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KnockGS:interaction-Grounded Calibrationof Physical Gaussian Representations

Chenchen Ge, Hanwen Shen, Bowen Jing, Jiyuan Cai, Xiaofeng Wang, Hongsen Lei, Weitao Zhou, Dandan Zhang, Haibao Yu

arXiv:2608.27365v1cs.CVcs.AI

TL;DR

PhysicalGS pipelines typically require known or manually specified material parameters, limiting inference from observed dynamics. KnockGS calibrates elasticity and density scales from a known interaction, then freezes the estimate for unseen-interaction prediction; it reduces joint scale error to 1.1% and held-out Probe-B trajectory error by about 3×.

  • Problem

    PhysicalGS must predict force-induced object behavior while existing pipelines assume material parameters are known or manually specified.

  • Method

    KnockGS uses a known Probe-A response, an object-specific response library, and hard-neighborhood local ridge regression to estimate continuous (sE, sρ) without per-target simulation or gradients through MPM.

  • Results

    1.1% joint scale error and about 3× lower held-out Probe-B trajectory error outperform KNN and global ridge under identical evidence, while frozen estimates remain predictive under shifted probes.

  • Takeaways & Limitations

    Known interaction responses can calibrate two MPM material scales for object-specific, discretization-conditioned unseen-interaction prediction in the same simulator family.

  • Takeaways & Limitations

    The experiments do not establish real RGB/RGB-D input, real force feedback, measured material ground truth, sim-to-real transfer, cross-object sharing, or full multi-parameter identification.

Abstract

from arXiv · show

Physics-integrated 3D Gaussian representations now allow reconstructed deformable objects to be simulated and rendered under explicit material models. Existing pipelines, however, assume that material parameters are known or manually specified, limiting their applicability when these parameters must be inferred from observed object dynamics. We propose KnockGS, an interaction-response PhysicalGS framework that estimates the elasticity and density scales of a 3D Gaussian object from its dynamics under a known applied force. Rather than treating physical simulation only as a forward process, we turn the force-induced response into a calibration signal: temporal response features are xtracted from the observed dynamics, the two material scales are estimated from those features, and the estimate is then frozen and written back into the same simulator so that it can be tested on an interaction it was never fitted to.We evaluate the framework on both parameter recovery and response-level fidelity. The estimated scales are compared against hidden ground truth, and the re-simulated object is measured against the target using 3D particle trajectories, response-curve statistics, and rendered-frame quality. Across five held-out material targets, our method recovers the scales substantially more accurately than response retrieval, global regression, or a fixed default material, and the frozen estimate remains predictive under interactions that differ in direction and in magnitude. Interaction response therefore carries enough information to calibrate material scales in physically grounded 3D Gaussian representations.Our study is a first step toward interactive PhysicalGS systems that calibrate a Gaussian asset whose rendered appearance and simulated response are consistent.

1 Introduction

KnockGS addresses material-scale inference for physics-integrated Gaussian assets by calibrating from one known interaction and testing the frozen estimate on another. Its object-specific local estimator improves recovery and held-out response prediction while exposing dependence on the fixed simulator contract.

  • PhysicalGS unifies appearance and mechanical state, but visual reconstruction alone does not determine elasticity, density, damping, friction, or internal structure.
  • KnockGS estimates elasticity and density scales θ = (sE, sρ) from a known Probe-A response, then freezes them before predicting a disjoint Probe-B response.The asset, solver, particle fill, constitutive family, and other simulator conditions remain fixed.
  • A five-dimensional response descriptor, object-specific library, hard top-10 retrieval, and local ridge fit produce continuous scale estimates without differentiating through MPM.The estimate is written back into the same simulator for evaluation using trajectory RMSE, response-curve statistics, PSNR, and SSIM.
  • The local estimator remains predictive when Probe B changes direction or magnitude and succeeds on Pillow, Ficus, and Vasedeck targets.The study frames this as object- and discretization-conditioned calibration rather than a universal material representation.
  • 1.1% joint scale error replaces 2.4% for KNN and global ridge, while held-out Probe-B trajectory error falls by about 3×.The comparison uses the same evidence and also reports improvement over per-target CMA-ES video optimization.

2 Related Work

Related work in the PhysGaussian ecosystem separates forward simulation, visual-prior assignment, and passive-video inverse methods. KnockGS targets interaction-grounded calibration rather than assuming material parameters or relying only on passive observations.

  • PhysGaussian established unified physics-based simulation and rendering for 3D Gaussian representations, while follow-up work spans forward simulation, editing, reconstruction, and generation.
  • Table 1 compares representative related work in the PhysGaussian ecosystem.
  • The ecosystem includes forward PhysicalGS methods that assume material parameters, visual-prior approaches that infer attributes from appearance, and passive-video inverse methods that use observed dynamics.

3 Method

KnockGS calibrates two effective material scales from a known Probe-A response using a reusable object-specific response library, then freezes and writes the estimate back into the same simulator for held-out Probe-B prediction. The method uses compact response descriptors and local interpolation while keeping the PhysicalGS asset and simulator contract fixed.

  • 3 Method: The fixed simulator contract holds the asset, particle fill, solver, grid, constitutive family, boundary conditions, camera, and renderer constant while calibrating only elasticity and density scales.The scales are effective calibration quantities relative to the fixed object-specific simulator template, not direct intrinsic material constants.
  • 3 Method: An object-specific response library is precomputed under Calibration Probe A and reused for targets governed by the same contract and interaction.Held-out targets and their hidden scales or Probe-B responses are excluded from library construction.
  • 3 Method: Hard top-10 neighborhood selection followed by equal-weight local ridge regression produces continuous scale estimates without additional simulator calls.The configuration k = 10 and α = 10^-3 is fixed before held-out evaluation; predictions are clipped to candidate-set bounds.
  • 3 Method: A deterministic five-dimensional descriptor compresses candidate and target trajectories into deformation-amplitude and timing cues using library-only standardization.Its entries summarize cumulative deformation, early deformation rate, peak frame-to-frame motion, cumulative motion, and the fraction of motion concentrated early.
  • 3 Method: After Calibration Probe A, the estimate is frozen and written back into the same simulator, while disjoint Probe B is reserved for final cross-interaction evaluation.Probe B may vary force direction, magnitude, duration, or contact location and contributes no information to estimator design or fitting.
  • 3 Method: Probe-B evaluation compares stable-identity Gaussian-associated particle trajectories and complements them with response-curve and rendered-frame measures.The evaluation targets cross-interaction prediction within the fixed object-specific simulator contract rather than arbitrary-interaction or real-material generalization.

4 Experiments

The experiments test same-information calibration, frozen held-out prediction, cross-object repeatability, observation robustness, and failure boundaries. Local ridge performs strongly under matched simulation contracts, while observation quality, discretization, and object transfer constrain validity.

  • Same-Information Calibration: Local ridge achieves 1.13% mean parameter error, versus 2.37% for response KNN, 2.45% for global ridge, and 6.75% for response-nearest.All deployable methods receive identical Probe-A evidence.
  • Frozen Probe-B Prediction: On standard_y, local ridge reaches 4.42 × 10−5 Probe-B trajectory RMSE, compared with 1.41 × 10−4 for KNN and 1.69 × 10−4 for global ridge.On strong_x, it reaches 7.79 × 10−5 versus 2.02 × 10−4 and 2.47 × 10−4, respectively.
  • Rendered Prediction: Local ridge reaches 41.20 dB foreground PSNR and 0.998 object-crop SSIM on the held-out Pillow visualization, exceeding global ridge and other reported baselines.The same frozen estimate generates the Probe-A reconstruction and held-out Probe-B trajectories.
  • Robustness Checks: The method has a stable mean advantage rather than universal target-wise dominance: a non-inferiority gate passes two of three alternative splits.The failed split has 3/5 non-inferior targets, while the others have 4/5 and 5/5; all six Probe-B response gates pass.
  • Object-Specific Repeatability: Across Pillow, Ficus, and Vasedeck, local ridge obtains 1.13%, 0.63%, and 1.21% parameter error, respectively, using independently object-specific libraries.On Vasedeck, its Probe-B trajectory RMSE is 1.37 × 10−5 versus 3.11 × 10−5 for response-nearest.
  • Observation Ladder: With ID-free LK tracks, local-ridge error rises to 8.67%, exceeding global ridge at 6.73% and KNN at 7.76%.Synthetic-depth noise increases local error from 0.21% clean to 28.26% at noise level 0.01.
  • Discretization and Object Boundaries: Changing fill density or grid resolution while retaining the original library raises error to 42.61% or 38.30%, whereas matched-library reconstruction restores 0.99% or 0.75%.Random fill seeds at the same specification remain stable, with 1.19% mean and 2.45% maximum error.
  • Identifiability Boundaries: The five-dimensional descriptor is not globally identifiable, with local-neighborhood condition numbers reaching a maximum of 6,539.Some compressed-space ambiguities become separable when the full trajectory is considered, but fixed-probe physical non-identifiability remains possible.

5 Conclusion

KnockGS calibrates two MPM material scales from a known interaction and tests the frozen estimate on unseen interactions within the same simulator family. The controlled, object-specific result is supported by trajectory and rendered-response fidelity, while stress tests identify its boundaries.

  • Conclusion: KnockGS uses an object-specific response library and local ridge estimator to recover elasticity and density scales from a known Probe-A response.The estimate is frozen and written back into the simulator before held-out prediction.
  • Conclusion: The frozen estimate predicts held-out direction- and magnitude-shifted probes more accurately than response retrieval, KNN, global ridge, and fixed default materials.The result repeats across Pillow, Ficus, and Vasedeck and is evaluated with particle trajectories and rendered visual fidelity.
  • Conclusion: Stress tests show that observation degradation, fill or grid mismatch, and cross-object transfer expose clear failure boundaries.The calibration mechanism is conditioned on the object and discretization used to build the response library.

6 Discussion

The supported claim is controlled, object-specific calibration of two MPM material scales from a known interaction, followed by unseen-interaction prediction under the same simulator conditions. The discussion identifies observation, discretization, transfer, and parameterization limits, alongside concrete directions for extending the method.

  • Scope: The method is limited to controlled, object-specific, discretization-conditioned calibration of two MPM material scales from a known interaction.Its supported prediction setting is an unseen interaction in the same simulator family.
  • Scope: The experiments do not establish real RGB/RGB-D input, real force feedback, measured material ground truth, sim-to-real transfer, shared cross-object estimation, or full multi-parameter identification.They also do not establish damage prediction or active-probe optimality.
  • Future work: Future work targets robust visual correspondence, uncertainty-aware estimation, active interaction selection, richer physical parameterizations, and validation with measured force and object-level deformation.These directions follow from the observed degradation, descriptor ambiguity, and simulation-to-reality gap.

A Response and Metric Details

The evaluation uses Gaussian-associated particles and fixed simulator exports to measure response fidelity, while the calibration library and probe contract define the tested material-scale setting. Probe-B information remains excluded until the estimate is frozen.

  • Response representation: The estimator may use all exported particles, but primary trajectory evaluation is restricted to Gaussian-associated particles with stable identity.This avoids confounds from internal fill particles, which are not directly renderable and may vary in count and correspondence.
  • Metrics: Secondary curve metrics summarize temporal response magnitude, whereas trajectory RMSE remains the spatial response metric.Reported secondary quantities include displacement, peak, AUC, and final-frame errors.
  • Metrics: Foreground PSNR and object-crop SSIM quantify same-simulator visual response fidelity using the same renderer and camera for target and prediction.PSNR pools RGB error across exported frames, while SSIM averages framewise object-crop similarity.
  • Simulation contract: The Pillow contract contains 624,324 Gaussian-associated particles and 71,660 internal fill particles, with primary trajectory evaluation sampling at most 100,000 associated particles.The table also records the fixed fill seed and exported initial state.
  • Probe contract: Probe values specify force vectors, contact boxes, and 0.1 ms MPM steps while preserving the nominal force-time integral or total force and impulse where stated.These probe definitions establish the interaction conditions used for comparison.
  • Calibration library: The candidate library contains 54 predeclared, non-Cartesian elasticity-density pairs, while target pairs are held out from that candidate set.Material scales multiply frozen object-specific base values, and standardization uses candidate data only.
  • Simulation contract: Geometry, transforms, constraints, gravity, damping, friction, camera, renderer, and object-specific grid settings remain fixed within each library.All objects use a 10^-4 s internal MPM substep.
  • Evaluation protocol: All parameters are estimated using only standard_x; Probe-B responses are generated only after the estimator and its hyperparameters are frozen.Although Probe-B rollouts exist in the library, their features do not enter estimation.

C Target-wise Results and Variability

Target-wise reporting distinguishes mean calibration performance from universal dominance. The primary protocol uses held-out targets and reports variability across targets rather than treating frames or particles as independent replicates.

  • Variability: Variability in Table 5 is sample standard deviation across five held-out targets, not simulator noise or independent frame- or particle-level replication.Deterministic estimators remain fixed once the library, fill seed, and evaluation sample are frozen.
  • Target-wise results: Global ridge outperforms local ridge on target (0.70, 1.20) for parameter and B-magnitude errors, while local ridge remains better on Probe A and B-direction.This exception motivates reporting target-wise gates alongside the best mean result.
  • Reporting: Table 5 reports Pillow means with sample standard deviations across five held-out targets, and Table 6 lists every target-method outcome without omission.Trajectory columns use units of 10^-5, while eθ is joint parameter error in percent.

D Duration and Contact-Shift Diagnostics

Duration-shift experiments support five-target transfer, while contact-location evidence is limited to a controlled single-target diagnostic. Both evaluate frozen Probe-A estimates under altered force protocols.

  • Duration diagnostics: The fine-duration experiment changes only the force time profile while preserving the same nominal force–time integral.It resolves 20 ms actuation with 5 ms exports over 0.6 s, rather than the main benchmark’s 20 ms exports.
  • Contact diagnostics: Contact-location testing compares equal-force-and-impulse probes at two locations on one predeclared target.The shifted-contact probe compensates for a smaller selected particle set by increasing per-particle force.
  • Scope: The contact result is retained as a controlled representative demonstration rather than five-target evidence.This limitation prevents selective overstatement of the location-shift finding.
  • Duration and contact diagnostics: Local ridge wins on all five duration targets and both contact locations for the diagnostic target.The duration result supports a five-target protocol-shift claim, whereas contact-location evidence remains a representative demonstration.

E Multiple Splits and Numerical Tests

Multiple splits and numerical tests distinguish average estimator performance from universal dominance and show that numerical-model mismatches, rather than random fill alone, drive large errors.

  • Multiple splits: Local ridge has the lower mean on every split, but the strict target-wise gate passes only two.Probe-B resimulation passes all six split–protocol gates, separating average performance from universal dominance.
  • Numerical conditioning: Random fill seeds yield 1.19% mean error, whereas fill-density and grid mismatches produce 42.61% and 38.30% error with the original library.These results separate random realization from changes to the numerical model.
  • Numerical conditioning: Rebuilding matched libraries restores fill- and grid-mismatch errors to 0.99% and 0.75%, respectively.Equal-total-force normalization alone leaves fill mismatch at 43.30%, so the failure is not explained only by selected-particle count or total impulse.

F Offline Estimator Sensitivity

Offline tests show that larger candidate libraries improve local-estimator accuracy and stability, while observation and external-route diagnostics define practical limits on the evidence used for calibration.

  • Library size: Increasing the library from 18 to 54 candidates reduces mean joint error from 2.078% to 1.130%.Subset-selection standard deviation contracts from 0.757% at 18 candidates to 0.151% at 45 candidates and vanishes for the unique full library.
  • Library size: Even the 18-candidate mean remains below the 2.374% full-library response-KNN baseline.This indicates that the local model’s advantage is not confined to the densest library.
  • Observation ladder: The observation ladder progresses from privileged simulator particles to Gaussian-associated particles, synthetic RGB-D depth, and ID-free LK tracks.The first four stages retain exact or clean geometric correspondence; the final stage breaks that correspondence and is not a substitute for captured RGB-D evaluation.
  • External routes: External-route comparisons use different parameter semantics or adapters, so the displayed representative case is diagnostic rather than an across-paper superiority claim.Aggregate claims continue to use all five targets, while CMA-ES is the main alternative inverse baseline for the current protocol.

I Reproducibility and Claim Boundaries

The released contracts and audits support reproducible evaluation, while the evidence remains bounded to controlled, object-specific calibration rather than real-world or complete physical identification.

  • Reproducibility: Released experiment contracts record assets, candidate sets, force definitions, splits, simulator settings, feature processing, and metric implementation.Result packages include per-case outputs and completion, leakage, missing-frame, NaN, and duplicate audits.
  • Claim boundaries: The supported claim is object-specific, discretization-conditioned calibration of two MPM material scales followed by unseen-interaction prediction in the same simulator family.The evidence does not establish real RGB/RGB-D identification, real force feedback, sim-to-real transfer, cross-object sharing, unknown-fill inversion, or complete physical representation.
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