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REVIEW 3 major objections 5 minor 51 references

This paper introduces a 2.4 TB benchmark for shock-driven compressible multiphase flows and shows that no single surrogate model wins across all datasets, while composite losses with interface- and structure-aware terms consistently improve

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2026-08-01 05:14 UTC pith:7QODXBRG

load-bearing objection The dataset and conservative downsampling are genuinely useful; the composite-loss comparisons are undermined by post-hoc selection of the training metrics. the 3 major comments →

arxiv 2607.22280 v2 pith:7QODXBRG submitted 2026-07-24 physics.flu-dyn cs.AI

Neptuna: A Comprehensive Machine Learning Framework for Benchmarking Complex Multiphase Flows

Harish Ramachandran , Bj\"orn Kimpel , Thomas Paula , Josef Winter , Steffen Schmidt , Nikolaus Adams This is my paper
classification physics.flu-dyn cs.AI
keywords compressible multiphase flowbenchmark datasetshock–bubble interactiondroplet breakupneural surrogatescomposite lossSoftAdaptspectral fidelity
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.

This paper sets out to give the scientific-machine-learning community the first large-scale benchmark built specifically for shock-driven compressible multiphase flows: 2.4 TB of 2D and 3D simulations of shock-induced bubble collapse and droplet breakup, spanning open and symmetry-wall boundary conditions. Trained across convolutional, spectral, transformer-based, and pre-trained surrogate families, the central empirical claim is that no single model wins on all datasets and metrics. The paper further argues that composite training objectives—pointwise MSE augmented with derivative, interface-focused, and structural-similarity terms—substantially improve interface preservation and spectral fidelity, and that among adaptive weighting schemes SoftAdapt delivers the most consistent gains at nearly no extra cost. A sympathetic reader would care because fast surrogates for these flows could relieve the cost of high-resolution simulation, and the public dataset gives a common ground for testing them.

Core claim

On the paper's own terms, the discovery is a negative result paired with a positive recipe: there is no architecture that dominates across shock–bubble and shock–droplet regimes, yet the training objective matters more than the architecture choice for the features that visual inspection cares about. Across six datasets, models trained with MSE alone reproduce the mean background flow (VRMSE below 1) but lose small-scale structure; augmenting with H1, SSIM and interface-weighted RMSE, with weights adjusted by SoftAdapt or GradNorm, cuts interface RMSE by 5–7% on bubble collapse and 40–50% on droplet breakup and improves wavelet-based spectral error and SSIM. SoftAdapt provides the most consis

What carries the argument

The central mechanism is the composite training objective built from four terms: MSE, H1-seminorm (first-derivative error), SSIM (local luminance/contrast/structure similarity), and IRMSE (error weighted by a soft mask around the density-derived interface), with per-term weights adapted during training by SoftAdapt (softmax-weighted recent loss slopes, no gradient storage). This objective counteracts the low-frequency bias of pure pointwise loss, and the benchmark measures its effects through autoregressive rollout evaluated by pointwise, wavelet-spectral, feature-focused, structure-aware, and physics-informed metrics.

Load-bearing premise

The gains claimed for composite losses depend on the loss terms and initial weights not being tuned on the same test distributions used to report the gains; the paper discloses in its limitations that the metrics were selected after observing which ones correlated positively, so a selection artifact could explain part of the improvement.

What would settle it

Run the same six datasets with the composite terms and initial weights fixed before any evaluation (no metric cherry-picking), compare MSE-only against SoftAdapt-trained models on a held-out set, and check whether IRMSE, MLW, and SSIM gains persist. If the improvements shrink or reverse, the benchmark's headline advantage is tied to the selection procedure, not to composite losses per se.

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

If this is right

  • If composite losses generalize as claimed, practitioners should not treat MSE as sufficient for shock-driven multiphase surrogates; adding derivative, interface, and structure terms is a cheap way to recover fine-scale fidelity.
  • Because no architecture wins everywhere, model selection must be regime- and metric-dependent: spectral operator models suit post-collapse dynamics where interfaces dissolve, while convolutional models hold a slight edge where coherent interfaces persist.
  • SoftAdapt's consistency suggests adaptive balancing can be adopted almost for free, whereas GradNorm's roughly 5–10% memory overhead buys gains only on selected configurations.
  • Conditioning matters: the pre-trained model with explicit conditioning/history windows leads; the one without underperforms despite its size, implying benchmark results depend on how simulation parameters are fed into the model.
  • The release of 2.4 TB of high-fidelity trajectories with conservative downsampling supports reproducible comparisons and gives the community a testbed for next-generation surrogates.

Where Pith is reading between the lines

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

  • (editorial inference) If the reported gains come from countering MSE's spectral bias, then losses acting directly on wavelet bands or vorticity may push further on the unresolved secondary droplets that the paper flags as a remaining gap.
  • (editorial inference) The benchmark's design—mixing two breakup regimes in one dataset—invites a test of whether surrogates can infer regime switches from conditioning; inspecting predictions near the Weber-number transition would be a natural next step the paper does not take.
  • (editorial inference) The conservative-downsampling result implies that earlier or future datasets that average primitive fields may embed O(10) momentum errors at interfaces; users of such datasets should verify conservation before attributing model errors to architecture.
  • (editorial inference) SoftAdapt's near-zero overhead and consistency suggest it could transfer to other PDE surrogate tasks, but the evidence here only supports this within the six studied flow configurations.

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

3 major / 5 minor

Summary. The paper introduces Neptuna, a benchmarking framework and dataset collection for shock-driven compressible multiphase flows, comprising six datasets (2D/3D bubble collapse and droplet breakup) with about 2.4 TB of high-fidelity simulation data generated with the ALPACA solver. It benchmarks six 2D baselines (ConvNeXt, CNO, FFNO, ScOT, DPOT-M, Poseidon-B) and two 3D baselines (ConvNeXt, FFNO), each trained with MSE alone and with a composite loss (MSE + H1 + SSIM + IRMSE) balanced by SoftAdapt or GradNorm. Evaluation covers pointwise, spectral, feature-focused, structure-aware, and physics-informed metrics. The main claims are that no single surrogate dominates across all datasets and metrics, that composite losses significantly improve interface preservation and spectral fidelity, and that SoftAdapt provides the most consistent improvements with negligible overhead. The paper also contributes a conservative downsampling method for multiphase data, detailed physics validation against external references, and a public benchmark repository and dataset.

Significance. If the benchmark is used as released, the datasets and conservative downsampling procedure are concrete, reusable contributions to the scientific-ML community; the physics validation against established references (Nourgaliev et al., Bempedelis and Ventikos, Meng and Colonius) strengthens trust in the data. The finding that no single architecture wins across all metrics is a useful calibration result. However, the headline loss-strategy claim currently rests on a post-hoc selection of the composite-loss terms that is disclosed but not quantified, and the aggregate tables lack uncertainty intervals and significance tests. These issues are fixable within the scope of the manuscript, but they must be addressed before the causal claim 'composite losses significantly improve...' can be accepted as stated.

major comments (3)
  1. [5.2 (Limitations)] The paper discloses that the composite loss terms H1, SSIM, and IRMSE "were obtained after analyzing results from a broad list of experiments and selectively picking the metric... when a positive correlation is obtained on the said metric or a diverse set of metrics during evaluation." It does not state whether this selection used the same test trajectories and metrics that appear in Tables 22-51, nor how many configurations were tried, nor whether any subset of the data was held out and untouched until final evaluation. Because the headline claim of improved interface preservation and spectral fidelity is based on exactly the metrics included in the training objective, the reported effect sizes may be selection artifacts. Please specify the selection protocol (e.g., a disjoint validation split) or re-run a nested evaluation that accounts for selection, or downgrade the causal claim acco
  2. [Tables 22-51 and Section 5.1] The aggregate tables report only scalar averages over trajectories and rollout steps, with no confidence intervals or significance tests. The papers' checklist points to Section C.2 for error bars, but those plots show trajectory variability bands, not uncertainty on the aggregated metrics used to support the "5-7%", "40-50%", and "consistent improvement" claims. The tables themselves contain counterexamples to "consistent": e.g., Table 24 shows ScOT IRMSE worsens from 0.9836 (MSE) to 1.0547 (SA), and Table 34 shows DPOT-M IRMSE worsens from 0.1522 (MSE) to 0.4103 (GN). A per-baseline win/loss/ite summary or a significance test is needed to support the consistency claim.
  3. [Section 5.1, Tables 25/30/35/40/45/50] SSIM is both a composite training term and a headline evaluation metric. The paper itself notes the SSIM improvement "may be partly attributed to the inclusion of SSIM as one of the terms in the composite training objective." This makes the SSIM result partially expected rather than independent evidence of better structure fidelity. Metrics not included in the training objective, such as SRMSE, wfRMSE, and iqRMSE, show mixed or negligible gains across the tables (e.g., Table 24 SRMSE is roughly flat or worse for several baselines). The paper should either weight non-training metrics in the headline comparison or explicitly frame the result as "training on these metrics improves the same metrics at inference" rather than as a general structure-fidelity improvement.
minor comments (5)
  1. [Section 3.3 / Figure 7] Typo: "Collaspe" should be "Collapse" in the section title and figure caption.
  2. [Section B.4.1] Typo: "Varience" should be "Variance" in the metric description.
  3. [Table 2] The end-time for 2D-SDBA is rendered as "91 - 1240" which is unclear; a unit or a range explanation would help.
  4. [Section B.2, Table 11] Typo in the row label: "Train time" appears as "Train timetime-restricted".
  5. [Section 5.1] Poseidon-B is excluded from the discussion with an explanation, but the radar charts still show it; this may confuse readers. Consider adding a footnote or explicit legend statement.

Circularity Check

1 steps flagged

Composite-loss improvement claims are partly selected on evaluation; the dataset and model-ranking results are self-contained.

specific steps
  1. fitted input called prediction [Section 5.2 (Limitations and Future Work); cf. Section 1 and Tables 12-13]
    "The training metrics selected in this work for the composite losses were obtained after analyzing results from a broad list of experiments and selectively picking the metric to be included in the composite train loss only when a positive correlation is obtained on the said metric or a diverse set of metrics during evaluation."

    The abstract's central loss claim ('composite losses significantly improve interface preservation and spectral fidelity') is certified using the same evaluation that was used to choose the composite terms (H1, SSIM, IRMSE, with MLW as a 'diverse' metric). The paper does not disclose a separate validation split, the number of configurations tried, or any hold-out that was untouched until final evaluation. Therefore the reported improvements on the selected metrics are not independent confirmations; they are the selection criterion itself. This affects only the loss-ablation claim: the benchmark data, model rankings, and the 'no single model best' conclusion remain externally supported by held-out test trajectories and references.

full rationale

The dataset generation is self-contained and externally validated: ALPACA/RDEMIC results are checked against Nourgaliev et al. (2006), Bempedelis & Ventikos (2020), and Meng & Colonius (2018), and the benchmark evaluations use held-out test trajectories with fixed metrics. No load-bearing self-citation chain or uniqueness import is present. The only circular component is the composite-loss ablation: H1, SSIM, and IRMSE appear both as training loss terms and as evaluation metrics, and Section 5.2 discloses that these terms were selected only after observing positive correlation during evaluation. Since no selection-on-validation protocol is reported, the headline improvements on those metrics are partly a post-hoc selection artifact. I therefore assign 4, not higher, because the dataset contribution, the per-metric tables, and the broader empirical comparisons retain independent content beyond the selected loss terms.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

The central claims rest on an empirical pipeline: solver fidelity, manually chosen loss and metric parameters, and post-hoc selection of composite-loss terms. These are enumerated above.

free parameters (5)
  • Initial composite loss weights (lambda_MSE, lambda_H1, lambda_SSIM, lambda_IRMSE) = 1.0, 2.0, 0.5, 1.0
    Table 12; hand-chosen defaults. The composite-loss results depend on these weights and no sensitivity analysis is reported.
  • IRMSE density threshold ranges and softness = SABW/SDBA: 350-550; SRBA: 4.5-8.5; softness 0.05; blur sigma 3.0
    Table 14; chosen per dataset to define the interface mask. These thresholds determine both the training objective and the evaluation metric, so interface-improvement claims are conditioned on this choice.
  • SoftAdapt temperature (beta) = 1.0
    Table 20; hand-selected. Controls how aggressively weights shift toward slow-improving losses.
  • GradNorm asymmetry (alpha) and loss-weight learning rate = 1.0; 0.001
    Table 21; hand-selected. Control GradNorm behavior and update magnitude.
  • wfRMSE level weights = (1,0,0)/(0,1,0)/(0,0,1)
    Table 17; define high/mid/low frequency binning used in inference metrics.
axioms (4)
  • domain assumption ALPACA with RDEMIC accurately solves the compressible Euler equations with stiffened-gas EOS for the simulated configurations.
    Used to generate all ground-truth data (Sections A.2-A.3). Validation is against two reference cases and one droplet COM trend, not against experiments across the full random parameter range.
  • ad hoc to paper The fixed density-threshold interface definition identifies physical phase boundaries in all trajectories.
    IRMSE uses thresholds from Table 14 for all trajectories; the same threshold is used as training objective and evaluation metric, so interface-preservation claims depend on this definition.
  • domain assumption Conservative downsampling preserves the information needed for surrogate training.
    Section A.4 demonstrates conservation on one 2D-SDBA trajectory; generalization to all datasets and 3D is assumed.
  • domain assumption The chosen evaluation metrics sufficiently capture surrogate reliability.
    Section B.4 lists the metrics; Section 5.2 admits none of the models recovers small secondary droplets, indicating the metrics underweight a defining feature of the SIE regime.

pith-pipeline@v1.3.0-alltime-deepseek · 59801 in / 13974 out tokens · 113435 ms · 2026-08-01T05:14:10.587007+00:00 · methodology

0 comments
read the original abstract

Compressible multiphase flows involving shocks and material interfaces arise in applications such as bubble collapse and droplet breakup, where strong nonlinear interactions produce complex interface deformation, mixing, and multiscale dynamics. Developing reliable machine learning surrogates for these flows remains challenging due to the simultaneous presence of compressibility, sharp discontinuities, and multiphase effects. In this work, we introduce the first large-scale benchmark specifically designed for shock-driven compressible multiphase flows, comprising 2.4 TB of high-fidelity 2D and 3D datasets featuring shock-induced bubble collapse and droplet breakup. We evaluate diverse surrogate model families on our benchmarking framework: Neptuna {https://github.com/tumaer/Neptuna}, including convolutional, spectral, transformer-based, and pre-trained PDE foundation models. Beyond standard MSE training, we investigate composite losses combining MSE with Sobolev, interface-aware, and structure-aware terms, together with adaptive loss balancing using SoftAdapt and GradNorm. Evaluation includes pointwise, spectral, feature-focused, structural, and physics-informed metrics. Results show that no single model performs best across all datasets and metrics, while composite losses significantly improve interface preservation and spectral fidelity. Among adaptive weighting strategies, SoftAdapt provides the most consistent improvements with almost no overhead compared to MSE-only training.

Figures

Figures reproduced from arXiv: 2607.22280 by Bj\"orn Kimpel, Harish Ramachandran, Josef Winter, Nikolaus Adams, Steffen Schmidt, Thomas Paula.

Figure 1
Figure 1. Figure 1: Dataset overview summarizing the provided datasets by dimensionality, boundary con [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic of the dataset generation setup. The full simulation domain is outlined in black, [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Uniformly spaced time snapshots of 2D-SABW at shock Mach number 1.70, with open [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Uniformly spaced time snapshots of 2D-SABW at shock Mach number 1.70, with [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Uniformly spaced time snapshots of 2D-SDBA at shock Mach number 2.0, with all droplets [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Uniformly spaced time snapshots of 2D-SDBA at shock Mach number 2.0, with all droplets [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Uniformly spaced time snapshots of 2D-SRBA at shock Mach number 1.70, with open [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Radar plot showcasing MSE-trained baselines across six datasets on five inference metrics [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Radar plot showcasing baselines trained with composite loss and SA loss-weighting across [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Radar plot showcasing baselines trained with composite loss and GN loss-weighting across [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Time evolution of density field for the 2D-SBAW-OOOO dataset. [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Single air bubble in water setup. The parameter details are presented in Table 3. The shock [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Comparing evolution of rate of change of volume with time for the single air bubble in [PITH_FULL_IMAGE:figures/full_fig_p019_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Three staggered air bubble in water setup. The parameter details are presented in Table [PITH_FULL_IMAGE:figures/full_fig_p019_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Peak pressure variation with time for the staggered three air bubble in water. The resolution [PITH_FULL_IMAGE:figures/full_fig_p020_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Uniformly spaced time snapshots of Shock-induced Air Bubble collapse in Water (SABW) [PITH_FULL_IMAGE:figures/full_fig_p021_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Uniformly spaced time snapshots of Shock-induced Air Bubble collapse in Water (SABW) [PITH_FULL_IMAGE:figures/full_fig_p022_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Uniformly spaced time snapshots of a 3D shock-induced air bubble collapse in water [PITH_FULL_IMAGE:figures/full_fig_p023_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Center-of-mass displacement in x-axis when a 4-mm droplet interacts with a shockwave [PITH_FULL_IMAGE:figures/full_fig_p025_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Uniformly spaced time snapshots of Shock-induced Droplet Breakup in Air (SDBA) at [PITH_FULL_IMAGE:figures/full_fig_p026_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Uniformly spaced time snapshots of Shock-induced Droplet Breakup in Air (SDBA) at [PITH_FULL_IMAGE:figures/full_fig_p027_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Uniformly spaced time snapshots of a 3D shock-induced droplet breakup in air (SDBA) at [PITH_FULL_IMAGE:figures/full_fig_p028_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Schlieren images showing the evolution of the interaction of shock with R22 bubble in air [PITH_FULL_IMAGE:figures/full_fig_p029_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Uniformly spaced time snapshots of Shock-induced R22 Bubble collapse in Water (SABW) [PITH_FULL_IMAGE:figures/full_fig_p030_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Comparison of mass, momentum and energy in the original grid [512x512] and downsam [PITH_FULL_IMAGE:figures/full_fig_p034_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: (a) y-momentum at the original resolution [512x512], (b) y-momentum at the downsampled [PITH_FULL_IMAGE:figures/full_fig_p035_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Illustration of the AdaNorm conditioning module, applicable to all baselines. [PITH_FULL_IMAGE:figures/full_fig_p038_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: H1 semi-norm metric. introduce discontinuities in the loss, a soft interface mask is constructed using sigmoid transitions around the density bounds ρmin and ρmax, which maintains differentiability: m = σ  ρ − ρmin s  σ  ρmax − ρ s  , (34) where s controls the softness of the transition [PITH_FULL_IMAGE:figures/full_fig_p042_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: IRMSE metric [PITH_FULL_IMAGE:figures/full_fig_p042_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: SRMSE metric [PITH_FULL_IMAGE:figures/full_fig_p043_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: Conceptual illustration of the DWT, recursively decomposing an input [PITH_FULL_IMAGE:figures/full_fig_p044_31.png] view at source ↗
Figure 32
Figure 32. Figure 32: Multilevel wavelet loss (MLW) metric. For each wavelet level i, the wfRMSE of the detail coefficients is computed as RMSEi = q HFi(ˆy) − HFi(y) 2 . (43) The total wavelet frequency-binned RMSE is defined as a weighted sum over scales, LwfRMSE = X i αi RMSEi , (44) where the weights αi control the relative contribution of different frequency bands. By adjusting αi , the metric can be tuned to prioritize s… view at source ↗
Figure 33
Figure 33. Figure 33: SSIM metric. The hyperparameters used for the SSIM metric are provided in [PITH_FULL_IMAGE:figures/full_fig_p046_33.png] view at source ↗
Figure 34
Figure 34. Figure 34: iqRMSE metric. B.5 Adaptive loss balancing framework Given a set of M loss components: {Li}M i=1, the scalar training objective is written as J (θ) = X M i=1 λiLi(θ), λi > 0, (53) where λi denotes the weight assigned to loss component i. A generalized loss-balancing framework is illustrated in [PITH_FULL_IMAGE:figures/full_fig_p047_34.png] view at source ↗
Figure 35
Figure 35. Figure 35: Conceptual illustration of the loss balancing framework. [PITH_FULL_IMAGE:figures/full_fig_p048_35.png] view at source ↗
Figure 36
Figure 36. Figure 36: (a) Reference density snapshot for a randomly chosen 2D-SDBA dataset at t=70 s. (b) [PITH_FULL_IMAGE:figures/full_fig_p050_36.png] view at source ↗
Figure 37
Figure 37. Figure 37: Peak GPU memory allocation during training [PITH_FULL_IMAGE:figures/full_fig_p051_37.png] view at source ↗
Figure 38
Figure 38. Figure 38: Epoch duration 51 [PITH_FULL_IMAGE:figures/full_fig_p051_38.png] view at source ↗
Figure 39
Figure 39. Figure 39: Pointwise evaluation of baselines on the 2D-SABW (OOOO) test dataset, reporting errors [PITH_FULL_IMAGE:figures/full_fig_p052_39.png] view at source ↗
Figure 40
Figure 40. Figure 40: Wavelet based spectral metrics for the 2D-SABW (OOOO) test dataset, averaged across [PITH_FULL_IMAGE:figures/full_fig_p053_40.png] view at source ↗
Figure 41
Figure 41. Figure 41: Feature focused metrics for capturing interface (IRMSE) and shocks (SRMSE) on the [PITH_FULL_IMAGE:figures/full_fig_p054_41.png] view at source ↗
Figure 42
Figure 42. Figure 42: Structure-aware metrics for the 2D-SABW (OOOO) test dataset, averaged across all fields [PITH_FULL_IMAGE:figures/full_fig_p054_42.png] view at source ↗
Figure 43
Figure 43. Figure 43: Physics-informed metrics reporting the nRMSE of integral quantities of interest on the [PITH_FULL_IMAGE:figures/full_fig_p055_43.png] view at source ↗
Figure 44
Figure 44. Figure 44: Pointwise evaluation of baselines on the 2D-SABW (SSOO) test dataset, reporting errors [PITH_FULL_IMAGE:figures/full_fig_p056_44.png] view at source ↗
Figure 45
Figure 45. Figure 45: Wavelet based spectral metrics for the 2D-SABW (SSOO) test dataset, averaged across all [PITH_FULL_IMAGE:figures/full_fig_p057_45.png] view at source ↗
Figure 46
Figure 46. Figure 46: Feature focused metrics for capturing interface (IRMSE) and shocks (SRMSE) on the [PITH_FULL_IMAGE:figures/full_fig_p058_46.png] view at source ↗
Figure 47
Figure 47. Figure 47: Structure-aware metrics for the 2D-SABW (SSOO) test dataset, averaged across all fields [PITH_FULL_IMAGE:figures/full_fig_p058_47.png] view at source ↗
Figure 48
Figure 48. Figure 48: Physics-informed metrics reporting the nRMSE of integral quantities of interest on the [PITH_FULL_IMAGE:figures/full_fig_p059_48.png] view at source ↗
Figure 49
Figure 49. Figure 49: Pointwise evaluation of baselines on the 2D-SRBA (OOOO) test dataset, reporting errors [PITH_FULL_IMAGE:figures/full_fig_p060_49.png] view at source ↗
Figure 50
Figure 50. Figure 50: Wavelet based spectral metrics for the 2D-SRBA (OOOO) test dataset, averaged across all [PITH_FULL_IMAGE:figures/full_fig_p061_50.png] view at source ↗
Figure 51
Figure 51. Figure 51: Feature focused metrics for capturing interface (IRMSE) and shocks (SRMSE) on the [PITH_FULL_IMAGE:figures/full_fig_p062_51.png] view at source ↗
Figure 52
Figure 52. Figure 52: Structure-aware metrics for the 2D-SRBA (OOOO) test dataset, averaged across all fields [PITH_FULL_IMAGE:figures/full_fig_p062_52.png] view at source ↗
Figure 53
Figure 53. Figure 53: Physics-informed metrics reporting the nRMSE of integral quantities of interest on the [PITH_FULL_IMAGE:figures/full_fig_p063_53.png] view at source ↗
Figure 54
Figure 54. Figure 54: Pointwise evaluation of baselines on the 2D-SDBA (SSOO) test dataset, reporting errors [PITH_FULL_IMAGE:figures/full_fig_p064_54.png] view at source ↗
Figure 55
Figure 55. Figure 55: Wavelet based spectral metrics for the 2D-SDBA (SSOO) test dataset, averaged across all [PITH_FULL_IMAGE:figures/full_fig_p065_55.png] view at source ↗
Figure 56
Figure 56. Figure 56: Feature focused metrics for capturing interface (IRMSE) and shocks (SRMSE) on the [PITH_FULL_IMAGE:figures/full_fig_p066_56.png] view at source ↗
Figure 57
Figure 57. Figure 57: Structure-aware metrics for the 2D-SDBA (SSOO) test dataset, averaged across all fields [PITH_FULL_IMAGE:figures/full_fig_p066_57.png] view at source ↗
Figure 58
Figure 58. Figure 58: Physics-informed metrics reporting the nRMSE of integral quantities of interest on the [PITH_FULL_IMAGE:figures/full_fig_p067_58.png] view at source ↗
Figure 59
Figure 59. Figure 59: Pointwise evaluation of baselines on the 3D-SABW (SSOOSS) test dataset, reporting [PITH_FULL_IMAGE:figures/full_fig_p068_59.png] view at source ↗
Figure 60
Figure 60. Figure 60: Wavelet based spectral metrics for the 3D-SABW (SSOOSS) test dataset, averaged across [PITH_FULL_IMAGE:figures/full_fig_p069_60.png] view at source ↗
Figure 61
Figure 61. Figure 61: Feature focused metrics for capturing interface (IRMSE) and shocks (SRMSE) on the [PITH_FULL_IMAGE:figures/full_fig_p070_61.png] view at source ↗
Figure 62
Figure 62. Figure 62: Structure-aware metrics for the 3D-SABW (SSOOSS) test dataset, averaged across all [PITH_FULL_IMAGE:figures/full_fig_p070_62.png] view at source ↗
Figure 63
Figure 63. Figure 63: Physics-informed metrics reporting the nRMSE of integral quantities of interest on the [PITH_FULL_IMAGE:figures/full_fig_p071_63.png] view at source ↗
Figure 64
Figure 64. Figure 64: Pointwise evaluation of baselines on the 3D-SDBA (SSOOSS) test dataset, reporting [PITH_FULL_IMAGE:figures/full_fig_p072_64.png] view at source ↗
Figure 65
Figure 65. Figure 65: Wavelet based spectral metrics for the 3D-SDBA (SSOOSS) test dataset, averaged across [PITH_FULL_IMAGE:figures/full_fig_p073_65.png] view at source ↗
Figure 66
Figure 66. Figure 66: Feature focused metrics for capturing interface (IRMSE) and shocks (SRMSE) on the [PITH_FULL_IMAGE:figures/full_fig_p074_66.png] view at source ↗
Figure 67
Figure 67. Figure 67: Structure-aware metrics for the 3D-SDBA (SSOOSS) test dataset, averaged across all [PITH_FULL_IMAGE:figures/full_fig_p074_67.png] view at source ↗
Figure 68
Figure 68. Figure 68: Physics-informed metrics reporting the nRMSE of integral quantities of interest on the [PITH_FULL_IMAGE:figures/full_fig_p075_68.png] view at source ↗
Figure 69
Figure 69. Figure 69: Rollout visualization of Density and Pressure fields for 2D Shock-induced Air Bubble [PITH_FULL_IMAGE:figures/full_fig_p089_69.png] view at source ↗
Figure 70
Figure 70. Figure 70: Rollout visualization of Velocity-X and Velocity-Y fields for 2D Shock-induced Air [PITH_FULL_IMAGE:figures/full_fig_p090_70.png] view at source ↗
Figure 71
Figure 71. Figure 71: Rollout visualization of Density and Pressure fields for 2D Shock-induced R22 Bubble [PITH_FULL_IMAGE:figures/full_fig_p091_71.png] view at source ↗
Figure 72
Figure 72. Figure 72: Rollout visualization of Velocity-X and Velocity-Y fields for 2D Shock-induced R22 [PITH_FULL_IMAGE:figures/full_fig_p092_72.png] view at source ↗
Figure 73
Figure 73. Figure 73: Rollout visualization of Density and Pressure fields for 2D Shock-induced Air Bubble [PITH_FULL_IMAGE:figures/full_fig_p093_73.png] view at source ↗
Figure 74
Figure 74. Figure 74: Rollout visualization of Velocity-X and Velocity-Y fields for 2D Shock-induced Air [PITH_FULL_IMAGE:figures/full_fig_p094_74.png] view at source ↗
Figure 75
Figure 75. Figure 75: Rollout visualization of Density and Pressure fields for 2D Shock-induced Droplet Breakup [PITH_FULL_IMAGE:figures/full_fig_p095_75.png] view at source ↗
Figure 76
Figure 76. Figure 76: Rollout visualization of Velocity-X and Velocity-Y fields for 2D Shock-induced Droplet [PITH_FULL_IMAGE:figures/full_fig_p096_76.png] view at source ↗
Figure 77
Figure 77. Figure 77: Rollout visualization of Density and Pressure fields for 2D Shock-induced Droplet Breakup [PITH_FULL_IMAGE:figures/full_fig_p097_77.png] view at source ↗
Figure 78
Figure 78. Figure 78: Rollout visualization of Velocity-X and Velocity-Y fields for 2D Shock-induced Droplet [PITH_FULL_IMAGE:figures/full_fig_p098_78.png] view at source ↗
Figure 79
Figure 79. Figure 79: Rollout visualization of Density and Pressure fields for 2D Shock-induced Air Bubble [PITH_FULL_IMAGE:figures/full_fig_p099_79.png] view at source ↗
Figure 80
Figure 80. Figure 80: Rollout visualization of Velocity-X and Velocity-Y fields for 2D Shock-induced Air [PITH_FULL_IMAGE:figures/full_fig_p100_80.png] view at source ↗

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