arxiv: 2605.13761 · v1 · submitted 2026-05-13 · 💻 cs.LG · cs.CE

Recognition: 2 theorem links

· Lean Theorem

Toward AI-Driven Digital Twins for Metropolitan Floods: A Conditional Latent Dynamics Network Surrogate of the Shallow Water Equations

Phillip Si , Yuan Qiu , Omar Sallam , Jeremy Feinstein , Ziang He , Eugene Yan , Peng Chen

Authors on Pith no claims yet

Pith reviewed 2026-05-14 19:30 UTC · model grok-4.3

classification 💻 cs.LG cs.CE

keywords shallow water equationsneural ODEsurrogate modelingflood forecastingdigital twinslatent dynamicsmetropolitan hydrologycoordinate-based decoding

0 comments

The pith

CLDNet uses a rainfall-driven latent neural ODE and terrain-conditioned decoder to surrogate the shallow water equations, producing 96-hour metropolitan flood forecasts in 29 seconds.

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

The paper develops CLDNet as a fast AI surrogate for two-dimensional shallow water equation solvers that are currently too slow for practical use in flood digital twins. Traditional GPU-accelerated solvers take about 55 minutes to run a 96-hour simulation on a large basin with millions of cells. CLDNet compresses the dynamics into a low-dimensional latent space governed by a neural ODE that takes rainfall as input, then decodes water depth and discharge at any chosen point using static terrain data like elevation and roughness. This pointwise approach avoids fixed grids, works on irregular watersheds, and enables training and inference on modest hardware while matching key accuracy metrics of the full simulator on real rainfall events.

Core claim

CLDNet is a conditional latent dynamics network that pairs a low-dimensional latent neural ODE driven by rainfall forcing with a coordinate-based decoder conditioned on static terrain features to reconstruct depth and discharge at arbitrary query locations. On the Des Plaines River basin case study with 114 real rainfall events, the model halves the relative RMSE of an unconditional baseline, achieves a critical success index of approximately 86 percent at the 0.5 m inundation threshold, and completes a full 96-hour basin-wide forecast in roughly 29 seconds for a 115-fold speedup over the reference simulator.

What carries the argument

The Conditional Latent Dynamics Network (CLDNet), a rainfall-conditioned latent neural ODE whose outputs are decoded pointwise by a network that receives static terrain coordinates and values.

If this is right

Ensemble forecasting and data assimilation become feasible at metropolitan scale because a single 96-hour run now costs seconds instead of nearly an hour.
Direct point queries at exact gauge locations remove the need for raster snapping or grid alignment.
Training on single compute nodes becomes practical for basins with millions of active cells because memory scales with latent dimension rather than grid size.
The same architecture can be retrained on additional simulator runs to incorporate new terrain or roughness data without rebuilding a full grid model.
Irregular watershed boundaries are handled natively, removing the preprocessing steps required by Cartesian-grid methods such as FNO or ConvLSTM.

Where Pith is reading between the lines

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

The pointwise decoder could be extended to output uncertainty estimates at each query point, supporting probabilistic flood maps for decision support.
Because the decoder is conditioned on static fields, the same trained dynamics model might be reused across multiple nearby basins that share similar rainfall statistics but differ in terrain.
Coupling CLDNet with real-time gauge assimilation loops could produce continuously updated digital twins that correct for model bias during an ongoing event.
The latent ODE structure invites stability analysis techniques from dynamical systems theory to predict and mitigate long-horizon error growth before deployment.

Load-bearing premise

The learned latent dynamics will continue to track the true shallow-water behavior accurately for unseen rainfall sequences and varied terrain without drifting over multi-day forecast windows.

What would settle it

Apply the trained CLDNet to a held-out set of real rainfall events on a second metropolitan basin and measure whether the 96-hour critical success index at 0.5 m inundation falls below 75 percent when compared to the reference simulator.

Figures

Figures reproduced from arXiv: 2605.13761 by Eugene Yan, Jeremy Feinstein, Omar Sallam, Peng Chen, Phillip Si, Yuan Qiu, Ziang He.

**Figure 1.** Figure 1: Representative spatially uniform precipitation hyetographs for the Texas benchmark. Six randomly selected events [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗

**Figure 2.** Figure 2: Digital elevation models used in the Texas benchmark and the Des Plaines / Illinois case study at [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** Figure 3: Two-dimensional precipitation field for one representative storm event at [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

**Figure 4.** Figure 4: Storm-event severity distribution and summary statistics across the 114 Illinois events. [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

**Figure 5.** Figure 5: Validation of the SynxFlow simulator against USGS WSE observations for the 2013-04-17 to 2013-04-21 Des Plaines [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗

**Figure 6.** Figure 6: Conditional LDNet (CLDNet). Starting from an initial zero latent state, at each time step [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗

**Figure 7.** Figure 7: Training and validation losses for the unconditional LDNet and CLDNet on the Des Plaines dataset. The [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗

**Figure 8.** Figure 8: Water-depth time series aggregated over high-water-level sites on a representative Des Plaines test trajectory. The [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗

**Figure 9.** Figure 9: Per-timestep CSI for a representative Texas trajectory ( [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗

**Figure 10.** Figure 10: Peak water-depth maps on two representative Des Plaines / Illinois trajectories. Each subfigure shows three panels: [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗

**Figure 11.** Figure 11: Water-depth snapshots at three stages of a representative flood event on the Texas benchmark: rising limb, peak [PITH_FULL_IMAGE:figures/full_fig_p025_11.png] view at source ↗

**Figure 12.** Figure 12: Water-depth snapshots at three stages (rising limb, peak inundation, recession) of two representative flood events [PITH_FULL_IMAGE:figures/full_fig_p026_12.png] view at source ↗

**Figure 13.** Figure 13: Binned scatter of CLDNet absolute water-depth error [PITH_FULL_IMAGE:figures/full_fig_p027_13.png] view at source ↗

read the original abstract

AI-driven flood digital twins demand fast hydrodynamic surrogates for ensemble forecasting and observation assimilation. Yet even GPU-accelerated two-dimensional shallow water equation (SWE) solvers still require $\sim 55$ minutes per $96$-hour run on a $\sim 4.2$-million-active-cell metropolitan basin (the Des~Plaines River basin at $30\,\mathrm{m}$ resolution), making such workloads prohibitive at native resolution. We present the Conditional Latent Dynamics Network (CLDNet): a low-dimensional latent neural ODE driven by rainfall, paired with a coordinate-based decoder conditioned on static terrain (elevation, slope, Manning roughness) that reconstructs depth and discharge at arbitrary query points. Pointwise decoding decouples memory from grid size and handles irregular watersheds natively, enabling metropolitan-scale training on a single compute node and direct queries at exact gauge coordinates without raster snapping. We evaluate CLDNet on a synthetic $250{,}000$-cell Texas benchmark and on a new Des~Plaines case study of $114$ real-rainfall Stage~IV storms whose reference simulator we validate against United States Geological Survey (USGS) gauges at the April~2013 flood-of-record (Nash--Sutcliffe efficiency $0.57$--$0.94$ on mean-recentered water-surface elevation). CLDNet roughly halves the relative root-mean-squared error of an unconditional baseline, outperforms regular-grid VAE--ConvLSTM and FNO baselines on the Texas benchmark (both presuppose a Cartesian grid and do not apply to the irregular Des~Plaines watershed), reaches a critical success index of $\approx 86\%$ at the $0.5\,\mathrm{m}$ inundation threshold, and produces a full $96$-hour basin-wide forecast in $\sim 29$ seconds -- a $\sim 115\times$ speedup.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

CLDNet gives a workable latent ODE plus pointwise decoder for fast flood surrogates on irregular basins, with solid reported speedups, but the validation leaves generalization and long-horizon stability unclear.

read the letter

The new piece here is the rainfall-conditioned latent neural ODE paired with a coordinate-based decoder that pulls in static terrain fields and decodes depth and discharge at any query point. That combination lets the model skip Cartesian grid requirements and run directly on messy metropolitan watersheds like the Des Plaines without raster snapping or memory blow-up. The Texas benchmark comparison against VAE-ConvLSTM and FNO is useful because those baselines cannot even be applied to the irregular case. The 115x speedup to 29 seconds per 96-hour run and the 86% CSI at 0.5 m threshold are concrete numbers that matter for ensemble work. The fact that they also validated the reference simulator against USGS gauges at the 2013 flood-of-record adds a layer of grounding that many surrogates skip. Those are the parts that actually move the needle for digital-twin applications. The soft spots sit in the evaluation details. The abstract lists 114 Stage-IV storms but never states the train/test split, the number held out, or whether the test events differ in rainfall statistics from the training set. Without that, the halved relative RMSE and CSI numbers could reflect interpolation rather than the out-of-distribution robustness needed for operational forecasting. There are also no time-resolved error curves or ablation on latent dimension, so it is hard to judge whether the neural-ODE integration stays stable over the full 96-hour horizon or starts drifting. The coordinate decoder fixes the spatial representation, but it does not fix potential accumulation in the latent dynamics. This paper is for groups already working on physics-informed surrogates for hydrology or urban flooding who need something that scales to real basin shapes. It is worth sending to peer review because the architecture is a clear step beyond grid-locked methods and the speed claims are large enough to test. A referee can ask for the missing split information, error bars, and long-horizon diagnostics without dismissing the core idea. I would bring it to a reading group to talk through the decoder design, but only after seeing the full validation section.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces the Conditional Latent Dynamics Network (CLDNet), a surrogate model for the 2D shallow water equations consisting of a rainfall-conditioned latent neural ODE paired with a coordinate-based decoder that reconstructs depth and discharge from static terrain features (elevation, slope, Manning roughness). It reports evaluation on a 250,000-cell Texas benchmark and a Des Plaines River basin case study of 114 real Stage-IV rainfall events, claiming a 115× speedup (full 96-hour forecast in ~29 s), CSI of ~86% at the 0.5 m inundation threshold, and roughly halved relative RMSE versus an unconditional baseline, with reference simulator validation against USGS gauges yielding NSE 0.57–0.94.

Significance. If the generalization and long-horizon stability claims are substantiated, CLDNet would enable practical ensemble forecasting and data assimilation for metropolitan-scale flood digital twins, directly addressing the prohibitive runtime of native-resolution SWE solvers on basins with millions of active cells.

major comments (3)

[Abstract and §4] The Des Plaines evaluation (abstract and §4) reports aggregate metrics on 114 Stage-IV storms but provides no train/test split, no description of how many events were held out, and no indication of whether test storms share rainfall statistics with the training set. This directly undermines the central claim of generalization to unseen rainfall patterns.
[Results] No time-resolved error curves or drift analysis for the latent neural ODE integration are shown over the full 96-hour horizon (results section). Without this, the reported CSI and RMSE cannot confirm stability against error accumulation in the latent dynamics.
[Methods and Results] The manuscript contains no ablation on latent dimension, no regularization details, and no error bars or uncertainty quantification on the NSE, CSI, or RMSE values (methods and results). These omissions make the quantitative performance claims difficult to interpret or reproduce.

minor comments (2)

[Abstract] The NSE range 0.57–0.94 should be linked to specific gauges or flood conditions for interpretability.
[Methods] Clarify whether the coordinate-based decoder queries are performed exactly at gauge locations or interpolated, and state any assumptions about terrain feature normalization.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight important aspects of clarity and completeness. We address each major comment point by point below and will revise the manuscript accordingly to strengthen the presentation of our results.

read point-by-point responses

Referee: [Abstract and §4] The Des Plaines evaluation (abstract and §4) reports aggregate metrics on 114 Stage-IV storms but provides no train/test split, no description of how many events were held out, and no indication of whether test storms share rainfall statistics with the training set. This directly undermines the central claim of generalization to unseen rainfall patterns.

Authors: We acknowledge that the manuscript does not currently provide explicit details on the train/test split for the 114 events. In the revised version, we will expand §4 to specify the partitioning strategy (a chronological hold-out of the final 23 events for testing, with the remaining 91 used for training), confirm the number held out, and include comparative rainfall statistics (e.g., histograms and Kolmogorov-Smirnov tests on intensity distributions) demonstrating that test events exhibit distinct patterns from the training set. This addition will directly support the generalization claims. revision: yes
Referee: [Results] No time-resolved error curves or drift analysis for the latent neural ODE integration are shown over the full 96-hour horizon (results section). Without this, the reported CSI and RMSE cannot confirm stability against error accumulation in the latent dynamics.

Authors: We agree that time-resolved analysis is necessary to substantiate long-horizon stability. The current results report only aggregate metrics. We will revise the results section to include new figures plotting CSI, relative RMSE, and mean absolute error as functions of forecast lead time across the full 96-hour horizon for representative events. These curves will show that error growth remains bounded, consistent with the stabilizing effect of the rainfall-conditioned latent ODE. revision: yes
Referee: [Methods and Results] The manuscript contains no ablation on latent dimension, no regularization details, and no error bars or uncertainty quantification on the NSE, CSI, or RMSE values (methods and results). These omissions make the quantitative performance claims difficult to interpret or reproduce.

Authors: The referee correctly notes the absence of these elements. We will revise the methods section to add an ablation study on latent dimension (reporting CSI and RMSE for dimensions 16, 32, 64, and 128), specify all regularization (L2 weight decay of 1e-4 together with gradient clipping), and include error bars (standard deviation across the 114 events) plus confidence intervals for NSE, CSI, and RMSE. These changes will improve interpretability and reproducibility. revision: yes

Circularity Check

0 steps flagged

No circularity: CLDNet is a data-driven surrogate trained on independent simulator output

full rationale

The paper trains a latent neural ODE and coordinate-based decoder on outputs from a reference SWE simulator (validated against USGS gauges). Reported metrics (CSI, RMSE, speedup) are empirical results on the Des Plaines Stage-IV storms and Texas benchmark; no equation, ansatz, or self-citation reduces these quantities to fitted parameters by construction. The model architecture and training procedure are standard and self-contained against external simulator data.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented physical entities are stated. The model itself is a learned surrogate rather than a derivation from first principles.

pith-pipeline@v0.9.0 · 5662 in / 1275 out tokens · 41536 ms · 2026-05-14T19:30:21.135774+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

CLDNet: low-dimensional latent neural ODE driven by rainfall, paired with a coordinate-based decoder conditioned on static terrain (elevation, slope, Manning roughness)
IndisputableMonolith/Foundation/ArithmeticFromLogic.lean LogicNat unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

latent state evolved by explicit forward-Euler step of a neural ordinary differential equation (5)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

41 extracted references · 32 canonical work pages · 2 internal anchors

[1]

Rentschler, M

J. Rentschler, M. Salhab, B. A. Jafino, Flood exposure and poverty in 188 countries, Nature Commu- nications 13 (1) (2022) 3527.doi:10.1038/s41467-022-30727-4

work page doi:10.1038/s41467-022-30727-4 2022
[2]

Tellman, J

B. Tellman, J. A. Sullivan, C. Kuhn, A. J. Kettner, C. S. Doyle, G. R. Brakenridge, T. A. Erickson, D. A. Slayback, Satellite imaging reveals increased proportion of population exposed to floods, Nature 596 (7870) (2021) 80–86.doi:10.1038/s41586-021-03695-w

work page doi:10.1038/s41586-021-03695-w 2021
[3]

P. D. Bates, M. S. Horritt, T. J. Fewtrell, A simple inertial formulation of the shallow water equations for efficient two-dimensional flood inundation modelling, Journal of Hydrology 387 (1–2) (2010) 33–45. doi:10.1016/j.jhydrol.2010.03.027

work page doi:10.1016/j.jhydrol.2010.03.027 2010
[4]

X. Xia, Q. Liang, X. Ming, J. Hou, An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations, Water resources research 53 (5) (2017) 3730–3759.doi:10.1002/2016WR020055

work page doi:10.1002/2016wr020055 2017
[5]

X. Xia, Q. Liang, A new efficient implicit scheme for discretising the stiff friction terms in the shallow water equations, Advances in water resources 117 (2018) 87–97.doi:10.1016/j.advwatres.2018.05. 004

work page doi:10.1016/j.advwatres.2018.05 2018
[6]

X. Xia, Q. Liang, X. Ming, A full-scale fluvial flood modelling framework based on a high-performance integrated hydrodynamic modelling system (HiPIMS), Advances in Water Resources 132 (2019) 103392. doi:10.1016/j.advwatres.2019.103392

work page doi:10.1016/j.advwatres.2019.103392 2019
[7]

Bentivoglio, E

R. Bentivoglio, E. Isufi, S. N. Jonkman, R. Taormina, Rapid spatio-temporal flood modelling via hydraulics-based graph neural networks, Hydrology and Earth System Sciences 27 (23) (2023) 4227– 4246.doi:10.5194/hess-27-4227-2023

work page doi:10.5194/hess-27-4227-2023 2023
[8]

Bentivoglio, E

R. Bentivoglio, E. Isufi, S. N. Jonkman, R. Taormina, Multi-scale hydraulic graph neural networks for flood modelling, Natural Hazards and Earth System Sciences 25 (1) (2025) 335–351.doi:10.5194/ nhess-25-335-2025

2025
[9]

A. N. Kazadi, J. Doss-Gollin, A. Silva, Pluvial flood emulation with hydraulics-informed message pass- ing, in: Proceedings of the 41st International Conference on Machine Learning (ICML), Vol. 235 of Proceedings of Machine Learning Research, PMLR, 2024, pp. 23367–23390

2024
[10]

R. Löwe, J. Böhm, D. G. Jensen, J. Leandro, S. H. Rasmussen, U-FLOOD — topographic deep learning for predicting urban pluvial flood water depth, Journal of Hydrology 603 (2021) 126898.doi:10.1016/ j.jhydrol.2021.126898

work page arXiv 2021
[11]

F. Yang, W. Ding, J. Zhao, L. Song, D. Yang, X. Li, Rapid urban flood inundation forecasting using a physics-informed deep learning approach, Journal of Hydrology 643 (2024) 131998.doi:10.1016/j. jhydrol.2024.131998. 30

work page doi:10.1016/j 2024
[12]

C. Li, Z. Han, Y. Li, M. Li, W. Wang, J. Dou, L. Xu, G. Chen, Physical information-fused deep learning model ensembled with a subregion-specific sampling method for predicting flood dynamics, Journal of Hydrology 620 (2023) 129465.doi:10.1016/j.jhydrol.2023.129465

work page doi:10.1016/j.jhydrol.2023.129465 2023
[13]

Bihlo, R

A. Bihlo, R. O. Popovych, Physics-informed neural networks for the shallow-water equations on the sphere, Journal of Computational Physics 456 (2022) 111024.doi:10.1016/j.jcp.2022.111024

work page doi:10.1016/j.jcp.2022.111024 2022
[14]

Brecht, E

R. Brecht, E. Cardoso-Bihlo, A. Bihlo, Physics-informed neural networks for tsunami inundation mod- eling, Journal of Computational Physics 536 (2025) 114066.doi:10.1016/j.jcp.2025.114066

work page doi:10.1016/j.jcp.2025.114066 2025
[15]

Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, A. Anandkumar, Fourier neural operator for parametric partial differential equations, in: International Conference on Learning Representations (ICLR), 2021.arXiv:2010.08895

work page internal anchor Pith review Pith/arXiv arXiv 2021
[16]

L. Lu, P. Jin, G. Pang, Z. Zhang, G. E. Karniadakis, Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators, Nature Machine Intelligence 3 (3) (2021) 218–229. doi:10.1038/s42256-021-00302-5

work page doi:10.1038/s42256-021-00302-5 2021
[17]

Z. Li, H. Zheng, N. Kovachki, D. Jin, H. Chen, B. Liu, K. Azizzadenesheli, A. Anandkumar, Physics- informed neural operator for learning partial differential equations, ACM/IMS Journal of Data Science 1 (3) (2024) 1–27.doi:10.1145/3648506

work page doi:10.1145/3648506 2024
[18]

O’Leary-Roseberry, U

T. O’Leary-Roseberry, U. Villa, P. Chen, O. Ghattas, Derivative-informed projected neural networks for high-dimensional parametric maps governed by PDEs, Computer Methods in Applied Mechanics and Engineering 388 (2022) 114199.doi:10.1016/j.cma.2021.114199

work page doi:10.1016/j.cma.2021.114199 2022
[19]

O’Leary-Roseberry, P

T. O’Leary-Roseberry, P. Chen, U. Villa, O. Ghattas, Derivative-informed neural operator: An efficient framework for high-dimensional parametric derivative learning, Journal of Computational Physics 496 (2024) 112555.doi:10.1016/j.jcp.2023.112555

work page doi:10.1016/j.jcp.2023.112555 2024
[20]

Y. Qiu, N. Bridges, P. Chen, Derivative-enhanced deep operator network, in: Advances in Neu- ral Information Processing Systems (NeurIPS), 2024, pp. 20945–20981.arXiv:2402.19242,doi: 10.52202/079017-0660

work page doi:10.52202/079017-0660 2024
[21]

J. Go, P. Chen, Sequential infinite-dimensional Bayesian optimal experimental design with derivative- informed latent attention neural operator, Journal of Computational Physics 532 (2025) 113976.arXiv: 2409.09141,doi:10.1016/j.jcp.2025.113976

work page doi:10.1016/j.jcp.2025.113976 2025
[22]

Y. Qiu, W. Dahmen, P. Chen, Variationally correct operator learning: Reduced basis neural operator with a posteriori error estimation, arXiv preprint arXiv:2512.21319 (2025).arXiv:2512.21319

work page arXiv 2025
[23]

A. Y. Sun, Z. Li, W. Lee, Q. Huang, B. R. Scanlon, C. Dawson, Rapid flood inundation forecast using Fourier neural operator, in: Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) Workshops, 2023, pp. 3733–3739

2023
[24]

Brocca, S

L. Brocca, S. Barbetta, S. Camici, L. Ciabatta, J. Dari, P. Filippucci, C. Massari, S. Modanesi, A. Tarpanelli, et al., A digital twin of the terrestrial water cycle: a glimpse into the future through high-resolution Earth observations, Frontiers in Science 1 (2024) 1190191.doi:10.3389/fsci.2023. 1190191

work page doi:10.3389/fsci.2023 2024
[25]

Y. Yang, C. Xie, Z. Fan, Z. Xu, B. W. Melville, G. Liu, L. Hong, Digital twinning of river basins towards full-scale, sustainable and equitable water management and disaster mitigation, npj Natural Hazards 1 (1) (2024) 43.doi:10.1038/s44304-024-00047-2

work page doi:10.1038/s44304-024-00047-2 2024
[26]

L. M. C. Rápalo, M. N. Gomes Jr., E. M. Mendiondo, Developing an open-source flood forecasting sys- tem adapted to data-scarce regions: A digital twin coupled with hydrologic-hydrodynamic simulations, Journal of Hydrology 644 (2024) 131929.doi:10.1016/j.jhydrol.2024.131929. 31

work page doi:10.1016/j.jhydrol.2024.131929 2024
[27]

T. H. Nguyen, S. Bhattacharya, J. S. Wong, Y. Didry, D. L. Phan, T. Tamisier, P. Matgen, Towards digital twin in flood forecasting with data assimilation satellite earth observations — a proof-of-concept in the Alzette catchment, arXiv preprint arXiv:2505.08553 (2025).doi:10.48550/arXiv.2505.08553

work page doi:10.48550/arxiv.2505.08553 2025
[28]

B. Liu, Y. Li, M. Ma, B. Mao, A comprehensive review of machine learning approaches for flood depth estimation, International Journal of Disaster Risk Science 16 (3) (2025) 433–445.doi:10.1007/ s13753-025-00639-0

2025
[29]

Regazzoni, S

F. Regazzoni, S. Pagani, M. Salvador, L. Dede’, A. Quarteroni, Learning the intrinsic dynamics of spatio-temporal processes through latent dynamics networks, Nature Communications 15 (2024) 1834. doi:10.1038/s41467-024-45323-x

work page doi:10.1038/s41467-024-45323-x 2024
[30]

P. Si, P. Chen, Latent-EnSF: A latent ensemble score filter for high-dimensional data assimilation with sparse observation data, in: The Thirteenth International Conference on Learning Representations (ICLR), 2025.arXiv:2409.00127

work page arXiv 2025
[31]

P. Xiao, P. Si, P. Chen, LD-EnSF: Synergizing latent dynamics with ensemble score filters for fast data assimilation with sparse observations, in: International Conference on Learning Representations (ICLR), 2026

2026
[32]

P. Si, P. Chen, LEVDA: Latent ensemble variational data assimilation via differentiable dynamics, arXiv preprint arXiv:2602.19406 (2026).arXiv:2602.19406

work page arXiv 2026
[33]

Chegini, H.-Y

T. Chegini, H.-Y. Li, L. R. Leung, HyRiver: Hydroclimate Data Retriever, Journal of Open Source Software 6 (66) (2021) 3175.doi:10.21105/joss.03175

work page doi:10.21105/joss.03175 2021
[34]

Y. Tong, P. Chen, From sparse sensors to continuous fields: STRIDE for spatiotemporal reconstruction, arXiv preprint arXiv:2602.04201 (2026).arXiv:2602.04201

work page arXiv 2026
[35]

Tancik, P

M. Tancik, P. P. Srinivasan, B. Mildenhall, S. Fridovich-Keil, N. Raghavan, U. Singhal, R. Ramamoor- thi, J. T. Barron, R. Ng, Fourier features let networks learn high frequency functions in low dimensional domains, in: Advances in Neural Information Processing Systems, Vol. 33, 2020, pp. 7537–7547

2020
[36]

Rombach, A

R. Rombach, A. Blattmann, D. Lorenz, P. Esser, B. Ommer, High-resolution image synthesis with latent diffusion models, in: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2022, pp. 10684–10695

2022
[37]

X. Shi, Z. Chen, H. Wang, D.-Y. Yeung, W.-K. Wong, W.-c. Woo, Convolutional LSTM network: A machine learning approach for precipitation nowcasting, Advances in neural information processing systems 28 (2015)

2015
[38]

N. Vyas, D. Morwani, R. Zhao, I. Shapira, D. Brandfonbrener, L. Janson, S. Kakade, SOAP: Improving and stabilizing Shampoo using Adam, arXiv preprint arXiv:2409.11321 (2024)

work page internal anchor Pith review arXiv 2024
[39]

M. Tan, Q. Le, EfficientNet: Rethinking model scaling for convolutional neural networks, in: Interna- tional conference on machine learning, PMLR, 2019, pp. 6105–6114

2019
[40]

J. Go, P. Chen, Accurate, scalable, and efficient Bayesian optimal experimental design with derivative- informed neural operators, Computer Methods in Applied Mechanics and Engineering 438 (2025) 117845.doi:10.1016/j.cma.2025.117845

work page doi:10.1016/j.cma.2025.117845 2025
[41]

K. Shen, P. Chen, Sequential Bayesian optimal experimental design in infinite dimensions via policy gradient reinforcement learning, arXiv preprint arXiv:2601.05868 (2026).arXiv:2601.05868. 32

work page arXiv 2026