamic inter-variable dependencies via learnable graph structures. It establishes principled design guidelines integrating graph neural networks (GNNs), spatiotemporal modeling, and deep temporal models (e.g., TCN and Informer variants). Furthermore, it proposes a reproducible evaluation protocol with built-in mechanisms to ensure interpretability and scalability. The framework shifts forecasting model development from empiricism toward first-principles reasoning, providing standardized guidance for relation-aware global modeling and articulating key open challenges. (149 words)

This paper addresses poor model reproducibility and insufficient open-source implementations in time-series forecasting by proposing a lightweight, fully reproducible LSTM/GRU modeling paradigm. Methodologically, it constructs univariate sequence samples via sliding windows and evaluates performance using two metrics—RMSE and directional accuracy (DA)—on both synthetic activity data (Activities) and real-world financial data (BSE BANKEX). A key finding is that effective training requires only a single time series exhibiting repetitive patterns, without complex preprocessing or large-scale datasets. Experiments show that the proposed implementation significantly outperforms the “repeat last value” baseline for 1-step and 20-step predictions on Activities, while achieving comparable performance on BSE BANKEX. All code, datasets, and complete experimental configurations are publicly released to ensure full reproducibility and out-of-the-box usability.

This work addresses the challenge of distribution drift in autoregressive neural surrogate models during long-term dynamical system simulation, which arises from error accumulation and undermines long-term consistency. To this end, the authors propose a unified mathematical framework that formally characterizes, for the first time, the inherent trade-off between short-term accuracy and long-term consistency. Building upon this framework, they introduce Self-Refining Neural Surrogates (SNS)—a novel class of surrogate models that require no hyperparameter tuning. SNS leverages a conditional diffusion mechanism to iteratively refine its own or existing surrogate outputs, enabling high-fidelity simulation over arbitrarily long time horizons. Experimental results demonstrate that SNS substantially improves both long-term stability and simulation accuracy, overcoming the limitations of conventional approaches that rely on empirical hyperparameter tuning.

This study addresses the fundamental challenge of deciphering the underlying structural and functional mechanisms—such as connectivity matrices, neuronal cell types, signaling dynamics, and latent external stimuli—from the complex spatiotemporal activity of heterogeneous neural systems. To this end, the authors propose an interpretable modeling framework based on graph neural networks that integrates neural dynamics simulation with graph structure learning. By doing so, the method overcomes the limitations of conventional black-box models while maintaining high predictive accuracy. Notably, it achieves the first joint inference of connectivity architecture, cell-type identity, signaling mechanisms, and hidden stimuli in large-scale simulated neural ensembles. The approach successfully reconstructs ground-truth connectivity matrices, neuronal types, and signal transmission functions at the scale of thousands of neurons and, in certain scenarios, accurately identifies unknown external inputs.

This study addresses the challenge of enhancing the long-term prediction accuracy and stability of deep learning surrogate models for chaotic dynamical systems while maintaining computational efficiency. By employing a unified training protocol and matching model capacity, the authors systematically evaluate the rolling prediction performance of several mainstream neural network architectures on the double pendulum, the Kuramoto–Sivashinsky equation, and Kolmogorov flow. They propose an integrator-inspired update structure that significantly reduces prediction bias and the amplification of perturbations. Stability differences among models are quantified using metrics including the Jacobian matrix, one-step relative error, and finite-time Lyapunov exponents. Experimental results demonstrate that the proposed architecture not only improves long-term predictive accuracy but also more faithfully reproduces the geometric structure of the system’s attractor.

Existing graph generation models struggle to balance scalability and novelty, often failing to efficiently produce realistic and diverse graph structures. This work proposes a lightweight autoregressive framework that serializes graphs into edge sequences via structure-guided topological ordering and employs a two-stage exploration–refinement training strategy to reduce computational complexity while enhancing generalization and controllable novelty. The approach is compatible with sequential architectures such as LSTM and Mamba and incorporates a large-memory acceleration technique to overcome GPU memory constraints. Experimental results demonstrate that, on both molecular and non-molecular benchmarks, the generated graphs achieve high validity and uniqueness while significantly improving novelty and diversity.

Temporal Graph Neural Networks (TGNNs) are pivotal in processing dynamic graphs. However, existing TGNNs primarily target one-time predictions for a given temporal span, whereas many practical applications require continuous predictions, that predictions are issued frequently over time. Directly adapting existing TGNNs to continuous-prediction scenarios introduces either significant computational overhead or prediction quality issues especially for large graphs. This paper revisits the challenge of { continuous predictions} in TGNNs, and introduces {\sc Coden}, a TGNN model designed for efficient and effective learning on dynamic graphs. {\sc Coden} innovatively overcomes the key complexity bottleneck in existing TGNNs while preserving comparable predictive accuracy. Moreover, we further provide theoretical analyses that substantiate the effectiveness and efficiency of {\sc Coden}, and clarify its duality relationship with both RNN-based and attention-based models. Our evaluations across five dynamic datasets show that {\sc Coden} surpasses existing performance benchmarks in both efficiency and effectiveness, establishing it as a superior solution for continuous prediction in evolving graph environments.