NeuroFlexMLP: A Low Complexity MLP Architecture for Long-Term Time Series Forecasting

DeRNN: Decomposed Recurrent Neural Network for Long-Term Time Series Forecasting

The Decomposed Recurrent Neural Network (DeRNN) is proposed, which decouples global trend modeling from local fluctuation extraction via an asymmetric dual-track architecture and exhibits superior robustness against noise and distribution shifts.

A transformer encoder architecture for node-level time series forecasting

This paper proposes a time-series data processing model based on the Transformer Encoder, designed to address the limitations of traditional Recurrent Neural Networks (RNNs) and Long Short-Term Memory networks (LSTM) in handling long sequences, such as long-term dependency issues, vanishing or exploding gradients, and low computational efficiency. By employing a self-attention mechanism along with learnable positional encoding and multi-head self-attention, the model effectively captures global dependencies in sequential data and significantly enhances its expressive power. To improve training stability, layer normalization is applied after the Transformer encoder, and the data processing flow is optimized through reorganization across batch and node dimensions. The model demonstrates clear advantages in parallel computation and long-term dependency modeling, enabling more efficient processing of complex time-series data. It exhibits superior computational efficiency and stronger generalization capabilities, particularly in real-time traffic flow prediction tasks based on large-scale datasets and long sequences. Experimental results show that the proposed model outperforms traditional RNN and LSTM models across various tasks, indicating promising potential for practical applications.

Early forecasting for time series: a framework for predicting future horizons with minimal lookback dependencies

MLPFormer: A Hybrid MLP–Transformer Architecture for Component-Specific Time Series Forecasting

Long-term time series forecasting requires models that can represent smooth global trends and irregular local fluctuations without assigning the same capacity to both. Existing decomposition-based neural forecasters often separate signals but continue to process the resulting components with architecturally homogeneous encoders, which can overfit simple trends and underfit nonlinear residuals. This paper proposes MLPFormer, a hybrid MLP–Transformer framework for component-specific forecasting. The input sequence is decomposed by a moving-average filter into trend and residual terms. A shallow channel-wise MLP encodes the low-frequency trend, providing a low-capacity inductive bias for smooth structures, whereas a Transformer encoder with depthwise separable convolution models high-frequency residual dynamics and cross-variable dependencies. The two paths are fused and decoded by parallel linear and nonlinear prediction heads. Experiments on nine public benchmarks, with results reported as the mean over three random seeds, show average reductions of 11.8% in MSE and 8.1% in MAE relative to the mean of seven competitive baselines spanning Transformer-based, linear/MLP-based, and RNN-based paradigms published between 2023 and 2025. Ablation studies confirm that the gains arise from matching encoder capacity to component complexity rather than from increasing parameter count. MLPFormer provides a practical hybrid artificial intelligence design for forecasting tasks in which trend and residual structures coexist.

Time series forecasting: a comparative analysis of ARIMA, LSTM, and TFT models with missing data handling

This study compares ARIMA, LSTM, and temporal fusion transformer (TFT) models across three applications and shows that TFT consistently achieved superior forecasting performance and demonstrated greater robustness to increasing missingness, while k-NN generally provided the most effective imputation performance across datasets.

Efficient and explainable multivariate time series forecasting: a survey of architectures, taxonomies, and open challenges

The rapid expansion of multivariate time series (MTS) data has made deep learning a central tool for forecasting across industrial and scientific domains. As these architectures move into settings such as clinical decision support, industrial monitoring, and financial risk management, researchers need to examine not only predictive accuracy but also computational cost and the kinds of explanations that a model can support. This survey re-examines deep learning models for MTS forecasting through the requirements of efficiency and explainability. Our contributions are threefold: (1) We synthesize the literature through a dual-axis scalability view over sequence length L and variate dimension N , together with a three-question explainability taxonomy covering temporal importance, variate importance, and pattern decomposition. (2) We review dominant architectural families, including Transformer variants, frequency-domain methods, linear and channel-independent backbones, state space models, and foundation-style forecasters, to describe how different designs occupy different efficiency–explainability profiles under specific data and deployment assumptions. (3) Building on this synthesis, we identify key open challenges—including the absence of standardized explainability benchmarks for time series, the interpretability gap in state space models, and the need to advance from correlational to causal explanations—and offer reporting considerations to guide more comparable future research.