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Physics-Guided Flow-Map Matching for Precipitation Nowcasting

Shunya Nagashima, Takumi Bannai, Makoto Misaizu, Keisuke Maeda, Takahiro Ogawa, Miki Haseyama

arXiv:2609.37487v1cs.CVcs.LG

TL;DR

Precipitation nowcasting must forecast rare, intense convective structures, but deterministic predictors blur them and some generative approaches inherit that blur. PG-FMM conditions a flow-map generator on a frozen advection prior instead of adding it to the output. Across four radar benchmarks, it outperforms AlphaPre on 18 of 24 metrics, with the largest gains at heavy-rain thresholds.

  • Problem

    Nowcasting must predict where and how strongly convective cells develop, but their small-scale growth and decay are only partly predictable and pixel-loss predictors blur high-intensity cores.

    Source: §1 · pp. 1–2

  • Method

    PG-FMM conditions a flow-map generative head on the history and a frozen Lagrangian advection prior’s rollout, rather than adding the prior as a residual.

    Source: §1 · p. 3

  • Results

    PG-FMM outperforms AlphaPre on 18 of 24 metrics across four radar benchmarks, with the largest gains at heavy-rain thresholds.

    Source: §1 · p. 3, §6 · p. 14

  • Takeaways & Limitations

    The results show that separating predictable advection from uncertain small-scale detail can outperform AlphaPre across the evaluated benchmarks, especially at heavy-rain thresholds.

    Source: §6 · p. 14

    Results use single-seed training on 128×128 rasters under one protocol with lead times up to 100 minutes; broader probabilistic use requires explicit spread calibration.

    Source: §6 · p. 14

Abstract

from arXiv · show

Precipitation nowcasting, generating future radar fields from past observations, is critical for flood warning and disaster response. It is also a demanding benchmark for spatiotemporal generative modeling, with chaotic dynamics, heavy-tailed intensities, and rare high-intensity structures that matter most. Deterministic models minimize a pixel loss and are driven toward the conditional mean, which blurs exactly those structures, while generative models that add a stochastic residual on top of a deterministic backbone inherit the same blur. We propose Physics-Guided Flow-Map Matching (PG-FMM), a conditional flow-map model that decouples predictable advection from uncertain small-scale detail. A frozen Lagrangian advection prior transports the radar field and supplies an explicit motion forecast, and a flow-map generative head, conditioned on the past frames and the prior rollout rather than summed onto it, produces sharp stochastic detail in four sampling steps. The prior serves only as guidance, so the head replaces blurred structure instead of inheriting it. Extensive experiments on four radar benchmarks show that PG-FMM outperforms state-of-the-art methods on 18 of 24 metrics, with the largest gains at heavy-rain thresholds, where the critical success index improves by up to 58.9%. The project page can be found at https://neurogica.github.io/PG-FMM.

1 Introduction

Precipitation nowcasting must locate and characterize rare, intense convective cells, but deterministic forecasts blur them and existing generative approaches either inherit blur or can drift from storm tracks. PG-FMM conditions a flow-map generator on a frozen advection prior and outperforms AlphaPre on 18 of 24 metrics across four benchmarks, with its largest gains at heavy-rain thresholds.

1 Introduction

  • Nowcasting supports flood warning and disaster response, and useful forecasts must predict where and how strongly convective cells develop, not merely whether rain occurs.Forecast value is concentrated in rare high-intensity structures.Source: §1 · pp. 1–2
  • Deterministic predictors blur high-intensity cores because pixel-loss training drives them toward the conditional mean, while purely generative models can drift off the observed storm track.Existing generative methods anchored on deterministic backbones inherit their blur at long lead times.Source: §1 · pp. 2–3
  • A frozen Lagrangian advection prior supplies an explicit motion forecast, while a flow-map head conditions on the radar history and prior rollout rather than adding a residual.The head can replace blurred structure with sharper detail while exploiting the prior’s motion skill.Source: §1 · p. 3
  • PG-FMM outperforms AlphaPre on 18 of 24 metrics across four radar benchmarks, with its largest gains at heavy-rain thresholds.The reported margins are largest where mean-seeking methods fail.Source: §1 · p. 3

2 Related Work

Related work spans deterministic video predictors, stochastic generative models, flow-map transport, and physics-informed forecasting. The paper positions PG-FMM at their intersection: a few-step generative head conditioned on a frozen, explicit advection prior.

2.1 Video Prediction and Precipitation Nowcasting

  • Deterministic video predictors tend to blur sharp convective cells under conditional-mean objectives, while stochastic models address blur but residual-anchored forecasts inherit it and unanchored generators may drift.Examples include PhyDNet, AlphaPre, CasCast, and DiffCast.Source: §2.1 · p. 4

2.2 Flow Matching and Flow Maps

  • Flow-Map Matching learns a finite-time transport operator, producing samples in a few evaluations rather than integrating an instantaneous velocity field over many steps.The paper adopts this approach to make multi-member inference ensembles affordable; FlowCast applies conditional flow matching in latent space for nowcasting.Source: §2.2 · p. 4

2.3 Physics-Informed and Lagrangian Forecasting

  • Lagrangian advection explicitly transports radar fields but cannot represent growth or decay; PG-FMM uses a lightweight, pretrained, frozen warp-and-source prior as conditioning for its generative head.Earlier learning-based approaches include NowcastNet, PhyDNet, and LUPIN.Source: §2.3 · p. 5

3 Preliminaries

The paper formulates nowcasting as conditional prediction of future radar fields from a history of past frames. It reviews flow-map transport, whose finite-time operator supports sampling in a few jumps.

3.1 Problem Setting

  • Given Tin past single-channel reflectivity frames on an H × W grid normalized to [0, 1], the task predicts Tout future frames stacked along the channel axis.Horizon lengths, grid size, and intensity scale vary by dataset.Source: §3.1 · p. 5
  • Because convective growth and decay are only partly determined by recent history, the model represents a conditional future distribution and draws an ensemble rather than predicting one field.Evaluation emphasizes mean CSI and high-threshold CSI alongside HSS, SSIM, and MSE.Source: §3.1 · p. 5

3.2 Flow Matching and Flow Maps

  • Flow-Map Matching learns a two-time solution operator whose composition obeys a semigroup identity, enabling samples in a few jumps rather than many small integration steps.The flow-map head is trained to enforce composition consistency.Source: §3.2 · p. 6, Figure 2 · p. 6

4 Method

PG-FMM separates predictable radar advection from uncertain detail: a frozen physical prior guides a conditional flow-map head without being added to its output. The method combines a learned advection rollout, flow-map training, and few-step ensemble inference.

4.1 Overview

  • The prior conditions the generative head rather than being added to its output, letting the head replace blurred structure while exploiting the prior’s motion skill.The decoupling can pair any per-step motion model with any conditional generative head.Source: §4.1 · p. 7

4.2 Lagrangian Advection Prior

  • The frozen prior predicts dense velocity and source/sink fields, then uses a parameter-free semi-Lagrangian rollout to transport intensity and model growth or decay.Its rollout is trained before the generative head, and the prior receives no gradient during generative training or inference.Source: §4.2 · pp. 7–8

4.3 Flow-Map Matching Generative Head

  • The generative head maps an interpolant state directly to an earlier state, conditioned on radar history and the prior rollout, while composition consistency regularizes the map.The consistency term stabilizes training and improves fidelity in this setting.Source: §4.3 · pp. 8–9

4.4 Inference: Few-Step Sampling and Ensemble

  • Few-step flow-map sampling makes an ensemble affordable, and probability-matched averaging restores high-amplitude peaks that direct averaging would smooth away.The probability-matched mean uses the ensemble-mean spatial pattern and remaps its values to the pooled ensemble value distribution.Source: §4.4 · p. 9

5 Experiments

Across four radar benchmarks, PG-FMM generally outperforms AlphaPre, with the largest gains at heavy-rain thresholds. Experiments also compare forecast quality, lead-time behavior, and the contributions of the prior and generative head.

5.1 Datasets and Protocol

  • The evaluation covers SEVIR, MeteoNet, Shanghai, and CIKM using five past frames to predict 20 future frames, except for 10 on CIKM.Frames are resized to 128×128 and normalized to [0, 1], using each benchmark’s official splits and native intensity scales, thresholds, and evaluator.Source: §5.1 · pp. 9–10

5.2 Implementation Details

  • The prior is trained first and frozen before the flow-map head is trained; inference uses four sampling steps and a 16-member probability-matched-mean ensemble.The headline SEVIR head is trained for 297.6k steps; the ensemble requires 64 network evaluations per forecast.Source: §5.2 · p. 10

5.3 Baselines and Metrics

  • The study compares against deterministic and generative baselines under the AlphaPre protocol and reports detection, fidelity, and ensemble-probability metrics.CSI-M and high-threshold CSI are primary; CRPS is reported for the model and generative ablations, not the Tab. 1 baselines.Source: §5.3 · pp. 10–11

5.4 Main Results

  • PG-FMM beats AlphaPre on 18 of 24 benchmark metrics and is best on every metric on SEVIR and MeteoNet; its heaviest-threshold SEVIR CSI rises from 0.0582 to 0.0925 (58.9%).On Shanghai it leads on four of six metrics, and on CIKM it leads on both heavy-rain thresholds; the SEVIR CSI-M gap widens from +0.006 at +5 minutes to +0.028 at +100 minutes.Source: Table 1 · p. 11, §5.4 · pp. 11–12

5.5 Qualitative Results

  • On the Nebraska storm and Hurricane Barry cases, PG-FMM preserves heavy-rain cores that AlphaPre blurs; a north Texas failure shows PG-FMM can instead drop a heavy band.In the failure case, CSI-160 is 0.218 for PG-FMM versus 0.299 for AlphaPre; AlphaPre scores higher on 351 of 2,672 heavy-rain SEVIR samples (13.1%).Source: Figure 4 · p. 12, §5.5 · pp. 12–13, Figure 5 · p. 13

5.6 Ablation Study

  • With the same generative head and matched training budget, the physics prior leads on every metric except SSIM, while the frozen prior alone trails the full model on every skill metric.Classical advection trails even the no-prior variant on detection metrics; further studies report that conditioning is more robust to prior quality than additive residual fusion, and one N=4 draw reaches CSI-M 0.3394.Source: §5.6 · pp. 13–14

6 Conclusion

The conclusion presents PG-FMM as a way to separate predictable advection from uncertain detail, with the physical prior conditioning rather than being added to the forecast. It reports gains over AlphaPre across four benchmarks while noting calibration, training, and forecast-scope limitations.

6 Conclusion

  • Under a unified protocol on four radar benchmarks, PG-FMM surpasses AlphaPre on 18 of 24 metrics, with the largest margins at heavy-rain thresholds.Controlled ablations isolate contributions from the prior and generative head.Source: §6 · p. 14
  • The raw ensemble is under-dispersive, with a spread-to-RMSE ratio of about 0.43; probabilistic use beyond reported CRPS and Brier scores requires explicit spread calibration.Results also use single-seed training, 128×128 rasters, and lead times up to 100 minutes; advection-based forecasts can under-forecast initiation or re-intensification, under-carry heavy bands, or over-persist dissipating storms.Source: §6 · p. 14

A Skill versus Lead Time for the Prior Ablation

On SEVIR, the physics prior’s detection-skill margin emerges at longer lead times and is largest for heavy rain. The comparison uses matched flow-map heads and training conditions, varying only the prior rollout.

A Skill versus Lead Time for the Prior Ablation

  • The physics prior’s skill margin appears at longer lead times and is largest at the heavy-rain threshold VIL=181.Fig. 6 reports CSI averaged over thresholds and CSI at VIL=181.Source: Figure 6 · p. 19, A Skill versus Lead Time for the Prior… · p. 19
  • All four variants use the same flow-map head, conditioning, and matched training budget; only the prior rollout content differs.Evaluation uses a 16-member probability-matched mean and four sampling steps.Source: A Skill versus Lead Time for the Prior… · p. 19
  • At short lead times the physics prior is indistinguishable from alternatives, while the classical advection prior falls below the no-prior variant.The authors interpret this as evidence that a poor prior can mislead the generative head and that gains depend on prior content, not conditioning alone.Source: A Skill versus Lead Time for the Prior… · p. 19

B Spread–Skill Diagnostic and Sampling-Seed Variability

The SEVIR ensemble is under-dispersive, with spread below ensemble-mean error, while reported sampling-seed variability is negligible. Improving member-level dispersion remains future work.

B Spread–Skill Diagnostic and Sampling-Seed Variability

C Ensemble-Size and Sampling-Step Sweeps

On SEVIR, the sweeps identify 16 ensemble members and four sampling steps as accuracy–compute operating points. A representative failure case is selected systematically for the probabilistic-diagnostics discussion.

C Ensemble-Size and Sampling-Step Sweeps

E Probabilistic Diagnostics

  • The probabilistic-diagnostics discussion adds success and failure cases to a representative failure selected systematically rather than by hand.The additional cases appear in the following section.Source: E Probabilistic Diagnostics · p. 21

F Additional Qualitative Results

Additional cases show PG-FMM restoring heavy-rain structure smoothed by the advection prior, but also expose failures when storms dissipate or convection repeatedly regenerates. The supplementary analyses describe implementation choices, a consistency-term trade-off, and checks against area inflation of heavy-rain skill.

F Additional Qualitative Results

  • The learned prior’s velocity forms coherent advection and agrees with Farnebäck optical flow at cosine similarity 0.865; its source field is small and sparse.Mean |s| is 1.3% of its bound, and 5.6% of pixels exceed 0.01.Source: Figure 8 · p. 22
  • The additional SEVIR gallery includes two successes and a failure where PG-FMM maintains a compact storm after the observed storm dissipates, while AlphaPre correctly fades.The cases are drawn from a systematic per-sample CSI-160 ranking rather than hand-picked.Source: F Additional Qualitative Results · p. 21, Figure 10 · p. 23
  • On MeteoNet indices 1138 and 962, PG-FMM restores prior-smoothed 32–40 dBZ cells, with CSI-32 0.338 vs. prior 0.230 and 0.309 vs. 0.296; on index 460, it only partly restores heavy cells.In the failure, observed convection regenerates heavy cells that the prior never carries; initiation and re-intensification remain hard for advection.Source: F Additional Qualitative Results · pp. 22, 25, Figure 11 · p. 24

G Implementation Details

  • The implementation details group hyperparameters by module; the prior’s soft-CSI term relaxes threshold exceedance masks with a sigmoid, and the warp uses border padding.The sigmoid sharpness is α and the relaxation is computed on the dataset’s native intensity scale.Source: G Implementation Details · p. 25

H Composition-Consistency Ablation

  • Removing composition consistency slightly raises detection metrics but degrades every fidelity and calibration metric; it is retained for sharper, better-calibrated forecasts, not detection skill.The detection gap is small relative to the margins over prior work.Source: H Composition-Consistency Ablation · p. 25

I Structural Verification of the Heavy-Rain Gain

  • PG-FMM’s heavy-rain gains are not explained by area inflation: frequency bias is 0.35 and 0.21 at VIL=181 and 219, versus AlphaPre’s 0.23 and 0.10.PG-FMM also has the highest POD and FSS at every evaluated neighborhood scale; direct averaging of 16 samples falls back to AlphaPre’s level at heavy thresholds, unlike the probability-matched mean.Source: I Structural Verification of the… · p. 25

J Fusion Ablation: Conditioning versus Additive Residual

In a matched-ensemble comparison, PG-FMM remains ahead of FlowCast in detection and calibration while using fewer network evaluations. The fusion ablation finds conditioning robust to prior quality, while prior content determines skill.

J Fusion Ablation: Conditioning versus Additive Residual

  • With a blurred deterministic prior, only additive residual fusion degrades heavy-rain skill and calibration.The authors attribute this to the summed conditional-mean forecast re-imposing blur, whereas conditioning leaves the head free to replace it.Source: J Fusion Ablation: Conditioning versus… · p. 27
  • With the Lagrangian physics prior, conditioning and additive fusion perform comparably; conditioning is robust to prior quality, while prior content determines skill.The ablation does not claim a skill advantage for conditioning in isolation.Source: J Fusion Ablation: Conditioning versus… · p. 27

K Matched-Ensemble Comparison with a Generative Baseline

  • PG-FMM remains ahead of FlowCast in detection and calibration while using 2.5 times fewer network evaluations per member.Both methods use eight members and the same probability-matched mean and evaluator on an unselected subset of 512 test sequences.Source: Table 9 · p. 28, K Matched-Ensemble Comparison with a… · p. 28

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