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REVIEW 5 major objections 7 minor 26 references

GTS_Forecaster: a novel deep learning based geodetic time series forecasting toolbox with python

T0 review · 5 major / 7 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read Adding Kolmogorov-Arnold Network layers to LSTM and BiLSTM improves long-term forecasting of GNSS, tide-gauge, and sea-surface-height time series, according to a new open-source Python toolbox.

desk verdict A genuinely useful open-source toolbox with real code, but the evaluation section has enough internal contradictions—especially the WQE direction—that the forecasting claims need major cleanup before they can be trusted. read the letter →

arxiv 2509.10560 v1 pith:MPOMKGF5 submitted 2025-09-10 cs.LG

Xuechen Liang , Xiaoxing He , Shengdao Wang , Jean-Philippe Montillet , Zhengkai Huang , Gaël Kermarrec , Shunqiang Hu , Yu Zhou
show 1 more author
Jiahui Huang
This is my paper
classification cs.LG
keywords geodetictimeseriesdeeplearningforecastingKolmogorov-ArnoldNetworksgap-fillingKalmanfilterGNSStidegaugeseasurfaceheight
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

GTS_Forecaster is an open-source Python toolbox that packages deep-learning models and preprocessing routines for forecasting geodetic time series—GNSS station positions, tide-gauge sea levels, and satellite altimetry sea-surface height. The paper argues that adding Kolmogorov-Arnold Network (KAN) layers to standard recurrent networks (LSTM, BiLSTM) improves long-term forecasting accuracy, while simpler MLP-based models remain competitive for short horizons. It also introduces KTIF, a Kalman-filter-and-attention gap-filling framework that reportedly recovers missing observations with R² up to 0.99. If these results hold, the toolbox gives geoscientists an accessible way to build early-warning systems for earthquakes, landslides, and storm surges from noisy, incomplete geodetic records.

What carries the argument

The load-bearing pieces are (1) KAN, a Kolmogorov-Arnold Network whose learnable B-spline activation functions on every connection replace fixed activations, letting LSTM/BiLSTM variants model complex long-range dependencies; (2) KTIF, a gap-filling framework combining a hidden Markov state-space model, forward-backward Kalman recursions, an attention-augmented interpolation operator, and an inverse-dynamics feature fusion gate; and (3) the WQE index, a weighted composite metric used to rank models. KAN supplies the expressive power claimed to improve long-horizon forecasting; KTIF supplies the mechanism for recovering missing points; WQE supplies the single scalar by which all models are ju

What would settle it

Run every model over 10 random seeds and report mean and standard deviation of WQE/R²; if the KAN-augmented advantage over plain LSTM vanishes or falls within noise, the central forecasting claim is refuted. Separately, apply KTIF to realistic gap patterns—consecutive weeks, seasonal outages, coseismic offsets—instead of random 5% deletion; if R² drops well below 0.95, the gap-filling claim does not generalize.

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Extended reading notes

Core claim

The paper's central claim is that a unified Python toolkit can make deep-learning forecasting practical for geodetic time series by pairing KAN-augmented recurrent architectures with a physics-informed interpolation scheme. Concretely, LSTM-EKAN and BiLSTM-EKAN achieve the highest weighted quality evaluation (WQE) scores across tide-gauge, GNSS, and sea-surface-height benchmarks in long- and medium-term forecasting, outperforming plain LSTM, GRU, and Transformer baselines; plain MLP-style models win only the shortest horizon. For missing data, the KTIF algorithm—built on bidirectional Kalman smoothing, a spatiotemporal attention correction, and inverse dynamics—reaches R² of 0.95 for GNSS an

Load-bearing premise

The forecasting and gap-filling conclusions rest on the evaluation design being unbiased: a single 80/20 chronological split with 'short-term' set to the first 1% of the test period, point estimates from single runs without error bars, and a self-defined WQE metric; plus the assumption that randomly deleting 5% of observations represents real geodetic missing-data patterns.

Editorial extensions

If this is right

  • If KAN-augmented models truly capture long-range dependencies better, they can improve forecasting of slow tectonic deformation and sea-level trends from GNSS and tide-gauge records.
  • The KTIF gap-filler at R² 0.95–0.99 could replace ad-hoc interpolation in geodetic time series analysis, reducing bias in velocity and trend estimates.
  • The toolbox's GUI and open-source code lower the barrier for geoscientists without deep-learning expertise to apply state-of-the-art forecasting.
  • The WQE index offers a single scalar for model selection across horizons, potentially standardizing comparisons in the field.
  • Because the package is adaptable to general time series, the KAN enhancements may transfer to other non-stationary Earth-science data such as groundwater or atmospheric records.

Reading between the lines

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

  • The KAN advantage may partly be an artifact of the WQE weightings; testing across multiple seeds and reporting error bars would clarify whether the reported gaps are statistically meaningful.
  • Real geodetic gaps are not random—they cluster around outages, maintenance, and seismic events—so KTIF should be tested on clustered missingness patterns before the R²=0.99 claim is generalized.
  • The definition of 'short-term' as the first 1% of a contiguous test block could give simple MLP models an unfair advantage because they can latch onto a single recent segment; a split with multiple short windows would be a more robust check.
  • The authors list physics-informed neural networks and multi-sensor fusion as future work; a natural extension would be to hook KTIF's interpolation into PINN-based forecasting so that physical laws constrain both gap-filling and prediction jointly.
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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 / 7 minor

Summary. The paper introduces GTS_Forecaster, an open-source Python toolbox for geodetic time series analysis, combining preprocessing (3IQR outlier removal and a proposed KTIF gap-filling framework) with a suite of deep learning forecasting models, including KAN-augmented LSTM/BiLSTM, GNN-GRU, TimeGNN, Transformers, and baselines. The authors evaluate these models on GNSS, tide gauge (TG), and sea surface height (SSH) time series using an 80/20 chronological split and short-, medium-, and long-term forecasting tasks. The central claim is that KAN-optimized models achieve superior forecasting performance, as measured by a weighted quality evaluation (WQE) index, and that KTIF delivers high-accuracy gap filling (R² = 0.95 for GNSS, 0.99 for TG).

Significance. If the results are correct, GTS_Forecaster could be a practically valuable, accessible tool for the geodetic time series community, and the KAN-augmented architectures would be a meaningful contribution. The paper's strengths include the open-source implementation, a GUI, and the integration of multiple modern architectures in one package. However, the quantitative evidence for the headline claims is currently undermined by internal inconsistencies in the WQE direction and calculations, mislabeled tables, and an underspecified evaluation protocol. The central comparison of KAN versus MLP models rests entirely on the self-defined WQE metric, which is not defined in this paper, and no external benchmark or classical geodetic baseline is provided. These issues must be resolved before the claims can be accepted.

major comments (5)
  1. [Section 4, Tables 2–4] The WQE direction is internally inconsistent. The text states the WQE value 'increased' by 44%, 27%, and 25% for LSTM_ekan versus LSTM, computed as (0.61-0.34)/0.61, (0.61-0.84)/0.84, and (0.61-0.85)/0.85. All three formulas yield relative decreases, not increases. Moreover, in Table 2, lower WQE coincides with lower RMSE/MAE and higher R² (e.g., LSTM_ekan long-term: R²=0.88, RMSE=18.35, WQE=0.61 vs LSTM: R²=0.84, RMSE=29.91, WQE=0.85), indicating WQE is lower-is-better. If WQE is in fact higher-is-better, then LSTM_ekan is worse on every horizon. The paper must define WQE (Eq. or reference), state its direction explicitly, and correct the 'increased' wording; otherwise the central KAN-superiority claim is unsupported.
  2. [Section 4, Tables 3 and 4] Tables 3 and 4 are both titled 'Tide Gauge', but the text describes Table 3 as GNSS results and Table 4 as SSH results. This makes it impossible to verify which dataset produced the claimed WQE improvements (e.g., 'BiLSTM_ekan shows more performance ... with WQE value increased by 10% over LSTM model' for GNSS, and 'BiLSTM_ekan demonstrated the best performance ... of tide gauge station sequences' for SSH). The tables must be retitled correctly and each dataset's provenance, station count, and time span must be described.
  3. [Section 4, Tables 2–4 and Figures 6–8] All reported metrics are point estimates from what appears to be a single run. No error bars, standard deviations across seeds, or statistical significance tests are given. Several comparisons are very close (e.g., Table 2 long-term LSTM R²=0.84 vs BiLSTM_ekan R²=0.84; Table 4 short-term LSTM R²=0.94 vs BiLSTM_ekan R²=0.94), so without repeated runs the 'outperforms' language is not justified. The authors should report mean±std over at least 5–10 seeds or perform a paired test.
  4. [Section 4, evaluation protocol] The definition of the forecasting tasks is ambiguous and potentially fragile. 'Short-term forecasting (Y1) ... within the first 1% of the test period' means, with an 80/20 split, only 0.2% of the total series is used. The paper does not state how many time steps constitute the short-term horizon, how the metrics are computed on such a small window, or whether this is a single-step or multi-step forecast. This ambiguity directly affects the credibility of the short-term comparisons. The authors must define the exact forecast horizons in samples/days and describe how R², RMSE, MAE, and WQE are computed over those horizons.
  5. [Section 3.2, KTIF gap-filling] The claim that KTIF achieves R²=0.95 (GNSS) and R²=0.99 (TG) after randomly deleting 5% of observations is not supported by experimental detail. The paper does not describe the datasets used for Figure 4, the number of stations, the gap lengths, the hyperparameters (F, Q, R, attention parameters), or any comparison to standard interpolation methods (e.g., cubic spline, linear interpolation, or Kalman smoothing). Random 5% deletion is also not representative of real geodetic data gaps, which often occur in blocks. This claim should be either substantially expanded or removed/tempered.
minor comments (7)
  1. [Section 1 and throughout] WQE is introduced as 'a weighted quality evaluation (WQE) index is proposed' but is never defined in this paper; it is only cited to reference [14]. Since WQE is the primary comparative metric, a brief definition (even in an appendix) is necessary.
  2. [Section 2.1] Typo: 'foand' should be 'and'.
  3. [Section 3.1] '3 interquartile range (3IQR)' should be written as '3×IQR' or 'three times the interquartile range'. There is also an unresolved citation marker '[REF?]' in the same paragraph.
  4. [Section 3.2] The algorithm name is inconsistently written: 'KTIF' in the text, 'KITF' in the caption of Figure 4. Please unify.
  5. [Table 3] Typo in model name: 'Tranformer_ekan' should be 'Transformer_ekan'.
  6. [Section 4] 'Tab. 2 4' should read 'Tables 2–4'.
  7. [Section 4, Figures 6–8] Figure captions do not match the described content: Figure 6 is described as TG, Figure 7 as GNSS, and Figure 8 as SSH, but the captions are nearly identical and do not identify the dataset. Please make captions dataset-specific.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the paper's central forecasting and gap-filling claims are empirical evaluations rather than derivations from their own definitions.

full rationale

The central claims (KAN-augmented models outperform baselines; KTIF recovers deleted observations with high R2) are supported by direct hold-out evaluations on an 80/20 chronological split, with standard metrics (R2, RMSE, MAE) reported alongside the WQE index. WQE is introduced by citation to the authors' prior work [14], but it is used as an evaluation metric, not as a fitted parameter or as a quantity derived from the models. The performance rankings in Tables 2-4 are also visible in the standard metrics, so the conclusion does not reduce to the WQE definition by construction. KTIF is tested by deleting 5% of observations and comparing interpolations to true values, which is a standard empirical validation. No equation in the paper defines a prediction in terms of the target output, and no result is forced by a self-citation chain or uniqueness theorem. The paper does contain non-circularity weaknesses: WQE is never defined in this manuscript; the text says WQE 'increased' when the reported values decrease (the improvement calculation is actually a relative reduction); Tables 3 and 4 are both labeled 'Tide Gauge' while the text refers to GNSS and SSH; and Section 3.1 contains a dangling '[REF?]'. These are correctness and reproducibility concerns, not circularity.

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

The paper's central claims rely on unspecified model hyperparameters, the self-defined WQE metric, and Kalman filter parameters without reported values. The domain assumptions about hidden Markov dynamics and missing-data mechanisms are taken from cited literature or asserted without testing. No new physical entities are introduced; KTIF is an algorithmic framework, not an entity.

free parameters (4)
  • Hyperparameters of deep learning models
    Learning rates, hidden sizes, number of layers, etc., are not reported; forecasting results depend on them, limiting reproducibility.
  • WQE index weights
    The weighted quality evaluation index is defined in the authors' prior work (ref [14]), but its weighting scheme is not described in this paper; all reported improvements are in terms of WQE.
  • KTIF state transition matrix F and noise covariances Q, R
    These Kalman filter parameters are learned or set by the DSPM step (Section 3.2.1) but their values are not provided.
  • KTIF chi-square threshold (alpha=0.05) = alpha=0.05
    The Dynamic Consistency Constraint uses a 95% confidence bound (Eq. 3); this is a chosen ad hoc parameter.
assumptions (4)
  • standard math Kolmogorov-Arnold Representation Theorem
    Used to justify KAN models; stated in Section 3.4.
  • domain assumption GNSS/TG observation sequences exhibit hidden Markov properties
    Invoked in Section 3.2.1, Step 1, citing ref [17], to justify the state-space representation.
  • domain assumption Missing data are missing at random
    The KTIF evaluation deletes 5% of observations randomly and reports R²; this tacitly assumes real gaps follow the same pattern.
  • domain assumption Geophysical priors (plate motion continuity) provide valid constraints
    Assumed in Section 3.2 where KTIF fuses physical priors with learned features.

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Cite this review

Pith. "Pith review of GTS_Forecaster: a novel deep learning based geodetic time series forecasting toolbox with python." pith.science (2026). https://pith.science/paper/MPOMKGF5

@misc{pith2026250910560,
  author       = {Pith},
  title        = {Pith review of: GTS_Forecaster: a novel deep learning based geodetic time series forecasting toolbox with python},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MPOMKGF5}},
  note         = {Machine review of arXiv:2509.10560}
}
read the original abstract

Geodetic time series -- such as Global Navigation Satellite System (GNSS) positions, satellite altimetry-derived sea surface height (SSH), and tide gauge (TG) records -- is essential for monitoring surface deformation and sea level change. Accurate forecasts of these variables can enhance early warning systems and support hazard mitigation for earthquakes, landslides, coastal storm surge, and long-term sea level. However, the nonlinear, non-stationary, and incomplete nature of such variables presents significant challenges for classic models, which often fail to capture long-term dependencies and complex spatiotemporal dynamics. We introduce GTS Forecaster, an open-source Python package for geodetic time series forecasting. It integrates advanced deep learning models -- including kernel attention networks (KAN), graph neural network-based gated recurrent units (GNNGRU), and time-aware graph neural networks (TimeGNN) -- to effectively model nonlinear spatial-temporal patterns. The package also provides robust preprocessing tools, including outlier detection and a reinforcement learning-based gap-filling algorithm, the Kalman-TransFusion Interpolation Framework (KTIF). GTS Forecaster currently supports forecasting, visualization, and evaluation of GNSS, SSH, and TG datasets, and is adaptable to general time series applications. By combining cutting-edge models with an accessible interface, it facilitates the application of deep learning in geodetic forecasting tasks.

Figures

Figures reproduced from arXiv: 2509.10560 by the authors.

Figure 1
Figure 1. Primary Interface of GTS_Forecaster Software [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. The structure diagram of GTS Forecaster. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Example of GNSS time series (AC03) outlier detection with 3IQR [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: The above figure shows the interpolation effect of the KTIF algorithm. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: elucidates the operational mechanism of KAN through a dual-panel illustration. The left panel depicts the propagation pathways of activation signals across network layers, while the right panel provides a detailed exposition of the dynamic modulation principles governi…
Figure 6
Figure 6. Figure 6: Comparison of LSTM_ekan, LSTM, GRU and Transformer model fits against true values on the test set (the [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Comparison of LSTM_ekan, LSTM, GRU and Transformer model fits against true values on the test set (the [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: Comparison of LSTM_ekan, LSTM, GRU and Transformer model fits against true values on the test set. [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

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Reviewed August 4, 2026 · model on record in the stance chip above.