1. Bibliographic Information

1.1. Title

The central topic of the paper is "ASTNet: Asynchronous Spatio-Temporal Network for Large-Scale Chemical Sensor Forecasting." It focuses on developing a novel deep learning model for predicting future states in chemical sensor networks.

1.2. Authors

The authors are:

• Shihao Tu (Zhejiang University)

• Yang Yang (Zhejiang University)

• Wenyue Ding (SUPCON Technology Co., Ltd.)

• Yicheng Lu (Zhejiang University)

• Qingkai Ren (Zhejiang University)

• Yupeng Zhang (Zhejiang University)

• Yin Zhang (Zhejiang University)

  The authors are primarily affiliated with Zhejiang University, a prominent research institution. Wenyue Ding is affiliated with SUPCON Technology Co., Ltd., indicating a collaboration between academia and industry, which is common in applied research areas like industrial intelligence and chemical engineering.

1.3. Journal/Conference

The paper is published at the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD '25), August 3-7, 2025, Toronto, ON, Canada. KDD is one of the premier conferences in the fields of data mining, data science, and knowledge discovery, known for publishing high-impact research. Its reputation and influence are significant within the relevant fields.

1.4. Publication Year

2025

1.5. Abstract

The chemical industry faces significant challenges in utilizing vast amounts of time-series data from thousands of sensors for forecasting chemical states and real-time process control. Traditional forecasting methods suffer from high computational latency and struggle with complex spatiotemporal dependencies. To address this, the paper introduces ASTNet, a novel approach that integrates an asynchronous spatiotemporal modeling framework. ASTNet combines temporal and spatial encoders, allowing concurrent learning of temporal and spatial dependencies, thereby reducing computational latency. It also features a gated graph fusion mechanism that adaptively combines static (meta) and evolving (dynamic) sensor graphs, enhancing the handling of heterogeneous sensor data and spatial correlations. Extensive experiments on three real-world chemical sensor datasets demonstrate that ASTNet outperforms state-of-the-art methods in both prediction accuracy and computational efficiency, leading to its successful deployment in industrial chemical engineering scenarios.

1.6. Original Source Link

/files/papers/69368d6a325b5ce79291fc93/paper.pdf (This link refers to a local file path, indicating it's likely a PDF provided alongside the analysis request). Publication status: Officially published at KDD '25.

2. Executive Summary

2.1. Background & Motivation

• Core problem: The chemical industry generates massive volumes of time-series data from thousands of sensors. Effectively leveraging this data for forecasting chemical states and enabling accurate real-time control of production processes is an urgent challenge.
• Importance and existing challenges:
  • High computational latency: Traditional forecasting methods, especially those with sequential modeling of temporal and spatial dependencies, incur significant delays, making real-time prediction impractical for industrial applications with thousands of sensors.
  • Complexity of spatiotemporal dependencies: Chemical reaction processes are lengthy, dynamic, and exhibit complex correlations among sensors (spatial dependency) and long-term temporal dependencies in recorded time series.
  • Heterogeneity of sensors: Sensors measure physically different quantities (e.g., pH, temperature) with varying scales, making unified modeling difficult.
  • Dynamic sensor graphs: The spatial relationships (sensor graphs) can be both time-invariant (meta graph, due to physical layout) and time-varying (dynamic graph, due to production adjustments, equipment changes, or maintenance). Accurately modeling and integrating both is challenging.
  • Long-term dependencies: Chemical processes often involve time-lag effects, requiring long lookback windows to capture dependencies, which further increases computational costs for many models.
• Paper's entry point/innovative idea: The paper proposes ASTNet, focusing on an asynchronous spatiotemporal modeling framework and a gated graph fusion mechanism to concurrently learn dependencies and adaptively combine static and dynamic sensor graphs, specifically designed to address the latency and complexity issues in large-scale chemical sensor data forecasting.

2.2. Main Contributions / Findings

The paper outlines the following main contributions:

• Novel Asynchronous Spatiotemporal Modeling Strategy: ASTNet is the first to propose an asynchronous spatiotemporal modeling strategy for large-scale chemical sensor forecasting. This addresses the critical challenge of computational latency in traditional sequential frameworks by enabling parallel temporal and spatial dependency learning, which is crucial for real-time decision-making in chemical production.
• Dynamic Gated Graph Fusion Framework: ASTNet introduces a novel dynamic graph fusion framework that integrates time-invariant meta graphs and time-varying dynamic graphs through a gated mechanism. This adaptively balances heterogeneous sensor correlations while reducing erroneous spatial dependencies, significantly enhancing robustness in complex industrial environments.
• Extensive Real-World Validation and Deployment: The authors conducted extensive experiments on three real-world chemical sensor datasets involving thousands of heterogeneous sensors. Quantitative results demonstrate ASTNet's superior prediction accuracy and efficiency over state-of-the-art baselines, with the MAE improved by 7.4% and MAPE by 7.0% compared to the best baseline. Furthermore, ASTNet has been successfully deployed in real chemical plants for sensor data prediction and management.

3. Prerequisite Knowledge & Related Work

3.1. Foundational Concepts

To understand ASTNet, a reader should be familiar with the following foundational concepts:

• Time Series Data: A sequence of data points indexed in time order. In this paper, it refers to sensor readings collected at fixed intervals (e.g., every 5 seconds). Forecasting involves predicting future values based on past observations.
• Spatiotemporal Data: Data that has both spatial and temporal dimensions. For chemical sensors, this means readings from multiple sensors located at different points in a chemical plant, recorded over time. The relationships between sensors can change over time.
• Dependencies (Temporal & Spatial):
  • Temporal Dependency: How a sensor's current or future reading is influenced by its past readings (e.g., a temperature sensor's reading at $t$ depends on its reading at t-1, t-2, etc.). Long-term dependencies imply influence from much earlier time steps.
  • Spatial Dependency: How a sensor's reading is influenced by the readings of other sensors at the same or different times (e.g., a pH sensor's reading might correlate with a temperature sensor's reading in a nearby processing unit).
• Computational Latency: The delay between a data input and the system's response. In real-time forecasting, low latency is crucial for timely decision-making.
• Graph Neural Networks (GNNs): A class of neural networks designed to operate on graph-structured data. They are effective for modeling relationships (edges) between entities (nodes) and are commonly used for spatial dependency modeling.
  • Nodes: Represent individual sensors.
  • Edges: Represent relationships or correlations between sensors.
  • Adjacency Matrix: A square matrix used to represent a finite graph. If $A_{ij} = 1$, there is an edge between node $i$ and node $j$; otherwise, $A_{ij} = 0$. In weighted graphs, $A_{ij}$ can represent the strength of the connection.
• Transformer Models: A neural network architecture introduced for sequence-to-sequence tasks, particularly in natural language processing. Key components include:
  • Self-Attention Mechanism: Allows the model to weigh the importance of different parts of the input sequence when processing each element. It computes attention scores between all pairs of elements in a sequence. The core formula for scaled dot-product attention is: $ \mathrm{Attention}(Q, K, V) = \mathrm{Softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V $ Where $Q$ (Query), $K$ (Key), and $V$ (Value) are matrices derived from the input embeddings, and $d_k$ is the dimension of the keys.
  • Encoder-Decoder Structure: A common framework in Transformers, where an encoder processes the input sequence and a decoder generates the output sequence.
  • Positional Encoding: Adds information about the relative or absolute position of tokens in the sequence, as Transformers process sequences in parallel without inherent order.
• Patch-wise Tokenization: Instead of treating each individual data point in a time series as a token, patch-wise tokenization groups a sequence of data points into "patches," which are then treated as tokens. This reduces sequence length, computational complexity, and can capture local patterns more effectively.
• Re-Normalization: A data preprocessing step where time series data is normalized (e.g., to have zero mean and unit variance) before model training, and then denormalized (restoring original mean and standard deviation) after prediction. This helps to handle non-stationarity and distribution shifts in time series.
• Gating Mechanism: A technique used in neural networks, often employing sigmoid activation, to control the flow of information. A gate produces values between 0 and 1, effectively deciding how much information to "let through" or "block."

3.2. Previous Works

The paper categorizes previous works into General Time Series Modeling and Spatiotemporal Modeling.

3.2.1. General Time Series Modeling

• Statistical Models:
  • ARIMA (AutoRegressive Integrated Moving Average) [22]: A statistical model used for time series forecasting that captures linear relationships.
  • ETS (Error, Trend, Seasonality) [13]: Exponential smoothing models that decompose time series into error, trend, and seasonal components.
  • Limitation: Limited modeling ability for complex, non-linear patterns.
• Deep Learning Models (RNN-based):
  • RNN (Recurrent Neural Network) [17] and LSTM (Long Short-Term Memory) [16]: Designed to capture sequential dependencies.
  • Limitation: Suffer from high computational latency due to sequential execution, especially for long sequences.
• Deep Learning Models (Transformer-based and others for temporal dependencies):
  • Informer [45], Autoformer [37]: Transformer-based models that improve efficiency through attention mechanisms and handle long sequences. They integrate data from diverse variables during embedding.
  • PatchTST [30]: Reduces computational latency and captures temporal semantics through patch-wise tokenization.
  • iTransformer [28]: Employs a self-attention module across variables, treating independent time series as tokens to capture inter-variate correlations.
  • TSMixer [6]: Uses an MLP (Multi-Layer Perceptron) module for inter-variable interactions, capturing intricate variable correlations through multi-level features.
  • Crossformer [44]: Utilizes a cross-attention mechanism to capture both local and global temporal patterns while modeling spatial dependencies simultaneously.
  • CCM [5]: Deploys a cluster-aware feedforward mechanism for customized cluster management.
  • DUET [31]: Uses a dual-encoder framework to separately capture spatiotemporal dependencies.
  • DWLR [24]: Focuses on improving temporal generalization under label shifts.
  • Limitation: While improving temporal modeling, many of these models either overlook explicit spatial correlations or struggle to scale efficiently for large-scale sensor data.

3.2.2. Spatiotemporal Modeling

This category leverages Graph Neural Networks (GNNs) [4, 9, 21, 40, 43] to model spatial structures.

• Predefined Graph Structures (Time-Invariant):
  • DCRNN [25], GWNet [39], DGCRN [23]: Combine predefined graphs with sequential modeling to establish static spatial dependencies.
  • Limitation: Rely on pre-defined graphs which might be biased or inaccurate and do not adapt to dynamic changes.
• Automated Time-Invariant Graph Learning:
  • MTGNN [38], AGCRN [41], StemGNN [3]: Automatically infer time-invariant graphs from data.
  • Limitation: Still limited to static spatial dependencies, missing dynamic relationships.
• Dynamic Spatial Dependency (Time-Varying Graphs):
  • HimNet [8], MegaCRN [19], DMSTGCN [26]: Model time-varying graphs.
  • Limitation: Often incur significant computational overhead.
• Efficiency-Oriented Approaches:
  • Linear/low-rank approximations (Lastjomer [12], BigST [15], HIEST [29]): Trade spatial expressiveness for speed.
  • Linear-based architectures (STID [33], SimST [27]): Preserve spatial dependency through learnable parameters.
  • PatchSTG [10]: Advances efficiency through irregular spatial patching.
  • Limitation: Many are designed for specific domains (traffic, weather) and underperform with chemical sensor data due to high latency with large-scale sensors, inability to capture long-term dependencies (often using short lookback windows), and handling sensor heterogeneity.

3.3. Technological Evolution

The field of time series forecasting has evolved from simple statistical models (e.g., ARIMA, ETS) that captured basic temporal patterns to more complex data-driven approaches. Early deep learning methods (RNN, LSTM) improved pattern recognition but suffered from sequential processing limitations. The advent of Transformer-based models (e.g., Informer, Autoformer, PatchTST) significantly enhanced efficiency and long-term dependency capture through attention mechanisms and patch-wise tokenization.

Concurrently, the need to model spatial relationships in multivariate time series led to the integration of Graph Neural Networks (GNNs). Initially, GNNs relied on predefined, static graph structures, but research quickly moved towards automatically learning these graphs (MTGNN, AGCRN) and then dynamically adapting them over time (HimNet, MegaCRN).

ASTNet builds upon this evolution by addressing specific challenges in the chemical industry. It combines the efficiency benefits of Transformer-like architectures with advanced graph modeling. Its core innovations — asynchronous spatiotemporal modeling and gated dynamic graph fusion — directly tackle the latency and dynamic spatial dependency issues that previous methods either struggled with or could not address simultaneously for large-scale, heterogeneous industrial data.

3.4. Differentiation Analysis

Compared to existing methods, ASTNet's core innovations and differentiations are:

• Asynchronous Spatiotemporal Modeling vs. Sequential Paradigms:
  • Traditional: Most spatiotemporal models (DCRNN, GWNet, AGCRN, Crossformer, PatchSTG, DUET) follow a sequential approach (e.g., temporal then spatial, or vice versa). This leads to high latency, especially with high-dimensional representations passed between encoders.
  • ASTNet: Proposes an asynchronous paradigm where temporal and spatial encoders operate concurrently. This allows parallel computation, significantly reducing latency, a critical need for real-time industrial applications.
• Gated Graph Fusion vs. Fixed/Simple Dynamic Graphs:
  • Time-Invariant: Models like MTGNN and AGCRN only learn time-invariant graphs, failing to capture dynamic changes in sensor relationships.
  • Time-Varying (without adaptive fusion): Models like MegaCRN and HimNet incorporate time-varying graphs, but they may not effectively distinguish between true correlations and erroneous dependencies, especially in complex industrial settings where some sensors might become irrelevant at certain times.
  • ASTNet: Integrates both time-invariant (meta graph) and time-varying (dynamic graph) sensor relationships. Crucially, it introduces a gated graph fusion mechanism that adaptively combines these graphs. This mechanism allows the model to selectively consider or suppress spatial dependencies based on current sensor states, enhancing robustness and preventing erroneous correlations.
• Patch-wise Tokenization with Dual Lengths for Temporal and Spatial Modeling:
  • Standard Patch-wise: Models like PatchTST, Crossformer, PatchSTG use patch-wise tokenization for efficiency.
  • ASTNet: Uses different patch lengths ($P_t < P_s$) for temporal and spatial modeling. A shorter patch for temporal modeling captures subtle changes, while a longer patch for spatial modeling captures coarser-grained trends. This optimizes both capacity and latency.
• Handling Sensor Heterogeneity:
  • Some models (STID, HimNet) utilize sensor-specific indicators.
  • ASTNet: Incorporates sensor-specific indicators ($E_{tag}$) to enrich both temporal and spatial representations, specifically designed to handle the strong heterogeneity (e.g., pH vs. temperature) prevalent in chemical sensor data.
• Scalability for Large-Scale Chemical Sensor Data: Many existing models struggle with the sheer number of sensors (thousands) and the long-term dependencies required in chemical processes, often designed for shorter lookback windows and fewer nodes (e.g., traffic data). ASTNet specifically targets and demonstrates efficiency and accuracy in such large-scale, long-term industrial scenarios.

4. Methodology

4.1. Principles

The core idea behind ASTNet is to efficiently and comprehensively model complex spatiotemporal dependencies in large-scale chemical sensor data by:

1. Asynchronous Processing: Breaking the traditional sequential modeling paradigm (temporal then spatial) into concurrent paths, enabling parallel computation and reducing computational latency.
2. Adaptive Graph Fusion: Dynamically combining static (meta) and evolving (dynamic) sensor graph structures using a gating mechanism to robustly capture complex, heterogeneous spatial correlations and filter out spurious ones.
3. Heterogeneity and Long-Term Dependency Handling: Incorporating sensor-specific indicators and using optimized patch-wise tokenization with dual patch lengths to address sensor heterogeneity and efficiently capture long-term temporal patterns.

4.2. Core Methodology In-depth (Layer by Layer)

The ASTNet framework (as shown in Figure 2 from the original paper) processes a pair of lookback and horizon windows, $\mathbf{x} \in \mathbb{R}^{C \times L}$ (input) and $\mathbf{y} \in \mathbb{R}^{C \times H}$ (output), where $C$ is the number of sensors, $L$ is the lookback window length, and $H$ is the horizon length. The process involves several key steps:

The following figure (Figure 2 from the original paper) shows the ASTNet Framework.

该图像是一个示意图，展示了ASTNet模型中大规模传感器数据的时空编码过程。图中包含了时间编码器和空间编码器的结构，以及它们如何通过同步机制结合静态与动态传感器图。公式中使用的 p(y) 表示概率，$σ(p(y))$ 为激活函数。

4.2.1. Spatiotemporal Embedding

This initial phase prepares the raw time series data for parallel processing by the temporal and spatial encoders.

4.2.1.1. Re-Normalization

Due to sensor heterogeneity and time series non-stationarity, ASTNet first normalizes each time series instance $\mathbf{x} \in \mathbb{R}^{C \times L}$ to $\mathbf{X}_{norm}$. This addresses the distribution shift problem (instability in mean and variance over time). After predictions are made, a re-normalization step restores the original mean and standard deviation to the output.

4.2.1.2. Tokenization

To capture meaningful patterns and reduce computational complexity, ASTNet adopts a patch-wise tokenization strategy. The normalized data $\mathbf{x}_{norm}$ is partitioned into multiple patches of length $P$ with stride $S$. The resulting patch sequence is: $ \mathbf{x}{norm}^P \in \mathbb{R}^{C \times N \times P} $ where $N = \left\lfloor \frac{L - P}{S}\right\rfloor + 2$. To ensure completeness, the original series is padded (last value repeated $S$ times) before partitioning. A linear projection then maps each patch to its latent representation: $ \mathbf{z} = \mathrm{Projection}(\mathbf{x}{norm}^P) \in \mathbb{R}^{C \times N \times d} \quad (1) $ Here, $d$ is the dimension of the token embedding.

A key innovation here is the use of different patch lengths for temporal and spatial modeling.

• Temporal Modeling: Uses a shorter patch length, $P_t$, to capture fine-grained subtle changes. This results in an embedding $\mathbf{h}_t^l \in \mathbb{R}^{C \times N_t \times d}$.
• Spatial Modeling: Uses a larger patch length, $P_s$, to capture coarser-grained trends. This results in an embedding $\mathbf{h}_s \in \mathbb{R}^{C \times N_s \times d}$.

4.2.1.3. Context Incorporation

To account for the heterogeneity of large-scale sensors, ASTNet incorporates sensor-specific indicators. A learnable parameter $\mathbf{E}_{tag} \in \mathbb{R}^{C \times d}$ is assigned to each sensor. Positional encodings $\mathbf{E}_{pos} \in \mathbb{R}^{N \times d}$ are also incorporated to retain sequence order information. The enhanced latent representation is obtained as follows: $ \mathbf{h} = \mathrm{Concatenate}(\mathbf{E}{tag},\mathbf{z} + \mathbf{E}{pos}) \in \mathbb{R}^{C \times (N + 1) \times d} \quad (2) $ This process yields fine-grained temporal embedding $\mathbf{h}_t^l$ and coarse-grained spatial embedding $\mathbf{h}_s$ which serve as inputs to their respective encoders.

4.2.2. Transformer Backbone

The Transformer backbone is used within both temporal and spatial encoders to obtain per-token representations. Given token embeddings $\mathbf{h} \in \mathbb{R}^{C \times N \times d}$, it applies Layer Normalization [1] after attention and feedforward layers for training stability. The self-attention mechanism is defined as: $ \begin{array}{r}\boldsymbol {\mathcal{A}}_{ij} = \mathbf{h}_i^\top \mathbf{W}_q\mathbf{W}_k^\top \mathbf{h}_j\ \mathrm{Attention}(\mathbf{h}) = \mathrm{Softmax}\left(\frac{\boldsymbol{\mathcal{A}}}{\sqrt{d}}\right)\mathbf{h}\mathbf{W}_o \end{array} \quad (4) $ Where:

• $\mathbf{W}_q, \mathbf{W}_k, \mathbf{W}_o \in \mathbb{R}^{d \times d}$ are projection matrices that map token embeddings $\mathbf{h}$ into $d$-dimensional queries, keys, and values, respectively.
• $\boldsymbol{\mathcal{A}}$ is the attention score matrix. $\boldsymbol{\mathcal{A}}_{ij}$ represents the raw attention score between token $i$ and token $j$.
• $\mathrm{Softmax}(\cdot)$ normalizes the attention scores.
• $\sqrt{d}$ is a scaling factor to prevent large dot products from pushing the softmax function into regions with tiny gradients.
• $\mathbf{h}$ on the right side of $\mathrm{Attention}(\mathbf{h})$ refers to the input embeddings (which act as values $V$ after linear projection). The Transformer backbone consists of multiple layers of this attention mechanism followed by a feedforward network (FFN), enhancing token-wise representations. By permuting $\mathbf{h}$, the attention mechanism can be applied separately along the temporal and spatial dimensions.

4.2.3. Temporal Modeling

The temporal encoder captures long-term dependencies and nonlinear dynamics inherent in chemical engineering time series. It receives the fine-grained temporal embedding $\mathbf{h}_t^l \in \mathbb{R}^{C \times N_t \times d}$ (obtained using a small $P_t$). The operation for the $l$-th layer is: $ \tilde{\mathbf{h}}_t^l = \mathrm{TransformerEncorder}(\mathbf{h}_t^l) \quad (5) $ Here, $\mathrm{TransformerEncorder}(\cdot)$ denotes a standard Transformer encoder block (as described in Section 4.2.2). This processes the temporal sequence for each sensor independently (or in parallel across sensors for the temporal dimension).

4.2.4. Spatial Modeling

The spatial encoder models both time-invariant (meta) and time-varying (dynamic) sensor graphs. It takes the coarse-grained spatial embedding $\mathbf{h}_s$ as input (obtained using a larger $P_s$).

4.2.4.1. Lightweight Temporal Encoder

Before spatial graph construction, a lightweight temporal encoder processes the coarse-grained spatial embedding $\mathbf{h}_s \in \mathbb{R}^{C \times N_s \times d}$. This helps to distill temporal information from the coarser patches efficiently. $ \tilde{\mathbf{h}}_s = \mathrm{TransformerEncoder}(\mathbf{h}_s) \quad (6) $ This step ensures that the input to the spatial graph modeling has some temporal context while remaining computationally light due to the larger patch size.

4.2.4.2. Meta Graph

The meta graph, $\mathbf{A}_{meta}$, represents static, time-invariant relationships between sensors (e.g., physical proximity, inherent causal links). It is derived from the sensor embeddings $\mathbf{E}_{tag}$ that capture sensor-specific properties. $ \mathbf{A}{meta} = \mathrm{Softmax}(\mathrm{ReLU}(\mathbf{E}{tag}\mathbf{E}_{tag}^\mathrm{T})) \quad (7) $ Where:

• $\mathbf{E}_{tag} \in \mathbb{R}^{C \times d}$ are the learnable sensor-specific indicator embeddings.
• $\mathbf{E}_{tag}\mathbf{E}_{tag}^\mathrm{T}$ computes the dot product similarity between all pairs of sensor embeddings, capturing inherent relationships.
• $\mathrm{ReLU}(\cdot)$ is the rectified linear unit activation function, used to introduce non-linearity and ensure non-negative correlation strengths.
• $\mathrm{Softmax}(\cdot)$ normalizes the correlation strengths, typically row-wise or globally, to form a valid adjacency matrix. Each element (i,j) in $\mathbf{A}_{meta}$ indicates the correlation strength between the $i$-th and $j$-th sensor embeddings.

4.2.4.3. Dynamic Graph

The dynamic graph, $\mathbf{A}_{dynamic}^l$, captures time-varying spatial dependencies that evolve due to changes in production conditions, equipment states, or control strategies. It is learned adaptively using a Transformer applied across the spatial dimension. $ \mathbf{A}{\text{dynamic}}^{l},\tilde{\mathbf{h}}{s}^{l + 1} = \mathrm{TransformerEncoder}(\mathbf{\tilde{h}}_{s}^{l}) \quad (8) $ This Transformer Encoder (similar to Section 4.2.2 but applied spatially) processes the refined spatial representation $\mathbf{\tilde{h}}_{s}^{l}$ from the previous layer (or from the lightweight temporal encoder for the first layer). It outputs an updated spatial representation $\tilde{\mathbf{h}}_{s}^{l + 1}$ and an adjacency matrix $\mathbf{A}_{\text{dynamic}}^{l}$ which represents the dynamic correlations between sensors, typically derived from attention weights.

4.2.4.4. Gated Graph Fusion

This mechanism addresses the problem of erroneous correlations that might arise if $\mathbf{A}_{meta}$ and $\mathbf{A}_{dynamic}$ contain non-zero values even when some sensors are not significantly correlated at certain times. It adaptively integrates the meta graph and dynamic graph using a gating mechanism. First, a gating matrix $\omega$ is generated based on the dynamic graph: $ \omega = \mathrm{Sigmoid}(p(\mathbf{A}_{\text{dynamic}}^l)) \in \mathbb{R}^C \quad (9) $ Where:

• $p(\cdot)$ is a learnable linear mapping function that extracts sensor state information from $\mathbf{A}_{\text{dynamic}}^l$. This could involve, for example, aggregating attention weights per sensor or projecting the dynamic adjacency matrix to a sensor-wise representation.
• $\mathrm{Sigmoid}(\cdot)$ squashes the output of $p(\cdot)$ to the range $(0, 1)$, creating gating weights for each sensor. A value close to 0 would suppress the influence of the graph for that sensor, while a value close to 1 would allow it. Then, the unified graph $\mathbf{A}^l$ is computed by element-wise multiplication of $\omega$ with the sum of $\mathbf{A}_{meta}$ and $\mathbf{A}_{\text{dynamic}}^{l}$: $ \mathbf{A}^{l} = \omega \cdot (\mathbf{A}{meta} + \mathbf{A}{\mathrm{dynamic}}^{l}) \quad (10) $ Here, $\cdot$ denotes element-wise multiplication. This effectively allows the model to adaptively suppress or amplify the influence of the combined static and dynamic graph structures for each sensor, correcting potential erroneous spatial dependencies.

4.2.5. Asynchronous Fusion

ASTNet employs an asynchronous fusion paradigm where temporal and spatial features are processed concurrently and then integrated. This contrasts with traditional sequential approaches to reduce latency.

The model uses a multi-layer composite encoder $z(\cdot)$ which consists of a temporal encoder $f(\cdot)$ and a spatial encoder $g(\cdot)$. At each layer $l$, $f(\cdot)$ and $g(\cdot)$ synchronize with each other during their parallel computation and then generate updated representations for the next layer. The total number of layers is denoted by $L$.

The operations for asynchronous fusion are defined as follows: $ \begin{array}{rl} & {\mathsf{h}_t^{l + 1},\tilde{\mathsf{h}}_s^{l + 1} = z(f(\mathsf{h}_t^l),g(\tilde{\mathsf{h}}_s^l))}\ & {\qquad \tilde{\mathsf{h}}_t^l = f(\mathsf{h}_t^l)}\ & {\qquad \tilde{\mathsf{h}}_s^{l + 1},\mathbf{A}^l = g(\tilde{\mathsf{h}}_s^l)}\ & {\qquad \mathsf{h}_t^{l + 1} = \mathrm{Norm}(\mathrm{FFN}(\mathbf{A}^l\tilde{\mathsf{h}}_t^l) + \tilde{\mathsf{h}}_t^l)} \end{array} \quad (14) $ Let's break down these equations, assuming a slight typo in the paper's original equation (14) for the first line, where the output is typically $\mathbf{h}_t^{l+1}$ and $\mathbf{\tilde{h}}_s^{l+1}$ after the overall fusion, and $\mathbf{h}_t^l$ and $\mathbf{\tilde{h}}_s^l$ are inputs to the composite encoder. Assuming the subsequent lines correctly describe the internal steps:

• Parallel Encoder Execution:

  • The temporal encoder $f(\cdot)$ (from Section 4.2.3) processes the temporal embedding $\mathbf{h}_t^l$ to produce $\tilde{\mathbf{h}}_t^l$.
  • The spatial encoder $g(\cdot)$ (encompassing lightweight temporal encoder, dynamic graph learning, and gated graph fusion, as detailed in Section 4.2.4) processes the spatial embedding $\tilde{\mathsf{h}}_s^l$ to produce the updated spatial representation $\tilde{\mathsf{h}}_s^{l + 1}$ and the unified graph $\mathbf{A}^l$. These two encoder operations occur concurrently.

• Fusion and Refinement: After parallel computation, the outputs are synchronized and integrated. The temporal representation $\tilde{\mathbf{h}}_t^l$ is refined by the spatial dependencies captured in the unified graph $\mathbf{A}^l$:

  • $\mathbf{A}^l \tilde{\mathbf{h}}_t^l$: This typically represents a graph convolution-like operation where the unified graph $\mathbf{A}^l$ propagates information across sensors, enhancing the temporal features $\tilde{\mathbf{h}}_t^l$ with spatial context.
  • $\mathrm{FFN}(\cdot)$: A feedforward network processes the spatially-enhanced temporal features.
  • $\mathrm{Norm}(\cdot)$: Layer Normalization is applied.
  • $+ \tilde{\mathbf{h}}_t^l$: A residual connection is added, preserving information from the original temporal features. The final output of this fusion step is $\mathsf{h}_t^{l + 1}$.

The outputs $\mathsf{h}_t^{l + 1}$ and $\tilde{\mathsf{h}}_s^{l + 1}$ from each layer then serve as inputs to the next layer of the asynchronous encoder, progressively refining the spatiotemporal representations.

Finally, after the last layer of the asynchronous encoder, a projection head maps the output temporal embedding $\mathbf{h}_t^{L}$ to the predicted horizon values, $\widehat{\mathbf{y}}_{horizon}$. The model is optimized using an objective function, typically a loss function like $|\mathbf{y}_{horizon} - \widehat{\mathbf{y}}_{horizon}|$.

5. Experimental Setup

5.1. Datasets

The experiments were conducted on three real-world, large-scale chemical sensor datasets, provided by SUPCON Technology Co., Ltd. These datasets are from typical scenarios in the chemical industry: chlor-alkali, petroleum, and coal chemical industries. Each plant has over 1000 sensors, with a data sampling frequency of 5 seconds.

The following are the results from Table 1 of the original paper:

• Source: Real industrial production environments, specifically three major chemical plants in China.
• Scale: Large-scale, with 1113 to 2377 sensors per dataset.
• Characteristics: High-frequency data (5-second sampling), capturing dynamic changes in chemical processes. The Timespan indicates over a year of data for each dataset.
• Domain: Chlor-alkali, petroleum, and coal chemical industries.
• Why chosen: These datasets represent realistic and challenging scenarios in industrial chemical engineering, validating the model's performance in environments with a large number of heterogeneous sensors, complex spatiotemporal dependencies, and real-time forecasting needs.

5.1.1. Preprocessing

The preprocessing steps included:

• Missing Values:
  • For missing values due to sub-production line suspensions or equipment maintenance, zero-filling was used, deemed appropriate by experts aligning with physical meaning.
  • For missing values due to sensor failures or data transmission interruptions, linear interpolation was used.
• Anomalous Values: SUPCON's data team screened for anomalous sequences using statistical methods and domain knowledge to eliminate outliers caused by equipment failures or measurement errors.
• Standardization: Sensor data with different units and ranges (e.g., temperature in $^\circ \mathrm{C}$ vs. pressure in MPa) were standardized to prevent certain parameters from overly influencing model training.

5.1.2. Dataset Split

To ensure rigor:

• Chronological Split: Each dataset was strictly divided in chronological order.
• Ratio: 6:2:2 ratio for training, validation, and test sets (first 60% for training, next 20% for validation, final 20% for testing). This prevents data leakage.
• Sliding Window: A sliding window method with a window size of 25 steps was used to obtain samples from each time slice.
• Lookback Window: The lookback window length for each time slice was set to 256, helping the model capture long-term dependencies.

5.2. Evaluation Metrics

Three common indicators are used to evaluate model performance: Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE).

5.2.1. Mean Absolute Error (MAE)

• Conceptual Definition: MAE measures the average magnitude of the errors in a set of predictions, without considering their direction. It indicates the average absolute difference between predicted values and actual values. MAE is robust against anomalous fluctuations and noise, making it suitable for sensor data where large errors might be caused by measurement inaccuracies rather than model failures.
• Mathematical Formula: $ \mathrm{MAE} = \frac{1}{H}\sum_{i = 1}^{H}\Big|\hat{\mathbf{y}} {horizon}^{(i)} - \mathbf{y}{horizon}^{(i)}\Big|\hfill (15) $
• Symbol Explanation:
  • $\mathbf{y}_{horizon}^{(i)}$: The actual value for the $i$-th future timestamp in the horizon.
  • $\hat{\mathbf{y}}_{horizon}^{(i)}$: The predicted value for the $i$-th future timestamp in the horizon.
  • $H$: The total number of future timestamps to be predicted in the horizon.

5.2.2. Root Mean Squared Error (RMSE)

• Conceptual Definition: RMSE quantifies the square root of the average of the squared differences between predicted and actual values. It is sensitive to large errors, as squaring the errors gives them proportionally much more weight than smaller errors. It helps assess model accuracy and provides an error measure in the same units as the original data.
• Mathematical Formula: $ \mathrm{RMSE} = \sqrt{\frac{1}{H}\sum_{i = 1}^{H}(\hat{\mathbf{y}} {horizon}^{(i)} - \mathbf{y}{horizon}^{(i)})^2} \quad (16) $
• Symbol Explanation:
  • $\mathbf{y}_{horizon}^{(i)}$: The actual value for the $i$-th future timestamp in the horizon.
  • $\hat{\mathbf{y}}_{horizon}^{(i)}$: The predicted value for the $i$-th future timestamp in the horizon.
  • $H$: The total number of future timestamps to be predicted in the horizon.

5.2.3. Mean Absolute Percentage Error (MAPE)

• Conceptual Definition: MAPE expresses the accuracy as a percentage of the actual value. It is particularly useful for comparing model performance across different datasets or series with varying scales and units, as it provides a relative error measure.
• Mathematical Formula: $ \mathrm {MAPE}=\frac {100%}{H}\sum {i=1}^{H}\left|\frac {\mathbf{y}{horizon}^{(i)}-\hat {\mathbf{y}}{horizon}^{(i)}}{\mathbf{y}{horizon}^{(i)}}\right|\tag{17} $
• Symbol Explanation:
  • $\mathbf{y}_{horizon}^{(i)}$: The actual value for the $i$-th future timestamp in the horizon.
  • $\hat{\mathbf{y}}_{horizon}^{(i)}$: The predicted value for the $i$-th future timestamp in the horizon.
  • $H$: The total number of future timestamps to be predicted in the horizon.
  • Note: MAPE is undefined when $\mathbf{y}_{horizon}^{(i)}$ is zero.

5.3. Baselines

The paper compares ASTNet against 11 state-of-the-art (SOTA) methods, categorized into three groups:

5.3.1. Non-spatial Modeling-based Methods

These models primarily focus on temporal dependencies.

• PatchTST [30]: A Transformer-based model for long-term time series forecasting, using fixed-length patches as tokens.
• PDF [7]: A periodicity decoupling framework that separates and models periodic and non-periodic components of time series.

5.3.2. Time-invariant Spatial-based Methods

These models learn static sensor graphs.

• STID [33]: A spatial-temporal identity framework using simple embeddings to capture dependencies without complex architectures.
• AGCRN [41]: An adaptive graph convolutional recurrent network that integrates GCNs and RNNs to dynamically capture spatial and temporal patterns.
• MTGNN [38]: A multivariate time series forecasting framework using GNNs to jointly model inter-series dependencies and temporal patterns.
• StemGNN [42]: A spectral temporal graph neural network combining Graph Fourier Transform (GFT) and temporal convolution for spatial and temporal dynamics in the spectral domain.

5.3.3. Time-varying Spatial-based Methods

These models dynamically capture spatial dependencies.

• MegaCRN [19]: A spatio-temporal meta-graph learning framework using meta-graphs and GCRN to adaptively model complex dependencies.
• HimNet [8]: A heterogeneity-informed meta-parameter learning framework that adaptively learns task-specific parameters through meta-learning.
• PatchSTG [10]: A Transformer-based framework using a patch-based approach for efficient spatial data management in large-scale traffic forecasting.
• Crossformer [44]: A Transformer-based model that explicitly leverages cross-dimension dependencies by integrating inter-series and intra-series relationships.
• DUET [31]: A dual clustering-enhanced framework that integrates clustering mechanisms to capture global and local patterns in multivariate time series.

5.3.4. Implementation Details

• Optimizer: Adam with a learning rate of 0.0003.
• Epochs: 40, with early stopping patience set to 5.
• Scheduler: Cosine learning rate scheduler.
• Batch Size: 8 for Dataset A, 4 for Datasets B and C (due to larger sensor count).
• Repeats: Each experiment repeated 5 times, average results reported.
• Hyperparameters:
  • Lookback window length: 256
  • Embedding dimension $d$: 128
  • Number of heads (for attention): 4
  • Feedforward network dimension: 512
  • Temporal patch length $P_t$: 16 (for all datasets)
  • Spatial patch length $P_s$: 64 (for all datasets)
  • Number of spatiotemporal layers: 2
• Hardware: 8 NVIDIA RTX 3090 24GB GPUs.

6. Results & Analysis

6.1. Core Results Analysis

The experimental results demonstrate that ASTNet significantly outperforms state-of-the-art baselines across all three real-world chemical sensor datasets and various prediction horizons (60, 120, and 360 timestamps). The improvements are consistent in terms of MAE, RMSE, and MAPE.

The following are the results from Table 2 of the original paper:

Note: The provided table data in the prompt shows ASTNet as the last row for Dataset A, and then ASTNet also appears as the first row for Dataset B, and then as first row for Dataset C. There's a clear inconsistency for Dataset C where many baselines are marked OOM (Out Of Memory) but PatchTST, PDF, STID are shown, and then ASTNet is listed, but the next 7 rows which should be baselines for Dataset C are all OOM. It seems some rows are shifted or repeated. However, following the strict instruction, I have transcribed the table exactly as given. Based on the abstract and discussion, ASTNet is stated to be the best.

Key observations and analysis:

• Superior Performance of ASTNet: ASTNet achieves the lowest MAE, RMSE, and MAPE across almost all horizons and datasets, with an average of 7.4% MAE and 7.0% MAPE improvement over the best competing methods. This strong performance validates the effectiveness of its proposed asynchronous modeling and gated graph fusion.
• Impact of Sensor-Specific Indicators: Models like STID and HimNet (which utilize sensor-specific indicators) generally perform better than PatchTST and PDF (which do not). This highlights the importance of handling sensor heterogeneity. ASTNet further leverages sensor indicators to enhance both temporal and spatial dependency modeling, contributing to its leading performance.
• Importance of Dynamic Graph Modeling: Models that incorporate time-varying graphs (MegaCRN, HimNet) tend to perform better than those relying solely on time-invariant graphs (MTGNN, AGCRN). ASTNet's ability to model both meta and dynamic graphs, and to adaptively integrate them, allows it to capture the evolving relationships in chemical processes more effectively.
• Adaptive Graph Fusion's Role: The success of ASTNet is partly attributed to its gated mechanism, which adaptively chooses whether to consider the sensor graph structure. This is particularly beneficial in chemical processes where sensor interference might be intermittent, allowing the model to avoid erroneous spatial dependencies.
• Computational Challenges for Baselines: Several baseline methods (AGCRN, MTGNN, StemGNN, MegaCRN, HimNet, Crossformer, DUET) run Out Of Memory (OOM) on datasets B and C, which have a larger number of sensors. This underscores the scalability issues of existing methods when applied to truly large-scale industrial data and highlights ASTNet's efficiency in handling such scenarios.

6.2. Ablation Studies / Parameter Analysis

6.2.1. Ablation Study (RQ2)

An ablation study was conducted to validate the contribution of ASTNet's key components by evaluating five variants:

The following are the results from Table 3 of the original paper:

• w/o A1 (likely w/o A^l): Removing spatial dependency modeling.
  • Result: Significant drop in accuracy (e.g., MAE increases from 0.1957 to 0.2382 on Dataset A).
  • Conclusion: Confirms the critical importance of capturing spatial dependencies for accurate forecasting.
• w/o ω: Replacing the gated mechanism with a static vector.
  • Result: Moderate performance degradation (e.g., MAE on A increases to 0.2228).
  • Conclusion: The adaptive nature of the gating mechanism is crucial for effectively integrating graph structures and adapting to dynamic sensor conditions, outperforming static integration.
• w/o Ameta (likely w/o A_{meta}): Removing the meta (time-invariant) graph.
  • Result: Performance decline (e.g., MAE on A increases to 0.2089).
  • Conclusion: Highlights that even static, inherent spatial relationships play a vital role in model robustness and accuracy.
• w/o Adynamic (likely w/o A_{dynamic}): Removing the dynamic graph and gated fusion.
  • Result: Performs the worst among all ablated variants (e.g., MAE on A increases to 0.2306).
  • Conclusion: Emphasizes that capturing time-varying spatial dependencies is essential for modeling dynamically evolving chemical production processes.
• w/o Etag (likely w/o E_{tag}): Removing the learnable sensor-specific indicator.
  • Result: Degrades model performance (e.g., MAE on A increases to 0.2134).
  • Conclusion: Underscores the necessity of sensor-specific indicators in addressing the inherent heterogeneity of chemical sensor data.

6.2.2. Efficiency Comparisons (RQ3)

The computational latency of ASTNet was evaluated against nine spatiotemporal baseline models in a large-scale scenario (1,000 sensors, 256-length lookback window).

The following are the results from Table 4 of the original paper:

Analysis:

• ASTNet's Superior Efficiency: ASTNet demonstrates the lowest Cost Time (26.49ms) among all models, with a moderate number of parameters and memory usage. This confirms its superior computational efficiency.
• Impact of Asynchronous Computation: The variant ASTNet w/o Async (37.59ms) is slower than the full ASTNet, indicating that the asynchronous modeling paradigm significantly reduces latency. However, even without asynchronous processing, it remains competitive, suggesting the other architectural choices (like patch-wise tokenization and efficient graph fusion) also contribute to efficiency.
• Inefficiency of RNN-based Models: Models relying on GCRU architectures (AGCRN, MegaCRN, HimNet) suffer from significant efficiency gaps due to the iterative nature of RNNs, leading to high latency and often OOM issues (AGCRN).
• Complexity of GNNs: Models with complex architectures and point-wise tokenization (StemGNN, MTGNN) incur high GPU memory usage and latency due to a large number of parameters.
• Patch-wise Benefits: Models using patch-wise tokenization and parallel computation (Crossformer, PatchSTG, DUET) are generally more efficient than RNN-based or complex GNN models, but still fall short of ASTNet's efficiency. PatchSTG and DUET also incur extra overhead from irregular spatial partitioning and dual clustering, respectively, and still use sequential spatiotemporal modeling.
• STID's Efficiency: STID performs well in efficiency due to its simple linear projection mechanism, but its performance in accuracy is not as high as ASTNet.

6.2.3. Hyper-parameters Study (RQ4)

The impact of key hyperparameters was examined using MAE and MAPE on Dataset A.

The following figure (Figure 3 from the original paper) shows the Hyperparameter Study of ASTNet.

该图像是一个图表，展示了不同参数设置对预测模型性能的影响，包括时间嵌入值 $P_t$、空间嵌入值 $P_s$、回溯窗口长度 $L$ 以及嵌入维度 $d$。每个子图中均显示了MAE（蓝色线条）和MAPE（红色线条）的变化趋势，反映了这些参数在不同范围内对预测精度的影响。

• Temporal Embedding Patch Length ($P_t$):
  • Observation: MAE improves as $P_t$ increases, reaching a minimum at $P_t = 32$, then slightly deteriorating. MAPE shows a similar trend.
  • Conclusion: A moderate patch length of 32 effectively captures temporal dependencies without excessive complexity, suggesting a balance between fine-grained detail and computational efficiency.
• Spatial Embedding Patch Length ($P_s$):
  • Observation: The model performs best at $P_s = 8$, with performance degrading as $P_s$ increases.
  • Conclusion: Spatial dependency modeling benefits from a shorter patch length, implying that coarser-grained trends are sufficient, and perhaps very long patches might obscure important spatial relationships or introduce too much irrelevant temporal context for spatial analysis. This contrasts with $P_t$, supporting the dual patch length strategy.
• Length of Lookback Window ($L$):
  • Observation: MAE decreases from $L = 64$ to $L = 128$, but then plateaus and slightly worsens for longer windows (e.g., $L = 1024$).
  • Conclusion: A moderate lookback window size (e.g., 128 or 256 as used in experiments) provides a good balance. Too short a window might miss long-term dependencies, while too long a window can introduce noise and redundant information, potentially leading to overfitting or reduced accuracy.
• Embedding Dimension ($d$):
  • Observation: Both MAE and MAPE improve significantly as $d$ increases from 32 to 128. Further increases show diminishing returns and stabilization.
  • Conclusion: An embedding dimension around 128 strikes a good balance between representational capacity and model complexity, avoiding both underfitting (too small $d$) and overfitting (excessively large $d$ without proportional gains).

7. Conclusion & Reflections

7.1. Conclusion Summary

The paper successfully introduces ASTNet, a novel Asynchronous Spatio-Temporal Network designed for large-scale chemical sensor forecasting. ASTNet addresses critical challenges in industrial applications, particularly high computational latency and complex spatiotemporal dependencies. Its core innovations include an asynchronous modeling strategy that enables parallel learning of temporal and spatial dependencies, significantly reducing latency, and a gated graph fusion mechanism that adaptively combines static meta graphs and evolving dynamic sensor graphs to robustly handle heterogeneous sensor data and intricate spatial correlations. Extensive experiments on three real-world chemical sensor datasets demonstrate ASTNet's superior performance in prediction accuracy and computational efficiency compared to state-of-the-art methods, leading to its successful deployment in real chemical engineering industrial scenarios.

7.2. Limitations & Future Work

The paper doesn't explicitly state "Limitations" and "Future Work" sections. However, based on the discussion, some implicit points can be inferred:

• Complexity for Hyperparameter Tuning: While the paper demonstrates ASTNet's effectiveness, the need for distinct patch lengths ($P_t$, $P_s$) and the interplay of various components (meta graph, dynamic graph, gating) suggest that hyperparameter tuning might be complex for new, diverse chemical processes.

• Generalizability to other domains: While shown effective in chemical engineering, its specific design for "thousands of heterogeneous sensors" and "long-term dependencies" may or may not translate directly to other spatiotemporal forecasting domains (e.g., traffic, weather) without re-tuning or adaptations.

• Interpretability: The paper focuses on performance and efficiency. For critical industrial applications, understanding why certain predictions are made (interpretability) can be crucial. While GNNs can offer some interpretability regarding spatial relationships, the asynchronous fusion and gating mechanisms might add layers of complexity.

  Potential future research directions implied by the paper's success and challenges:

• More advanced gating mechanisms: Exploring more sophisticated adaptive fusion methods beyond a simple element-wise multiplication with a sigmoid gate.

• Automated hyperparameter optimization: Developing methods to automatically determine optimal patch lengths, embedding dimensions, and other hyperparameters for new datasets.

• Cross-domain adaptation: Investigating how ASTNet could be adapted or generalized to other large-scale spatiotemporal forecasting problems, potentially with different types of heterogeneity or graph dynamics.

• Enhanced Interpretability: Integrating interpretability techniques to better explain the model's decisions, especially for sensor-specific anomaly detection or root cause analysis.

7.3. Personal Insights & Critique

ASTNet presents a compelling solution to a pressing industrial problem, demonstrating a strong understanding of both deep learning architectures and the specific constraints of chemical engineering. The asynchronous modeling paradigm is a practical and ingenious way to tackle the latency challenge, which is often overlooked in academic benchmarks that prioritize accuracy over real-world operational speed. The dual patch-length strategy for temporal and spatial encoders is another clever optimization, acknowledging that different types of dependencies require different granularities of input.

The gated graph fusion mechanism is particularly innovative. By explicitly combining a static meta graph (representing inherent physical relationships) with a dynamically learned graph, and then adaptively filtering their influence, ASTNet effectively addresses the real-world complexity where sensor relationships are neither purely fixed nor entirely fluid. This approach is highly relevant for robust industrial applications where erroneous correlations can lead to costly mistakes.

One area for potential improvement or further exploration could be the automatic inference of the meta graph. While the paper mentions deriving it from $E_{tag}$, the details of how $E_{tag}$ is learned or initialized to effectively capture "inherent and static relationships" could be expanded. For a beginner, it would be beneficial to understand if $E_{tag}$ is purely random initialized and learned or if it incorporates some domain knowledge or pre-analysis of sensor types.

Another point of critique relates to the "OOM" results for many baselines on larger datasets. While this clearly highlights ASTNet's scalability, it also means that direct performance comparisons on these datasets are limited, as the baselines simply cannot run. This might suggest that ASTNet is not just "better," but in some cases, the only viable deep learning solution for such scale, making its contribution even more significant.

The deployment in real chemical plants further validates the practical utility and robustness of ASTNet, moving beyond theoretical performance to tangible industrial impact. This is a strong indicator of the model's maturity and effectiveness. The methods and conclusions are highly transferable to other large-scale industrial IoT scenarios, smart city management, or any complex system with numerous heterogeneous, interdependent sensors where real-time forecasting and dynamic relationship modeling are crucial.