On the Numerical Reliability of Differentiable Physics-Based Optimization for Robotic Material Manipulation
Authors: Xintong Yang, Minglun Wei, Yu-Kun Lai, Ze Ji
Organizations: School of Engineering, Cardiff University, Cardiff, United Kingdom · School of Computer Science and Informatics, Cardiff University, Cardiff, United Kingdom · College of Mechanical and Electrical Engineering, Hohai University, China
Differentiable physics is increasingly used in robotic material manipulation for system identification, trajectory or skill optimization, demonstration generation, and robot or end-effector design. These applications depend on gradients propagated through long, contact-rich simulation rollouts. We study the numerical reliability of those gradients using two Material Point Method (MPM) system-identification benchmarks derived from elastoplastic and granular manipulation. The benchmarks provide controlled cases for three effects that also arise in broader differentiable physics-based optimization. GPU many-to-one sums whose order depends on thread scheduling changed long-horizon gradients and reversed the sign of one parameter gradient relative to a deterministic reference. Finite-difference checks became less reliable for longer rollouts because repeated-run loss variation grew much faster than the loss change produced by the tested parameter perturbations. Observation and loss definitions changed optimization behaviour and the solution preferred by an independent metric. These results motivate reproducible accumulation, finite-difference validation that compares perturbation-induced loss changes with repeated-run variation, and explicit reporting of objective construction when differentiable simulation is used for robotic optimization.
Figures & tables
Fig. 1: Robotic material-manipulation settings motivating this study. Top: Real elastoplastic interaction and the corresponding MPM simulation from the DPSI-derived setting [ 8 ] . Bottom: Real and simulated granular digging from the DDBot-derived setting [ 9 ] .
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
Setting
Configuration
DPSI-derived elastoplastic
Fixed-corotated elasticity with von Mises plasticity; 218, 451, or 876 particles; 94 global steps with 50 MPM substeps per step; PRT-CD, PRT-EMD, PCD-CD, and PCD-EMD.
DDBot-derived granular
Hencky/Saint Venant-Kirchhoff elasticity with Drucker-Prager plasticity; 27,440 particles; 200 or 311 global steps with 20 MPM substeps per step; HMD and PCD-EMD.
Appendix
TABLE I: Benchmark configurations used in the objective matrix.
Global steps
f64 worst error
f32 loss spread
FD time
2
4.4×10−6 to 1.5×10−5
2.2×10−7 to 1.4×10−6
25 s
5
2.75×10−5
2.9×10−5
38 s
10
2.93×10−5
7.1×10−5
59 s
20
3.41×10−1
4.7×10−5
99 s
40
2.70×10−1
2.8×10−5
178 s
Appendix
TABLE II: DPSI-derived horizon experiment. The f64 column reports the worst relative AD/FD discrepancy across the tested material components.
Objective
Descending epochs
Mean HMD (mm)
PRT-CD
78/80 (97.5%)
3738.4
PRT-EMD
54/80 (67.5%)
3698.6
PCD-CD
43/80 (53.8%)
3711.2
PCD-EMD
46/80 (57.5%)
3708.6
Appendix
TABLE III: Reference-density DPSI-derived optimization behaviour. Descent count is the number of epochs whose post-update objective is lower than the entry value for that epoch, aggregated over two seeds and both precisions. HMD is an independent terminal evaluation.
Case
Runtime or outcome
DPSI 94-step SDF contact, CPU loop vs. GPU kernels
260.821 s → 20.488 s (12.73 × )
DPSI FD validation, 2 steps vs. 40 steps
25 s → 178 s
DDBot HMD epoch, 200 steps
about 115 s; about 154 s with the extended line-search set
DDBot PCD-EMD epoch, 311 steps
about 170 s; about 227 s with the extended line-search set
DPSI particle-density change
about +1.5% wall time for denser f32 cases; recorded device memory unchanged
Deterministic repeat cells
5/5 bit-identical across selected f32/f64 and DPSI/DDBot-derived cases