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REVIEW 5 major objections 5 minor 27 references

APS-LSTM: Exploiting Multi-Periodicity and Diverse Spatial Dependencies for Flood Forecasting

T0 review · 5 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read APS-LSTM claims that splitting rainfall and flow into multiple FFT-detected period views, each with its own spatial attention, cuts average RMSE by 4.1% and 11.3% on two Chinese basins.

desk verdict Competent incremental application of TimesNet-style period division to flood forecasting, with a real empirical question but evaluation gaps (single seed, unspecified graph, unclear split) that need fixing before the average gains are credible. read the letter →

arxiv 2412.06835 v1 pith:J327VBSH submitted 2024-12-07 cs.LG cs.AI

Jun Feng , Xueyi Liu , Jiamin Lu , Pingping Shao This is my paper · ORCID
classification cs.LGcs.AI
keywords floodforecastingmulti-periodicityFastFourierTransformspatialself-attentionLSTMspatio-temporalpredictionhydrologicaldataadaptiveaggregation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

APS-LSTM is a flood-forecasting model that tries to show that hydrological time series should be treated as a mixture of several overlapping periods, not one fixed seasonality, and that rainfall-to-flow spatial relationships should be learned separately for each period view. The paper claims that using the Fast Fourier Transform to find the strongest frequencies, reshaping the series into period-versus-trend tensors, and applying periodic and spatial self-attention on each view, followed by amplitude-weighted aggregation, improves 1-to-6-hour-ahead flow prediction. On two real watersheds in China, it reports average RMSE reductions of 4.1% and 11.3% over the second-best baseline, with the advantage growing from the third hour onward. The wider point is that multi-periodicity and per-period spatial attention are complementary signals worth exploiting in flood forecasting.

What carries the argument

The load-bearing object is the Adaptive Periodic and Spatial Self-Attention Block (APS-Block). It first uses FFT amplitudes to pick the top-$k$ frequencies and reshape the input into $k$ two-dimensional tensors whose axes are "within a period" and "across periods"; then it applies periodic self-attention with 2D convolution projections and spatial self-attention with 1D convolution projections inside each division; finally it sums the $k$ outputs with softmax weights derived from the FFT amplitudes. The block is stacked with residual connections, and its aggregated output is encoded by an LSTM and decoded by a linear layer, with a graph Laplacian embedding injected at the input.

What would settle it

On a third basin with an independently validated station graph, run APS-LSTM against its second-best baseline and check the average RMSE gap; if the gap disappears or reverses, the advantage is dataset-specific. Alternatively, replace $A$ with a random or identity adjacency matrix and re-run: a large RMSE change would show the graph matters, while a negligible change would show spatial attention is not actually using it.

Watch

Extended reading notes

Core claim

The paper's central claim, stated in Section V-D, is that APS-LSTM "performs best on average compared to the other 6 baselines." Table I supports this with average RMSE, MAE, and MAPE on the TunXi and ChangHua basins, where APS-LSTM reduces average RMSE by 4.1% and 11.3% relative to the second-best model and leads all baselines from the third forecast hour onward. The ablation study reports that removing either the periodic or the spatial self-attention module raises average RMSE, and the case-study visualizations show attention weights shifting across period divisions and stations. The authors read these results as evidence that discovering multiple periods with FFT and attending to spatial structure within each period division captures information that single-period spatio-temporal models miss.

Load-bearing premise

The load-bearing premise is that the predefined station graph $G=(V,E,A)$ correctly encodes rainfall-to-flow spatial connections, yet the paper never explains how $A$ is constructed, so if that graph is wrong the spatial attention can amplify noise and the reported gains may not transfer.

Editorial extensions

If this is right

  • If the FFT period division is doing the work, models that assume a single fixed period should be systematically worse on basins with overlapping rainfall and flow cycles.
  • The slower RMSE growth from T+1 to T+6 implies that the advantage concentrates in longer-horizon predictions, where peak-flow timing errors normally grow.
  • Since both ablations hurt, periodic and spatial self-attention provide complementary gains, and a model with only one of them is expected to be inferior.
  • The approach produces interpretable attention maps, so it can be used to identify which rainfall stations matter at which period and lead time.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A test this paper does not run is applying APS-LSTM to a basin with weak periodicity, such as a flash-flood catchment dominated by single storm pulses; if the FFT division adds nothing there, the reported gains may be specific to basins with regular seasonal cycles.
  • Because the paper never specifies how the adjacency matrix $A$ is built, a concrete extension is to learn the graph from rainfall-to-flow cross-correlation or delay estimates, which would test whether the spatial gains are sensitive to graph quality.
  • The reported metrics are averaged over the whole test set, while the peak-flow case study is qualitative; evaluating peak error and time-to-peak across all flood events would sharpen the claim.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper proposes APS-LSTM, a flood-forecasting model that combines multi-periodicity discovery via Fast Fourier Transform (FFT), periodic and spatial self-attention modules, and adaptive aggregation of period-wise representations, followed by LSTM encoding and a linear decoder. The method is evaluated on two Chinese watershed datasets (TunXi and ChangHua) against six baselines (LSTM, GRU, DLinear, STA-LSTM, GraphWaveNet, TimesNet). The central claim, stated in Section V-D, is that APS-LSTM performs best on average across the 6-hour forecasting horizon, with reported average RMSE reductions of 4.1% (TunXi) and 11.3% (ChangHua) over the second-best model. The paper also includes an ablation study and qualitative visualizations of spatial and periodic attention.

Significance. If the empirical claim holds, APS-LSTM offers a novel combination of FFT-based multi-period division with spatial self-attention for hydrological forecasting, and the paper's code release (github.com/oopcmd/APS-LSTM) is a concrete reproducibility asset. I found no circularity: the FFT amplitude weights used for aggregation are computed from the input window, not from the test target, and the evaluation is on held-out data. The significance is nevertheless bounded by the current experimental rigor: single-seed results, no error bars, an unspecified graph construction, and an unspecified split protocol could all affect the reported ranking. The architectural ideas are interesting and the paper is clearly written, but the evidence needs strengthening before the superiority claim can be accepted.

major comments (5)
  1. [Section V-C / Table I] The central claim that APS-LSTM 'performs best on average' is supported only by single-seed results (Section V-C states 'The random seed is set to 2') with no standard deviations, confidence intervals, or significance tests. The reported average RMSE gains are modest (4.1% on TunXi, 11.3% on ChangHua), and at T+1 on TunXi APS-LSTM is substantially worse than DLinear (RMSE 21.58 vs. 15.31). Without repeated trials, the average ranking could be within run-to-run variability. Please report multiple seeds with error bars and, where feasible, statistical significance tests.
  2. [Sections III-A and IV-A] The graph G=(V,E,A) is introduced as a predefined input, and both the Laplacian embedding (Section IV-A) and the spatial self-attention (Section IV-B.2) depend on the adjacency matrix A, but the paper never states how A is constructed. This makes the method irreproducible and leaves open whether the reported gains transfer to basins without a reliable graph. Please specify the graph construction (e.g., distance thresholds, k-nearest neighbors, or basin topology) and any normalization applied.
  3. [Section V-C] The dataset split is described as '80% training set, 5% validation set and 15% test set' but it is not stated whether the split is chronological. For time series with overlapping sliding windows, a random split can leak future information into the training set and inflate the apparent skill of all models. Please state explicitly that the split is temporal and that no test-set statistics are used in preprocessing (the Min-Max normalization in Eq. (12) already uses only the training set, which is good).
  4. [Section V-C / Eq. (11)] The MAPE metric masks out flow values less than 1, but this threshold is introduced ad hoc and is not justified. Since MAPE is one of the three headline metrics and the reported ranking changes across metrics, please justify the threshold (e.g., by the physical range of the flow data) and discuss its influence on the MAPE comparisons.
  5. [Section V-C] No hyperparameter details are given for the six baselines, such as hidden dimensions, number of layers, learning rates, number of epochs, or early-stopping criteria. Without evidence that the baselines were tuned to a comparable degree, the claim of superiority over them is not yet established. Please provide the baseline configurations or explicitly state that the original published settings were used.
minor comments (5)
  1. [Eq. (2) and Eq. (3)] The notation is inconsistent: Eq. (2) uses ⊙ between weight matrices and the concatenated input [h_{t-1}, x_t], while Eq. (3) defines ⊙ as element-wise multiplication. The LSTM equations should use matrix multiplication (or an explicit concatenated weight matrix notation) to avoid confusion.
  2. [Eq. (10)] The subscript in 'Wf1 , · · ·, Wf2' appears to be a typo; the last index should be k, giving 'W_f1, ..., W_fk'.
  3. [Section V-C] The word 'Ubantu' should be 'Ubuntu'.
  4. [Section III-A] The notation X_t ∈ R^{1×N} and X_t^i ∈ R^{1×1} is confusing, especially because the flow station is indicated by i=N but the target Y_{t+1} is a scalar. Please clarify the station indexing and the relationship between X and the target.
  5. [Section III-A] The set of edges E in G=(V,E,A) is defined but never used in the paper; either use it or remove it from the notation to avoid dead conceptual weight.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the multi-period division and adaptive aggregation are computed from the input series, and the empirical claim rests on held-out test evaluation.

full rationale

The paper's derivation chain is self-contained rather than circular. The multi-period division in Eq. (4) selects the top-k frequencies from the FFT amplitude of the input embedding X_e, and the adaptive aggregation weights in Eq. (10) are a softmax over those same input-derived amplitudes. These quantities depend on the historical input series, not on the target flow values, the test set, or any fitted parameter that already encodes the prediction. The periodic and spatial self-attention parameters are learned on the 80% training split, with model selection performed on the 5% validation split, and all reported metrics are computed on the held-out 15% test split. The predefined graph G = (V, E, A) is an input assumption rather than a quantity derived from the output; its construction is not documented, which is a practical weakness, but it is not an instance of circular reasoning. The paper does cite prior work by the same research group, including reference [18] (STA-LSTM) and reference [19] (a graph-convolution LSTM flood model), but those citations appear in related work and baseline selection, and they are not load-bearing for the central claim that APS-LSTM outperforms the baselines on held-out data. Concerns about single-seed runs, missing error bars, and an unspecified chronological split are evaluation-robustness issues, not circularity. Thus no step in the paper reduces by construction to its own inputs, and the central empirical claim has independent content.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The model introduces no new physical entities. Its empirical claim depends on several hyperparameters and on assumptions about periodicity, graph quality, and missing-data handling.

free parameters (5)
  • k (number of top frequencies) = 2
    Hyperparameter controlling the number of period divisions; set to 2 (Section V-C).
  • L (number of APS blocks) = 2
    Depth of the adaptive periodic and spatial self-attention stack (Section V-C).
  • hidden layer dimension = 80-90
    Hidden dimension searched between 80 and 90 (Section V-C).
  • MAPE mask threshold = 1
    Flow values below 1 are masked when computing MAPE (Section V-C), which systematically excludes low-flow errors.
  • random seed = 2
    Single seed used for training (Section V-C).
assumptions (4)
  • domain assumption FFT amplitude of the input sequence identifies the most relevant periods for forecasting.
    Used in Eq. 4 to select top-k periods; hydrological periodicities may not be stationary or captured by the two strongest frequencies.
  • domain assumption A predefined spatial graph adjacency matrix A is available and accurate.
    Used in Sections III-A and IV-A; construction is not described.
  • domain assumption Linear interpolation adequately fills missing values.
    Stated in Section V-A without validation.
  • standard math Standard properties of FFT, attention, and LSTM.
    Underlying the architecture (Eqs. 2 through 10).

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Cite this review

Pith. "Pith review of APS-LSTM: Exploiting Multi-Periodicity and Diverse Spatial Dependencies for Flood Forecasting." pith.science (2026). https://pith.science/paper/J327VBSH

@misc{pith2026241206835,
  author       = {Pith},
  title        = {Pith review of: APS-LSTM: Exploiting Multi-Periodicity and Diverse Spatial Dependencies for Flood Forecasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/J327VBSH}},
  note         = {Machine review of arXiv:2412.06835}
}
read the original abstract

Accurate flood prediction is crucial for disaster prevention and mitigation. Hydrological data exhibit highly nonlinear temporal patterns and encompass complex spatial relationships between rainfall and flow. Existing flood prediction models struggle to capture these intricate temporal features and spatial dependencies. This paper presents an adaptive periodic and spatial self-attention method based on LSTM (APS-LSTM) to address these challenges. The APS-LSTM learns temporal features from a multi-periodicity perspective and captures diverse spatial dependencies from different period divisions. The APS-LSTM consists of three main stages, (i) Multi-Period Division, that utilizes Fast Fourier Transform (FFT) to divide various periodic patterns; (ii) Spatio-Temporal Information Extraction, that performs periodic and spatial self-attention focusing on intra- and inter-periodic temporal patterns and spatial dependencies; (iii) Adaptive Aggregation, that relies on amplitude strength to aggregate the computational results from each periodic division. The abundant experiments on two real-world datasets demonstrate the superiority of APS-LSTM. The code is available: https://github.com/oopcmd/APS-LSTM.

Figures

Figures reproduced from arXiv: 2412.06835 by the authors.

Figure 1
Figure 1. Illustration of Diverse Spatial Dependencies To address the above challenges, inspired by Times￾Net [16], we introduce the Adaptive Periodic and Spa￾tial Self-Attention model based on LSTM (APS-LSTM) [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. The Overall Framework of APS-LSTM. A. Data Embedding The main role of the data embedding layer is to process the predefined graph structure using graph Laplacian eigenvec￾tors [23], which allows the input data to contain the necessary spatial information. We first convert the original adjacency matrix to a normal￾ized Laplacian matrix by L = I−D− 1 2 AD− 1 2 , where I is the identity matrix and D is the degree matri… view at source ↗
Figure 7
Figure 7. [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Trends in MAE from T+1 to T+6 for different models [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: Trends in MAPE from T+1 to T+6 for different models that perform the best on the validation set are used as the final results, and the metrics are evaluated on the test set. We use three evaluation metrics, RMSE, MAE and MAPE, to validate the model performance on the t…
Figure 8
Figure 8. Figure 8: Case Study of Spatial Self-Attention [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]
Figure 9
Figure 9. Figure 9: Case Study of Periodic Self-Attention which show the changes in the spatial association degree between the stations in different time periods under the same period divisions. Then, we compared [PITH_FULL_IMAGE:figures/full_fig_p006_9.png]

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Reference graph

Works this paper leans on

27 extracted references · 15 canonical work pages

  1. [1]

    Analysis of flash flood disaster characteristics in china from 2011 to 2015,

    B. He, X. Huang, M. Ma, Q. Chang, Y . Tu, Q. Li, K. Zhang, and Y . Hong, “Analysis of flash flood disaster characteristics in china from 2011 to 2015,” Natural Hazards, vol. 90, pp. 407–420, 2018

    work page 2011

  2. [2]

    Long short-term memory,

    S. Hochreiter and J. Schmidhuber, “Long short-term memory,” Neural computation, 1997

    work page 1997

  3. [3]

    Diffusion convolutional recur- rent neural network: Data-driven traffic forecasting,

    Y . Li, R. Yu, C. Shahabi, and Y . Liu, “Diffusion convolutional recur- rent neural network: Data-driven traffic forecasting,” arXiv preprint arXiv:1707.01926, 2017

    arXiv 2017

  4. [4]

    N-beats: Neural basis expansion analysis for interpretable time series forecast- ing,

    B. N. Oreshkin, D. Carpov, N. Chapados, and Y . Bengio, “N-beats: Neural basis expansion analysis for interpretable time series forecast- ing,” arXiv preprint arXiv:1905.10437 , 2019

    arXiv 1905

  5. [5]

    Daily long-term traffic flow forecasting based on a deep neural network,

    L. Qu, W. Li, W. Li, D. Ma, and Y . Wang, “Daily long-term traffic flow forecasting based on a deep neural network,” Expert Systems with applications, vol. 121, pp. 304–312, 2019

    work page 2019

  6. [6]

    Periodic-crn: A con- volutional recurrent model for crowd density prediction with recurring periodic patterns

    A. Zonoozi, J.-j. Kim, X.-L. Li, and G. Cong, “Periodic-crn: A con- volutional recurrent model for crowd density prediction with recurring periodic patterns.” in IJCAI, vol. 18, 2018, pp. 3732–3738

    work page 2018

  7. [7]

    Modeling and forecasting vehicular traffic flow as a seasonal arima process: Theoretical basis and empirical results,

    B. M. Williams and L. A. Hoel, “Modeling and forecasting vehicular traffic flow as a seasonal arima process: Theoretical basis and empirical results,” Journal of transportation engineering , vol. 129, no. 6, pp. 664–672, 2003

    work page 2003

  8. [8]

    Are transformers effective for time series forecasting?

    A. Zeng, M. Chen, L. Zhang, and Q. Xu, “Are transformers effective for time series forecasting?” in AAAI, vol. 37, no. 9, 2023, pp. 11 121– 11 128

    work page 2023

Show all 27 references
  1. [9]

    Semi-supervised classification with graph convolutional networks,

    T. N. Kipf and M. Welling, “Semi-supervised classification with graph convolutional networks,” arXiv preprint arXiv:1609.02907 , 2016

    2016 arXiv

  2. [10]

    Spatial-temporal graph ode networks for traffic flow forecasting,

    Z. Fang, Q. Long, G. Song, and K. Xie, “Spatial-temporal graph ode networks for traffic flow forecasting,” in Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining , 2021, pp. 364–373

    2021

  3. [11]

    Spatial-temporal synchronous graph convolutional networks: A new framework for spatial-temporal network data forecasting,

    C. Song, Y . Lin, S. Guo, and H. Wan, “Spatial-temporal synchronous graph convolutional networks: A new framework for spatial-temporal network data forecasting,” in AAAI, vol. 34, no. 01, 2020, pp. 914–921

    2020

  4. [12]

    Spatial-temporal identity: A simple yet effective baseline for multivariate time series forecasting,

    Z. Shao, Z. Zhang, F. Wang, W. Wei, and Y . Xu, “Spatial-temporal identity: A simple yet effective baseline for multivariate time series forecasting,” in Proceedings of the 31st ACM International Conference on Information & Knowledge Management , 2022, pp. 4454–4458

    2022

  5. [13]

    St-mlp: A cascaded spatio-temporal linear framework with channel-independence strategy for traffic forecasting,

    Z. Wang, Y . Nie, P. Sun, N. H. Nguyen, J. Mulvey, and H. V . Poor, “St-mlp: A cascaded spatio-temporal linear framework with channel-independence strategy for traffic forecasting,” arXiv preprint arXiv:2308.07496, 2023

    2023 arXiv

  6. [14]

    Attention based spatial-temporal graph convolutional networks for traffic flow fore- casting,

    S. Guo, Y . Lin, N. Feng, C. Song, and H. Wan, “Attention based spatial-temporal graph convolutional networks for traffic flow fore- casting,” in AAAI, vol. 33, no. 01, 2019, pp. 922–929

    2019

  7. [15]

    Learning dynamics and heterogeneity of spatial-temporal graph data for traffic forecasting,

    S. Guo, Y . Lin, H. Wan, X. Li, and G. Cong, “Learning dynamics and heterogeneity of spatial-temporal graph data for traffic forecasting,” IEEE Transactions on Knowledge and Data Engineering , vol. 34, no. 11, pp. 5415–5428, 2021

    2021

  8. [16]

    Timesnet: Temporal 2d-variation modeling for general time series analysis,

    H. Wu, T. Hu, Y . Liu, H. Zhou, J. Wang, and M. Long, “Timesnet: Temporal 2d-variation modeling for general time series analysis,” in ICLR, 2023

    2023

  9. [17]

    A new flood forecasting model based on svm and boosting learning algorithms,

    S. Li, K. Ma, Z. Jin, and Y . Zhu, “A new flood forecasting model based on svm and boosting learning algorithms,” in 2016 IEEE Congress on evolutionary computation (CEC) . IEEE, 2016, pp. 1343–1348

    2016

  10. [18]

    Interpretable spatio- temporal attention lstm model for flood forecasting,

    Y . Ding, Y . Zhu, J. Feng, P. Zhang, and Z. Cheng, “Interpretable spatio- temporal attention lstm model for flood forecasting,” Neurocomputing, vol. 403, pp. 348–359, 2020

    2020

  11. [19]

    Graph convolution based spatial-temporal attention lstm model for flood forecasting,

    J. Feng, H. Sha, Y . Ding, L. Yan, and Z. Yu, “Graph convolution based spatial-temporal attention lstm model for flood forecasting,” in 2022 International Joint Conference on Neural Networks (IJCNN) . IEEE, 2022, pp. 1–8

    2022

  12. [20]

    Graph wavenet for deep spatial-temporal graph modeling,

    Z. Wu, S. Pan, G. Long, J. Jiang, and C. Zhang, “Graph wavenet for deep spatial-temporal graph modeling,” arXiv preprint arXiv:1906.00121, 2019

    1906 arXiv

  13. [21]

    Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting,

    J. Xu, J. Wang, M. Long et al. , “Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting,” NeurIPS, 2021

    2021

  14. [22]

    Deep residual learning for image recognition,

    K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition , 2016, pp. 770–778

    2016

  15. [23]

    Laplacian eigenmaps for dimensionality reduction and data representation,

    M. Belkin and P. Niyogi, “Laplacian eigenmaps for dimensionality reduction and data representation,” Neural computation, vol. 15, no. 6, pp. 1373–1396, 2003

    2003

  16. [24]

    Pdformer: Propagation delay-aware dynamic long-range transformer for traffic flow predic- tion,

    J. Jiang, C. Han, W. X. Zhao, and J. Wang, “Pdformer: Propagation delay-aware dynamic long-range transformer for traffic flow predic- tion,” arXiv preprint arXiv:2301.07945 , 2023

    2023 arXiv

  17. [25]

    Neural machine trans- lation by jointly learning to align and translate,

    D. Bahdanau, K. Cho, and Y . Bengio, “Neural machine trans- lation by jointly learning to align and translate,” arXiv preprint arXiv:1409.0473, 2014

    2014 arXiv

  18. [26]

    Attention is all you need,

    A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, and I. Polosukhin, “Attention is all you need,” Advances in neural information processing systems , vol. 30, 2017

    2017

  19. [27]

    Empirical evaluation of gated recurrent neural networks on sequence modeling,

    J. Chung, C. Gulcehre, K. Cho, and Y . Bengio, “Empirical evaluation of gated recurrent neural networks on sequence modeling,” arXiv preprint arXiv:1412.3555, 2014

    2014 arXiv

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Reviewed August 11, 2026 · model on record in the stance chip above.