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REVIEW 4 major objections 4 minor 49 references

Decomposing radar features by frequency before flow generation preserves heavy-rain cores over 60 minutes.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review

2026-08-04 23:57 UTC pith:3XVX4UH2

load-bearing objection A novel architecture with honest limitations, but the headline gains are marginal and single-run; worth peer review for the architecture, not for the numbers as reported. the 4 major comments →

arxiv 2608.01626 v1 pith:3XVX4UH2 submitted 2026-08-03 cs.LG cs.AI

QWRF-Net: A Quantum-Wavelet Framework with Rectified Flow for Short-Term Precipitation Nowcasting

Zhuo Wang , Chaorong Li , Wenjie Luo , Chuanhu Deng This is my paper
classification cs.LG cs.AI
keywords short-term precipitation nowcastingwavelet decompositionquantum-inspired modulationrectified flowmulti-scale precipitation representationextreme precipitation coresnon-autoregressive generationradar-based nowcasting
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper is trying to establish a specific architectural claim: short-term precipitation nowcasting improves when the conditional representation is explicitly reorganized by scale before future frames are generated. It argues that radar fields entangle broad precipitation organization with localized intense cores, and that this entanglement, combined with error accumulation in multi-step prediction, is why forecasts blur at later lead times. Its proposed remedy, QWRF-Net, decomposes the bottleneck latent feature into four wavelet sub-bands, enhances each band with its own classically simulated quantum-inspired nonlinearity, and then generates the full 12-frame, 60-minute sequence through a rectified-flow decoder using ODE integration rather than frame-by-frame rollout. Under a unified 6-to-12-frame protocol on the KNMI and SEVIR benchmarks, the paper reports the best overall scores, with its most consistent advantages at medium-to-high rain thresholds, on an extreme-event subset, and at the 40–60 minute lead times most relevant to flash-flood and urban-inundation warning. The claim matters because it names a concrete, reusable design principle — decompose by scale, modulate per band, generate with flow — that targets structural fidelity of intense rainfall rather than only average reconstruction error.

Core claim

The central claim, stated on the paper's own terms, is that warning-relevant precipitation nowcasting is best served by a representation-to-generation sequence rather than by either better representation or better generation alone. At the deepest level of a U-Net, a single-level 2D discrete wavelet transform decomposes the latent feature into LL, LH, HL, and HH sub-bands; each sub-band is compressed by global average pooling into a channel descriptor, projected into a qubit-aligned angle vector, processed by an independent trainable variational quantum circuit simulated on classical hardware, read out through Pauli-Z expectations, and projected back to produce a differentiated modulation of

What carries the argument

The load-bearing object is the quantum–wavelet bottleneck, a frequency-aware reorganization of the latent space: a discrete wavelet transform (DWT) splits the bottleneck feature into four sub-bands — LL for low-frequency background, LH/HL/HH for directional high-frequency detail — and each band is modulated by its own classically simulated variational quantum circuit (angular embedding, parameterized rotations and entangling gates, Pauli-Z readout) before an inverse DWT plus residual fusion restores the spatial feature. The second mechanism is the rectified-flow decoder, which trains a conditional velocity field v_θ(Z_t, t, X_in) against the target displacement (Z_1 − Z_0) along a linear noi

Load-bearing premise

The reported gains rest on the assumption that the unified evaluation protocol — hand-adjusted baseline hyperparameters and one shared validation checkpoint criterion — is genuinely fair to all seven compared models, so that the margins reflect the proposed architecture rather than under-tuned baselines.

What would settle it

Rerun the KNMI and SEVIR comparisons under identical splits but with each baseline fitted to its own reported best-case configuration (native sampling schedules for DiffCast and CoDiCast, full hyperparameter search for NowcastNet); if QWRF-Net's CSI lead at r≥10 and r≥30 mm/h, and its extreme-event-subset margin, shrink to within run-to-run noise or flip sign, the central claim collapses. A second decisive check: replace the variational quantum circuit with a per-band classical nonlinearity of matched parameter count and test whether the reported full-model gap over that variant persists.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • Nowcasting backbones should consider explicit frequency decomposition of latent features as a standard conditioning step, rather than relying on convolutional stacks to mix scales implicitly.
  • Warning-oriented metrics (thresholded CSI, an extreme-event subset, SSIM) become primary evaluation targets: the reported gains concentrate where warnings are decided, while low-threshold averages look more even.
  • Flow-based, non-autoregressive decoding is a practical alternative to diffusion-based and recursive generation for time-sensitive 60-minute forecasting, since it produces the whole sequence in one ODE pass.
  • The ablation pattern implies that per-sub-band, differentiated modulation — not the mere presence of a wavelet step — drives the high-threshold improvement, giving subsequent architectures a specific constraint to test.
  • If structure-preserving nowcasts hold up, they supply a more useful precipitation basis for downstream distributed hydrological and inundation models than point-estimate outputs with similar average error, a corollary the paper states as motivation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • I read the quantum-inspired module as carrying a separable claim: if a per-band classical MLP with matched parameter counts reproduces the gains (the paper's own QWRF-Net-C variant), then the variational-circuit form is an implementation detail, and the load-bearing effect is differentiated band-wise nonlinearity — a hypothesis the paper's ablations support but do not fully close.
  • An unstated, directly testable extension is to transplant the decompose–modulate–generate recipe to other spatiotemporal prediction tasks (storm surge, wind gusts, convection-allowed NWP downscaling) to see whether scale disentanglement transfers beyond radar VIL fields.
  • The paper explicitly defers the downstream question, so the natural next experiment is coupling QWRF-Net's nowcasts to a distributed hydrological or inundation model and measuring whether the extreme-core and SSIM gains convert into actual warning lead time or flood-stage skill.
  • Because the comparison rests on a unified protocol with hand-adjusted baselines, an independent replication that tunes each baseline to its own best-case configuration is the cheapest decisive test of whether the reported margins are architectural or procedural.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. QWRF-Net proposes a U-Net-based conditional generative model for radar nowcasting (6-frame input, 12-frame output). A discrete wavelet transform at the bottleneck splits latent features into four sub-bands, each modulated by a classically simulated variational quantum circuit, then recombined; a rectified-flow objective (Eq. 14) trains a velocity field that is integrated by Euler steps at inference. Experiments on KNMI and SEVIR under a unified 6→12 protocol compare against ConvLSTM, RainNet, SmaAt-UNet, SimVP, DiffCast, CoDiCast, and NowcastNet. The paper reports generally best or near-best CSI/HSS/MAE/RMSE/SSIM values, larger relative gains at higher thresholds and later lead times, better scores on an extreme-event subset, and ablations supporting each component.

Significance. If the comparative results are robust, QWRF-Net offers a transferable representation-to-generation design: explicit scale disentanglement before flow-based decoding, with a clearly stated non-quantum interpretation of the quantum-inspired operator. The paper correctly avoids overclaiming quantum advantage and uses public benchmarks. The ablations are internally coherent and the components are well motivated. However, the key evidence is currently single-run and the closest flow baselines (FlowCast, MeanFlow) are absent, so the significance is conditional on strengthening the evaluation.

major comments (4)
  1. [Tables 1–2; §4.4] The headline comparative claim rests on single-run results. Several differences are very small: KNMI CSI at r≥5 is 0.3610 vs 0.3607 for NowcastNet (Table 1); SEVIR CSI at x≥181 is 0.2581 vs 0.2571 (Table 2). With no error bars, seed variance, or significance tests, a single favorable checkpoint can produce such margins. Given §4.2 says baseline hyperparameters are 'adjusted within a comparable training setting,' the deltas cannot be distinguished from tuning/seed noise. Please provide multi-seed mean±std and paired tests, or restrict the claims to metrics where the difference is material.
  2. [§2.4, Tables 1–3] FlowCast and MeanFlow are described as the closest flow-based predecessors and are central to positioning the flow decoder, but they do not appear in any comparison table. Since the flow-based decoder is a core claimed contribution, omitting these baselines underdetermines whether the gain comes from the flow formulation itself or from the quantum–wavelet bottleneck. Add these baselines under the same protocol, or explicitly justify their exclusion.
  3. [§4.3, Table 3] The extreme-event subset is defined with thresholds (peak VIL≥219, exceedance ratio ≥2%) but its size is not given. Without N, the reported improvements (RMSE 33.281 vs 36.443) are hard to interpret; a small subset can make differences unstable. Please report the number of samples and, ideally, the sensitivity of the ranking to the threshold choice.
  4. [§4.4] The manuscript states that the goal is 'not to reproduce every method under its task-specific best-case setting.' This is a reasonable protocol, but it weakens the comparative claim unless the authors show that the unified protocol does not systematically disadvantage specific baselines. Please include a hyperparameter sensitivity analysis or use the baselines' official recommended settings for the 6→12 task; the current assertion that differences are 'more directly attributable to model design' is not demonstrated.
minor comments (4)
  1. [Abstract/§1] There are missing spaces between words throughout the text (e.g., 'sub-bandsandperforming', 'space,beforegenerating'); please run a text-cleaning pass.
  2. [§2.4] FlowCast and MeanFlow are discussed but no dedicated references are given; please add citations.
  3. [Figs. 3, 5] The panels are small; consider zoomed insets of the intense-core region to make visual differences legible.
  4. [§5.1, Tables 4–5] Tables 4 and 5 list QW-Net before QWRF-Net-A although §5.1 describes the variants in a different order; consider ordering consistently.

Circularity Check

0 steps flagged

No circular derivation: QWRF-Net's predictive claims are empirical, its loss is the standard rectified-flow objective, and no fitted parameter encodes the target results.

full rationale

The paper's derivation chain is not circular. The core training objective (Eq. 14) is the standard rectified-flow conditional velocity matching loss, with the interpolation state defined in Eq. 13 and inference via Euler integration of Eq. 15; these are standard formulations from the cited rectified-flow literature and are not constructed from the paper's own results. The wavelet–quantum bottleneck (Eqs. 3–12) is a fixed architectural transform with learnable parameters trained by the same loss; nothing in it is defined in terms of the KNMI/SEVIR test metrics. The extreme-event subset (Section 4.3) is defined by ground-truth VIL thresholds and used only for test-set evaluation, so the gains reported there are measurements, not fitted predictions. The ablations compare the full model against variants under the same protocol, and the paper itself restricts its claims (Section 6 limitations) to a 60-minute horizon, a classically simulated quantum module, and no downstream hydrological assessment. The Section 4.4 caveat that baselines are not run under their task-specific best-case settings is an evaluation-fairness threat, not a circularity: it questions comparability of the empirical deltas, but does not make those deltas equivalent to an input by construction. No self-citations are load-bearing; the related-work references are used for context and standard formulations. Consequently, there is no exhibitable spot where Eq. X reduces to Eq. Y by definition or where a fitted parameter is renamed as a prediction. The correct circularity verdict is 0.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 1 invented entities

The paper introduces a new architectural component (quantum-wavelet bottleneck) and several hand-chosen hyperparameters. The axioms are mostly standard math plus domain assumptions about wavelet scale separation and evaluation fairness. No new physical entities or forces are postulated.

free parameters (5)
  • Quantum circuit parameters theta = learned during training
    Rotation angles in the variational circuit (Eq. 8), fitted to the training data.
  • Projection matrices W_enc, b_enc = learned
    Map the GAP sub-band descriptor to qubit-aligned angular inputs (Eq. 6).
  • Number of qubits N = not specified
    Architectural hyperparameter of the quantum module; defaults unclear, affecting model capacity.
  • Euler integration steps = 50 at inference, 10 in training
    Sampling schedule for the rectified-flow ODE (Section 3.3); chosen by hand, not optimized.
  • Extreme-event thresholds = peak VIL >= 219, exceedance ratio >= 2%
    Post hoc definition of the SEVIR extreme subset (Section 4.3); affects which samples enter Table 3.
axioms (6)
  • standard math DWT/IDWT is an orthogonal, invertible transform that separates frequency sub-bands without loss
    Used in Eq. 3 and 12; standard signal processing.
  • standard math Rectified flow objective (Eq. 14) trains a velocity field that transports noise to data
    From Liu (2022); assumed for the decoder.
  • domain assumption Euler integration with 50 steps approximates the ODE solution well
    Inference uses 50 steps (Section 3.3); convergence not validated.
  • domain assumption Latent wavelet sub-bands correspond to physically meaningful precipitation scales
    Core premise of Section 3.2: LL=background, LH/HL/HH=structural details.
  • ad hoc to paper Sub-band-specific nonlinear modulation is more effective than shared or classical modulation
    No a priori theory; supported only by the ablation comparisons (Tables 4-5).
  • domain assumption The unified evaluation protocol is a fair basis for comparison
    Baseline hyperparameters are hand-adjusted; fairness is assumed (Section 4.4).
invented entities (1)
  • Quantum-wavelet bottleneck no independent evidence
    purpose: Decomposes latent features into wavelet sub-bands and applies sub-band-specific quantum-inspired modulation before reconstruction
    A new architectural module; its benefit is demonstrated only in the paper's own ablations, with no external validation or theoretical guarantee.

reviewed 2026-08-04 · how reviews work

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Cite this review

Pith. "Pith review of QWRF-Net: A Quantum-Wavelet Framework with Rectified Flow for Short-Term Precipitation Nowcasting." pith.science (2026). https://pith.science/paper/3XVX4UH2

@misc{pith2026260801626,
  author       = {Pith},
  title        = {Pith review of: QWRF-Net: A Quantum-Wavelet Framework with Rectified Flow for Short-Term Precipitation Nowcasting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3XVX4UH2}},
  note         = {Machine review of arXiv:2608.01626}
}
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read the original abstract

Short-term precipitation nowcasting is important for hydrometeorological early warning, especially when intense convective rainfall may trigger urban flooding, flash floods, and other high-impact hazards. A key challenge in warning-oriented nowcasting is that radar precipitation fields contain strongly coupled multi-scale structures, while forecast quality often degrades at later lead times, making it difficult to preserve intense precipitation cores and their spatial organization over the full warning-relevant horizon. To address this problem, we propose QWRF-Net, a quantum-wavelet framework with rectified flow for short-term precipitation nowcasting. The core idea is to improve the conditional representation of precipitation by explicitly decomposing latent features into wavelet sub-bands and then performing differentiated quantum-inspired modulation in the decomposed latent space, before generating future sequences through a rectified-flow-based non-autoregressive decoder. Experiments on the KNMI radar and SEVIR benchmarks under a unified evaluation protocol show that QWRF-Net achieves favorable overall performance, with relatively consistent gains at medium-to-high precipitation thresholds, on an extreme-event subset, and in preserving intense precipitation cores and fine-scale structures. Ablation results further indicate that wavelet-based scale disentanglement, differentiated sub-band modulation, and flow-based generation provide complementary benefits within the proposed framework. Overall, these results suggest that jointly enhancing multi-scale precipitation representation and stable multi-step generation is a promising direction for warning-oriented short-term precipitation nowcasting. The observed improvements may also provide a more useful precipitation basis for downstream hydrological and warning-related applications.

Figures

Figures reproduced from arXiv: 2608.01626 by Chaorong Li, Chuanhu Deng, Wenjie Luo, Zhuo Wang.

Figure 1
Figure 1. Figure 1: Overall architecture of QWRF-Net for radar-based nowcasting. Given the past 6 frames (30 minutes) as condition, the model generates the next 12 frames (60 minutes). The encoder extracts multi-scale features, the quantum–wavelet bottleneck refines scale-aware precipitation representation, and the flow-based decoder generates the future sequence through ODE-based sampling. rather than on the original mixed f… view at source ↗
Figure 2
Figure 2. Figure 2: Structure of the quantum–wavelet bottleneck. The bottleneck feature is decomposed into four wavelet sub-bands (LL, LH, HL, and HH) through DWT. Each sub-band is processed by an independent quantum-inspired transformation followed by pointwise projection and normalization. The transformed sub-bands are then fused through IDWT and residual fusion to form the output bottleneck representation. map, respectivel… view at source ↗
Figure 3
Figure 3. Figure 3: Visual comparison of QWRF-Net with representative methods on two benchmark datasets. (a) KNMI radar dataset. (b) SEVIR VIL dataset. In each panel, the first row shows the input sequence, the second row shows the ground truth, and the remaining rows show the predictions produced by different models from T+10 min to T+60 min. A sample is regarded as extreme if, over the 12-frame target stack, the peak VIL in… view at source ↗
Figure 4
Figure 4. Figure 4: Lead-time curves of CSI and HSS for different models on the KNMI dataset. CSI and HSS values across the reported thresholds, to￾gether with the lowest MAE and RMSE and the highest SSIM. Although the margins over the strongest baselines are moderate for some metrics, the gains are relatively consis￾tent across threshold-based verification and reconstruction￾oriented evaluation. From a hydrometeorological fo… view at source ↗
Figure 5
Figure 5. Figure 5: Visual comparison of QWRF-Net and its ablation variants on two benchmark datasets. (a) KNMI radar dataset. (b) SEVIR VIL dataset. In each panel, the first row shows the input sequence, the second row shows the ground truth, and the remaining rows show the predictions of the full model and different ablation variants from T+10 min to T+60 min. two benchmark datasets are shown in [PITH_FULL_IMAGE:figures/fu… view at source ↗

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Reference graph

Works this paper leans on

49 extracted references · 42 canonical work pages

  1. [1]

    S. I. Seneviratne, X. Zhang, M. Adnan, W. Badi, C. Dereczynski, A.D.Luca,S.Ghosh,I.Iskandar,J.Kossin,S.Lewis,etal.,Weather and climate extreme events in a changing climate, Climate change 2021: The physical science basis: Working group I contribution to thesixthassessmentreportoftheintergovernmentalpanelonclimate change (2021) 1513–1766

    work page 2021

  2. [2]

    Woo, Deep learning for precipitation nowcasting: A benchmark and a new model, Advances in neural information processing systems 30 (2017)

    X.Shi,Z.Gao,L.Lausen,H.Wang,D.-Y.Yeung,W.-k.Wong,W.-c. Woo, Deep learning for precipitation nowcasting: A benchmark and a new model, Advances in neural information processing systems 30 (2017)

    work page 2017

  3. [3]

    Barbero, P

    H.J.Fowler,G.Lenderink,A.F.Prein,S.Westra,R.P.Allan,N.Ban, R. Barbero, P. Berg, S. Blenkinsop, H. X. Do, et al., Anthropogenic intensification of short-duration rainfall extremes, Nature Reviews Earth & Environment 2 (2) (2021) 107–122

    work page 2021

  4. [4]

    Al-Yahyai, Y

    S. Al-Yahyai, Y. Charabi, A. Gastli, Review of the use of numerical weatherprediction(nwp)modelsforwindenergyassessment,Renew- able and Sustainable Energy Reviews 14 (9) (2010) 3192–3198

    work page 2010

  5. [5]

    thesis, University of Leeds (2025)

    J.A.Smith,Nowcastingconvectiveweather:Evaluation,development and application of techniques, Ph.D. thesis, University of Leeds (2025)

    work page 2025

  6. [6]

    Amini, M

    A. Amini, M. Dolatshahi, R. Kerachian, Adaptive precipitation now- casting using deep learning and ensemble modeling, Journal of Hy- drology 612 (2022) 128197

    work page 2022

  7. [7]

    D.Han,J.Im,Y.Shin,J.Lee,Keyfactorsforquantitativeprecipitation nowcasting using ground weather radar data based on deep learning, Geoscientific Model Development 16 (20) (2023) 5895–5914

    work page 2023

  8. [8]

    Prudden, S

    R. Prudden, S. Adams, D. Kangin, N. Robinson, S. Ravuri, S. Mo- hamed, A. Arribas, A review of radar-based nowcasting of precip- itation and applicable machine learning techniques, arXiv preprint arXiv:2005.04988 (2020)

    Pith/arXiv arXiv 2005

  9. [9]

    Cheng, Y

    Q. Cheng, Y. Su, Y. He, Y. Wu, F. Liu, Y. Rao, Y. Chao, K. Wang, Z. Liu, J. Liu, et al., Enhanced radar echo extrapolation for precipita- tion nowcasting quality using the convolutional kolmogorov–arnold networks, Journal of Hydrology (2025) 134134

    work page 2025

  10. [10]

    Wang et al.:Preprint submitted to ElsevierPage 15 of 16 QWRF-Net for short-term precipitation nowcasting

    Y.Zeng,J.Wu,Areviewofend-to-endprecipitationpredictionusing remote sensing data: from divination to machine learning, arXiv preprint arXiv:2510.22855 (2025). Wang et al.:Preprint submitted to ElsevierPage 15 of 16 QWRF-Net for short-term precipitation nowcasting

    work page arXiv 2025

  11. [11]

    Sokol, J

    Z. Sokol, J. Mejsnar, L. Pop, V. Bližňák, Probabilistic precipitation nowcasting based on an extrapolation of radar reflectivity and an ensemble approach, Atmospheric research 194 (2017) 245–257

    work page 2017

  12. [12]

    W. Li, X. Zhou, Precipitation nowcasting method based on spatial- temporal dual discriminators, in: Journal of Physics: Conference Series, Vol. 2816, IOP Publishing, 2024, p. 012038

    work page 2024

  13. [13]

    Asperti, F

    A. Asperti, F. Merizzi, A. Paparella, G. Pedrazzi, M. Angelinelli, S. Colamonaco, Precipitation nowcasting with generative diffusion models: A. asperti et al., Applied Intelligence 55 (3) (2025) 187

    work page 2025

  14. [14]

    Y. Ye, F. Gao, S. Zhang, C. Liu, Improving precipitation nowcasting via multiphysical parameter fusion in radar echo extrapolation, Jour- nal of Hydrology (2026) 134947

    work page 2026

  15. [15]

    J.-H.Ha,H.Lee,Adeeplearningmodelforprecipitationnowcasting using multiple optical flow algorithms, Weather and Forecasting 39 (1) (2024) 41–53

    work page 2024

  16. [16]

    M.Berenguer,D.Sempere-Torres,G.G.Pegram,Sbmcast–anensem- blenowcastingtechniquetoassesstheuncertaintyinrainfallforecasts by lagrangian extrapolation, Journal of Hydrology 404 (3-4) (2011) 226–240

    work page 2011

  17. [17]

    J. Li, L. Li, T. Zhang, H. Xing, Y. Shi, Z. Li, C. Wang, J. Liu, Flood forecasting based on radar precipitation nowcasting using u-net and its improved models, Journal of Hydrology 632 (2024) 130871

    work page 2024

  18. [18]

    M. Chen, Z. Li, S. Gao, M. Xue, J. J. Gourley, R. L. Kolar, Y. Hong, A flood predictability study for hurricane harvey with the crest-imap model using high-resolution quantitative precipitation forecasts and u-netdeeplearningprecipitationnowcasts,JournalofHydrology612 (2022) 128168

    work page 2022

  19. [19]

    T.T.Ngan,H.G.Son,M.Omar,N.T.Thang,N.L.Giang,T.M.Tuan, N. A. Tho, A hybrid of rainnet and genetic algorithm in nowcasting prediction, Earth Science Informatics 16 (4) (2023) 3885–3894

    work page 2023

  20. [20]

    Y. Liao, S. Lu, G. Yin, Short-term and imminent rainfall prediction model based on convlstm and smaat-unet, Sensors 24 (11) (2024) 3576

    work page 2024

  21. [21]

    Mihoc, V.-S

    A. Mihoc, V.-S. Ionescu, I.-G. Mircea, G. Czibula, E. Mihulet, T. Aspenes, Convsnow: a tailored conv-lstm architecture for weather nowcasting based on satellite imagery, Procedia Computer Science 225 (2023) 298–307

    work page 2023

  22. [22]

    X. Wang, H. Zhao, G. Zhang, Q. Guan, Y. Zhu, Spatiotemporal pre- dictivelearningforradar-basedprecipitationnowcasting,Atmosphere 15 (8) (2024) 914

    work page 2024

  23. [23]

    Z. Niu, W. Huang, S. Huang, Z. Wang, M. Mu, M. Yang, X. Han, H. Sun, Z. Huo, B. Qin, A data-driven regional model for skillful medium-range typhoon prediction, arXiv preprint arXiv:2603.15127 (2026)

    work page arXiv 2026

  24. [24]

    Ravuri, K

    S. Ravuri, K. Lenc, M. Willson, D. Kangin, R. Lam, P. Mirowski, M. Fitzsimons, M. Athanassiadou, S. Kashem, S. Madge, et al., Skilful precipitation nowcasting using deep generative models of radar, Nature 597 (7878) (2021) 672–677

    2021

  25. [25]

    Chirigati, Accurate short-term precipitation prediction, Nature Computational Science 1 (11) (2021) 709–709

    F. Chirigati, Accurate short-term precipitation prediction, Nature Computational Science 1 (11) (2021) 709–709

    work page 2021

  26. [26]

    Zhang, M

    Y. Zhang, M. Long, K. Chen, L. Xing, R. Jin, M. I. Jordan, J. Wang, Skilful nowcasting of extreme precipitation with nowcastnet, Nature 619 (7970) (2023) 526–532

    work page 2023

  27. [27]

    Z. Gao, X. Shi, B. Han, H. Wang, X. Jin, D. Maddix, Y. Zhu, M. Li, Y. B. Wang, Prediff: Precipitation nowcasting with latent diffusion models, Advances in Neural Information Processing Systems 36 (2023) 78621–78656

    work page 2023

  28. [28]

    D. Yu, X. Li, Y. Ye, B. Zhang, C. Luo, K. Dai, R. Wang, X. Chen, Diffcast: A unified framework via residual diffusion for precipitation nowcasting, in: Proceedings of the IEEE/CVF Conference on Com- puter Vision and Pattern Recognition, 2024, pp. 27758–27767

    work page 2024

  29. [29]

    J. Shi, B. Jin, J. Han, S. Gopalakrishnan, G. Narasimhan, Codicast: Conditional diffusion model for global weather prediction with un- certainty quantification, arXiv preprint arXiv:2409.05975 (2024)

    Pith/arXiv arXiv 2024

  30. [30]

    Richter, W

    T. Richter, W. Wang, A. Palma, F. J. Theis, Generative models of cell dynamics: from neural odes to flow matching, Communications Biology (2026)

    work page 2026

  31. [31]

    Othman, D

    G. Othman, D. Q. Zeebaree, The applications of discrete wavelet transform in image processing: A review, Journal of soft computing and data mining 1 (2) (2020) 31–43

    work page 2020

  32. [32]

    Liu, Rectified flow: A marginal preserving approach to optimal transport, arXiv preprint arXiv:2209.14577 (2022)

    Q. Liu, Rectified flow: A marginal preserving approach to optimal transport, arXiv preprint arXiv:2209.14577 (2022)

    Pith/arXiv arXiv 2022

  33. [33]

    L. Liu, X. Liang, Y.-P. Xu, Y. Guo, Q. J. Wang, H. Gu, Enhanced rainfallnowcastingoftropicalcyclonebyaninterpretabledeeplearn- ing model and its application in real-time flood forecasting, Journal of Hydrology 644 (2024) 131993

    work page 2024

  34. [34]

    Zheng, X

    J. Zheng, X. Zhang, Z. Qi, R. Qiu, D. Wang, H. Zhang, D. Yu, Multi-scale physics-informed transformer with spatio-temporal fea- ture adapter for extreme precipitation nowcasting, in: Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V. 2, 2025, pp. 4014–4025

    work page 2025

  35. [35]

    Bojinski, D

    S. Bojinski, D. Blaauboer, X. Calbet, E. De Coning, F. Debie, T. Montmerle, V. Nietosvaara, K. Norman, L. Bañón Peregrín, F. Schmid, et al., Towards nowcasting in europe in 2030, Meteoro- logical applications 30 (4) (2023) e2124

    work page 2030

  36. [36]

    Khalili Sadaghiani, B

    A. Khalili Sadaghiani, B. Forouzandeh, Image interpolation based on 2d-dwt and hdp-hmm, Pattern Analysis and Applications 25 (2) (2022) 361–377

    work page 2022

  37. [37]

    C. Shi, H. Xu, Y. Li, Y.-L. Wei, Y. Feng, Y. Zhang, D. Niu, Wavec2r: Wavelet-driven coarse-to-refined hierarchical learning for radar retrieval, in: Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 40, 2026, pp. 8951–8959

    work page 2026

  38. [38]

    Veillette, S

    M. Veillette, S. Samsi, C. Mattioli, Sevir: A storm event imagery dataset for deep learning applications in radar and satellite meteorol- ogy, Advances in neural information processing systems 33 (2020) 22009–22019

    work page 2020

  39. [39]

    Z. Yi, Y. Liang, H. Situ, Enhancing variational quantum circuit training: An improved neural network approach for barren plateau mitigation, Physica Scripta 100 (8) (2025) 086004

    work page 2025

  40. [40]

    Tabarraei, Variational quantum latent encoding for topology opti- mization, Engineering with Computers 41 (6) (2025) 4549–4573

    A. Tabarraei, Variational quantum latent encoding for topology opti- mization, Engineering with Computers 41 (6) (2025) 4549–4573

    work page 2025

  41. [41]

    Iovane, Quantum-inspired algorithms and perspectives for opti- mization, Electronics 14 (14) (2025) 2839

    G. Iovane, Quantum-inspired algorithms and perspectives for opti- mization, Electronics 14 (14) (2025) 2839

    work page 2025

  42. [42]

    Lipman, R

    Y. Lipman, R. T. Chen, H. Ben-Hamu, M. Nickel, M. Le, Flow matching for generative modeling, arXiv preprint arXiv:2210.02747 (2022)

    Pith/arXiv arXiv 2022

  43. [43]

    J. Dai, J. Yan, J. Yang, L. Luo, Straighten viscous rectified flow via noise optimization, in: Proceedings of the IEEE/CVF International Conference on Computer Vision, 2025, pp. 15005–15014

    work page 2025

  44. [44]

    A.Tong,N.Malkin,G.Huguet,Y.Zhang,J.Rector-Brooks,K.Fatras, G. Wolf, Y. Bengio, Conditional flow matching: Simulation-free dynamic optimal transport, arXiv preprint arXiv:2302.00482 2 (3) (2023)

    Pith/arXiv arXiv 2023

  45. [45]

    K.Mori,A.Christodoulou,Reviewofsustainabilityindicesandindi- cators: Towards a new city sustainability index (csi), Environmental impact assessment review 32 (1) (2012) 94–106

    work page 2012

  46. [46]

    Hyvärinen, A probabilistic derivation of heidke skill score, Weather and Forecasting 29 (1) (2014) 177–181

    O. Hyvärinen, A probabilistic derivation of heidke skill score, Weather and Forecasting 29 (1) (2014) 177–181

    work page 2014

  47. [47]

    M. A. Error, Mean absolute error, Retrieved September 19 (2016) (2016) 14

    work page 2016

  48. [48]

    T. O. Hodson, Root mean square error (rmse) or mean absolute error (mae): When to use them or not, Geoscientific Model Development Discussions 2022 (2022) 1–10

    work page 2022

  49. [49]

    Nilsson, T

    J. Nilsson, T. Akenine-Möller, Understanding ssim, arXiv preprint arXiv:2006.13846 (2020). Wang et al.:Preprint submitted to ElsevierPage 16 of 16

    Pith/arXiv arXiv 2006

This paper was first reviewed by deepseek-v4-flash on August 4, 2026.