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REVIEW 4 major objections 6 minor 111 references

Rigid Body Adversarial Attacks

T0 review · 4 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read Objects with identical shape and mass can be engineered to diverge sharply in deformable simulation while remaining indistinguishable in rigid-body simulation.

desk verdict A novel, well-executed construction of rigid-body adversarial objects, but the stiff-only control leaves open whether any compliant material would do the same. read the letter →

arxiv 2502.05669 v1 pith:TLCVFY23 submitted 2025-02-08 cs.CV cs.GR

Aravind Ramakrishnan , David I.W. Levin , Alec Jacobson This is my paper · ORCID
classification cs.CVcs.GR
keywords adversarialattacksrigidbodysimulationdeformabledifferentiablephysicstopologyoptimizationmassmomentsfiniteelementmethodrobustness
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Rigid-body simulators assume objects are infinitely stiff, so they describe an object by its external shape, total mass, center of mass, and inertia tensor. This paper tries to establish that this idealization is attackable: one can design an object with exactly the same external geometry and the same first three mass moments as a reference, made only of ordinary stiff materials, that behaves identically in a rigid-body simulator but follows a very different trajectory once its internal compliance is taken into account. The authors build a differentiable deformable simulator and optimize the interior material distribution to maximize trajectory divergence subject to those matching constraints. In a basketball-like ball, a bunny, a star, stacked cubes, and a swung bat, the optimized objects produce qualitatively different outcomes from their rigid-body references, while uniformly stiff baseline objects stay close to the rigid-body trajectories. If the construction is sound, it exposes a failure mode that matters for robotics planning, learned physics models, and safety-critical simulation.

What carries the argument

The central machinery is the constrained optimization problem of Eq. 5, which maximizes the final-state distance between the adversarial and reference trajectories while keeping the collision geometry and the first three mass moments fixed. The degrees of freedom are per-tetrahedron material parameters—Young's modulus, Poisson's ratio, mass density, and an occupancy $\alpha$ (a per-element solid/void indicator) that can carve out internal voids—with boundary occupancy fixed to one so the exterior surface never changes. A moments-of-mass operator $S(V,T)$ maps the effective density field to the ten scalar mass moments (total mass, center of mass, and inertia tensor), enforced as a soft constraint with weight $\beta$. Occupancy gradients are smoothed with a mesh-Laplacian filter to suppress checkerboard artifacts, then sharpened to 0/1 in postprocessing. Gradients for the descent are obtained by differentiating a finite-element simulation that uses the stable Neohookean hyperelastic energy, a second-order backward-difference time integrator (BDF-2), and an interpenetration-barrier contact model, with the adjoint method providing the per-timestep derivatives needed to run ADAM.

What would settle it

Run the adversarial objects in at least two independent high-resolution deformable simulators with converged timesteps and refined meshes, and compare against both the rigid-body reference and a uniformly stiff baseline; the central claim is falsified if the adversarial trajectory divergence collapses to the baseline's roughly two-degree level or disappears entirely, since that would indicate the divergence is solver artifact rather than physical compliance.

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Extended reading notes

Core claim

The paper's central claim is that there exist perceptually rigid objects—built solely from materials with stiffnesses in ranges such as 2.5–650 GPa—whose external collision geometry and first three mass moments (total mass, center of mass, and inertia tensor) exactly match a reference object, so that a rigid-body simulator treats them as indistinguishable, yet whose simulated trajectories under a deformable model diverge maximally from the reference. This divergence is manufactured, not coincidental: the authors solve an optimization problem that maximizes final-state trajectory separation subject to matching boundary geometry, matching mass moments, and confining all material parameters to physically plausible boxes. Their experiments show qualitative outcome changes in several scenarios—a ball that misses a hoop, a bunny that misses a bin, a cube stack that collapses, a struck ball sent toward a target—while Table 1 reports moment matches to roughly six significant figures. The authors' stiff-uniform-material baseline simulations track the rigid-body references closely, which they take as evidence that the adversarial divergence comes from the engineered internal material distribution rather than from simulator mismatch.

Load-bearing premise

The central claim stands only if the deformable simulator used for optimization and evaluation is a faithful model of real physics; the paper's own baseline control, which shows a very stiff uniform object diverging by about two degrees from the rigid-body reference, is the place where this premise could give way.

Editorial extensions

If this is right

  • Any application that uses a rigid-body simulator as a stand-in for a more accurate deformable simulator carries a hidden failure mode: objects that look identical to the rigid-body solver can produce qualitatively wrong outcomes such as a ball missing a hoop or a stack of cubes collapsing.
  • Learned physics models and robotics planners that are trained or validated exclusively on rigid-body simulation inherit this vulnerability, and adversarial objects of this kind could be used as test cases for robustness.
  • Because the divergence is driven by the internal distribution of material properties, it cannot be detected by inspecting external shape or by matching total mass, center of mass, and inertia tensor.
  • The attack is not limited to generic divergence: changing the cost function produces directed attacks, such as a bat engineered to send a struck ball toward a target trajectory.
  • The effects are reproducible in commercially available simulators, so they are not confined to the authors' custom code.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: if real materials always have some compliance, the same construction suggests rigid-body simulation of stiff objects carries an irreducible modeling risk, and the paper's examples provide lower bounds on the divergence that real objects could produce.
  • Beyond the paper: a cross-simulator replication with a much smaller timestep, a finer mesh, and independent FEM solvers would separate physical compliance effects from simulator-specific error; the paper's own baseline shows about two degrees of divergence for uniformly stiff objects, so some fraction of the adversarial divergence could be numerical rather than physical.
  • Beyond the paper: a promising next test is physical fabrication of the optimized internal structures with real materials; the paper's own limitation section notes that the constructed materials may not currently exist, so manufacturability remains open.
  • Beyond the paper: the method could be inverted as an acceptance test for new stiff-material simulation techniques—any improved simulator should reproduce the reference trajectory on these adversarial objects or explain why not.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper introduces adversarial attacks on rigid body simulators. The authors formulate an optimization problem that, given a reference object, searches for an object with the same external collision geometry and the same first three mass moments (mass, center of mass, moment of inertia) but with an internal material distribution and internal geometry chosen so that the object behaves identically under a rigid body simulation yet diverges maximally under a finite-element deformable simulation. The optimization uses a differentiable implicit BDF-2 stable-Neohookean simulator with IPC barrier contact and adjoint gradients, with moment constraints imposed softly. Demonstrations are presented for five scenarios: a ball bouncing off a backboard and rim, a star bouncing between two planes, a bunny bouncing into a bin, a cube toppling a stack, and a bat directing a ball's trajectory. All evaluations are carried out in PolyFEM and compared against rigid body trajectories computed in BULLET.

Significance. The problem formulation is original and timely: it identifies a failure mode of the rigid body abstraction that is relevant to robotics sim-to-real, learned physics, and safety-critical simulation. The paper correctly identifies the set of quantities that determine rigid body behavior---mass, center of mass, and moment of inertia---and provides a clean, explicit derivation of the forward optimization and adjoint gradient computations. The moment-matching results in Table 1 are precise, and the authors are transparent about the limitations of their approach, including the continuity of the material range and post-processing topology issues. However, the empirical evidence as presented does not yet isolate the optimized internal material distribution as the cause of the observed trajectory divergence. The control experiment in Supplemental D uses a material stiffness far outside the paper's own permitted range, and the reference objects' deformable material parameters are never stated. The significance of the existence claim is therefore conditional on additional control experiments that are entirely within the scope of the manuscript to add.

major comments (4)
  1. [Supplemental D; Eq. (2a)] The baseline control uses a uniform object with Young's modulus 1e13 Pa, which is roughly 15,000 times larger than Ymax=650 GPa and four million times larger than Ymin=2.5 GPa. The paper explicitly claims that materials down to 2.5 GPa are 'perceptually rigid' and within the admissible range. This control therefore cannot rule out the possibility that a uniform object made of an allowed material (e.g., 650 GPa, or even 2.5 GPa) already produces a trajectory divergence comparable to the adversarial examples. To support the central attribution, the authors should add uniform-material baseline simulations at Ymin, Ymax, and preferably at the reference object's own stiffness, with otherwise identical settings, and show that their trajectory deviation from the rigid body reference is substantially smaller than that of the optimized adversarial object.
  2. [Section 4; Eq. (1)] The material parameters of the reference object used in the deformable simulations (q_ref in Eq. (1)) are never reported. The paper only states that a constant mass density of 2.5 g/cc is used for computing reference moments, but q_ref is obtained by deforming the reference object in the same FEM simulator, which requires a Young's modulus, Poisson's ratio, and density. If the reference is simulated as effectively rigid while the adversarial object is allowed to be orders of magnitude softer, the comparison is favorable by construction. Please state Y_ref, nu_ref, and rho_ref for every reference, and justify that the reference belongs to the same perceptually rigid class as the adversarial candidates.
  3. [Table 1; Section 4] The moment matching in Table 1 is reported to many digits, but the central claim that the adversarial objects 'behave identically in rigid body simulations' is never directly tested. The adversarial objects are not simulated in a rigid body simulator; only the reference objects are run in BULLET. Since the moment constraints are enforced as soft constraints (Eq. (5)), a small residual mismatch exists and its effect on rigid body trajectories is only asserted to be negligible. Please run the adversarial objects in BULLET (or an equivalent rigid body integrator) using their actual Table 1 moments, and report the rigid body trajectory difference against the reference to quantify the effect of the soft-constraint residuals.
  4. [Supplemental C.2, C.5; Figs. 3, 9] All demonstrations are single runs with no repeated optimization seeds or perturbation analysis. Given the chaotic nature of contact dynamics and the fact that the Supplemental D baseline itself shows roughly 2 degrees of divergence, the 5-8 degree adversarial divergences could in principle be within run-to-run variability of a generic, non-optimized stiff object. For the star and bat examples, please report results over multiple optimization runs (with different initializations of the material fields) and/or over small perturbations of the optimized parameters, so the reader can assess whether the divergence is robust and attributable to the optimization rather than to chance.
minor comments (6)
  1. [Abstract] The phrase 'objects of interest can considered very stiff' is missing the word 'be'; please correct the grammar.
  2. [Section 3.3] The phrase 'it's superior damping' should be 'its superior damping'.
  3. [Section 3.2, Eq. (5)] The norm subscript M in ||q_adv(tend) - q_ref(tend)||^2_M is never defined; please clarify whether M is a mass matrix, a metric, or a typo.
  4. [Section 1] The paper calls PolyFEM a 'commercially available simulator'; it may be more accurate to describe it as a publicly available open-source simulator, unless commercial licensing is specifically intended.
  5. [Section 5] The postprocessing step that repairs disconnected pieces after rounding occupancies is only described by a reference to a Steiner tree method; a sentence explaining how the repair affects the mass-moment constraints would improve reproducibility.
  6. [Supplemental B] The adjoint derivative formulas in Eq. (16) would benefit from a short derivation or at least a pointer to the corresponding equation in the main text, as the notation GRAD OUTPUT is specific to the PyTorch implementation.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the paper constructs adversarial objects by explicit optimization and validates them in held-out commercial simulators, so the central claim does not reduce to its inputs.

full rationale

This paper poses an explicit inverse problem: maximize trajectory divergence in a deformable simulator subject to matching the reference object's external geometry and first three mass moments (Eqs. 1-2), then solves it with a differentiable simulator and reports the resulting trajectories. The observed divergence is a property of the constructed object, not a fitted parameter renamed as a prediction. The evaluation is externally benchmarked: adversarial objects are optimized in the authors' custom simulator but demonstrated in Bullet for rigid-body motion and in PolyFEM for deformable motion, and the PolyFEM results are not fed back into the optimization. The equivalence of same collision geometry plus same moments to identical rigid-body behavior is a known reduction of rigid-body mechanics, not a derived result of this paper. Self-citations (Jacobson's Laplacian smoothing [43], libigl [44], CHOLESPY [70]) are implementation tools and do not carry the load-bearing argument. The control weakness in Supplemental D - the uniform stiff baseline uses Y=1e13 Pa, outside the paper's allowed 2.5-650 GPa range - is a genuine threat to isolating the optimized material distribution as the cause of divergence, but it is a correctness/control limitation rather than circularity, since it does not exhibit an equation or fitted value that reduces the central claim to its inputs. Accordingly, no circular step meeting the evidentiary bar is identified.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central construction rides on standard physics (rigid-body reduction, FEM) and hand-chosen feasibility bounds rather than new entities. The most significant ledger entries are the unreported beta and smoothing parameters, and the unvalidated fidelity of the deformable simulator as ground truth.

free parameters (4)
  • soft-constraint weight beta = not reported (determined experimentally)
    Controls the trade-off between trajectory divergence and moment matching in Eq. 5; the claim of identical rigid behavior depends on this weight being large enough, but no value or sensitivity study is provided.
  • material bounds (Ymin, nu_min/max, rho_min/max) = 2.5-650 GPa, 0.2-0.4, 0.8-11.3 g/cc (per-example Ymin varies)
    Hand-chosen ranges defining 'perceptually stiff' materials; these bounds encode the domain assumption that such objects would reasonably be simulated as rigid.
  • Laplacian smoothing strength gamma = not reported
    Eq. 8 applies (Mtilde - gamma Ltilde)^-1 smoothing to occupancy gradients; gamma is not specified, affecting final topology.
  • per-example simulation parameters (timestep, barrier distance) = 0.01s, 1e-3 (star 1/30s, cubes 1e-3s)
    Chosen per example and affect trajectory divergence; no sensitivity analysis is provided.
assumptions (4)
  • standard math Rigid body dynamics of an object is fully determined by its external collision geometry and first three mass moments.
    Used in Eq. 1(f-h) to define the perturbation bounds; standard rigid body mechanics (cited Den Hartog [22]).
  • domain assumption The deformable FEM simulator (stable Neohookean material with IPC barrier contact) is a more accurate model of reality than the rigid body simulator.
    The entire attack's danger narrative treats deformable simulation as ground truth; Section 3.3 and Supplemental D rely on this, while Supplemental D admits roughly 2 degree disagreement for ultra-stiff baselines.
  • ad hoc to paper Materials with Young's modulus as low as 2.5 GPa are 'perceptually rigid' for the simulated scenarios and would plausibly be simulated with a rigid body model.
    The paper asserts this in Section 3.1.1 without perceptual or engineering validation; the bat example raises Ymin to 25 GPa and the star to 5 GPa, showing the bound matters.
  • domain assumption The reference object's material parameters in the deformable simulation are well-defined and representative.
    The paper specifies reference density (2.5 g/cc) but never states the Young's modulus and Poisson's ratio used to compute qref in Eq. 1, leaving the baseline of the attack unspecified.

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Cite this review

Pith. "Pith review of Rigid Body Adversarial Attacks." pith.science (2026). https://pith.science/paper/TLCVFY23

@misc{pith2026250205669,
  author       = {Pith},
  title        = {Pith review of: Rigid Body Adversarial Attacks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TLCVFY23}},
  note         = {Machine review of arXiv:2502.05669}
}
read the original abstract

Due to their performance and simplicity, rigid body simulators are often used in applications where the objects of interest can considered very stiff. However, no material has infinite stiffness, which means there are potentially cases where the non-zero compliance of the seemingly rigid object can cause a significant difference between its trajectories when simulated in a rigid body or deformable simulator. Similarly to how adversarial attacks are developed against image classifiers, we propose an adversarial attack against rigid body simulators. In this adversarial attack, we solve an optimization problem to construct perceptually rigid adversarial objects that have the same collision geometry and moments of mass to a reference object, so that they behave identically in rigid body simulations but maximally different in more accurate deformable simulations. We demonstrate the validity of our method by comparing simulations of several examples in commercially available simulators.

Figures

Figures reproduced from arXiv: 2502.05669 by the authors.

Figure 1
Figure 1. We construct an adversarial ball (right) out of perceptually stiff materials (with a minimum Young’s modulus of 2.5 GPa), [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. For a given geometry, there can be many mass den [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. We simulate a star colliding off of the ground and a wall in a rigid body simulator (left). From it, we construct an adversarial [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Our differentiable physics simulator allows us to construct adversarial objects using a first order optimization method. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 6
Figure 6. Figure 6: Using our geometrically motivated smoothing operator [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Starting with a reference bunny (blue) which has a trajectory going into a bin, we construct an adversarial bunny (pink). A greater [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 9
Figure 9. Figure 9: We construct an adversarial bat that aims to get the tra [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: Following the setup from Fig [PITH_FULL_IMAGE:figures/full_fig_p017_10.png]
Figure 11
Figure 11. Figure 11: Following the setup from Fig [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]
Figure 12
Figure 12. Figure 12: The trajectory of the baseline simulation (gold) cor [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.