A mixed leading variable physics-informed neural network for nonsmooth dynamics simulation in contact systems
Abstract
High-accuracy computation of nonsmooth dynamics is a challenging problem in systems with multiple frictional contacts. This study proposes a general physics-informed neural network framework, termed the mixed leading variable physics-informed neural network (MLV-PINN). By using the governing equations and contact-friction laws as physical constraints, this framework provides common solution approaches for computing nonsmooth dynamics not only in discrete systems but also in continuum systems. Specifically, the network represents accelerations, normal contact forces and friction margins as independent outputs and determines them simultaneously, without first reducing the dynamics to discrete velocity-impulse complementary subproblems. A composite physics-informed loss is constructed from the equations of motion in their original form, contact-friction complementary conditions and a friction-margin consistency relation. To improve stick-slip state identification during PINN optimisation, a mixed leading variable combining relative tangential velocity and acceleration is introduced to reformulate the tangential complementary conditions. Four benchmark simulations cover one-dimensional (1-D) nonsmooth dynamics involving single-contact stick-slip, 1-D nonsmooth dynamics involving multi-contact stick-slip, two-dimensional (2-D) nonsmooth dynamics with coupled normal contact-separation and tangential stick-slip, and 2-D nonsmooth dynamics in a continuum system involving moving contact on an elastic beam. Benchmark comparisons show substantial reductions in displacement and velocity errors relative to the corresponding conventional methods at large time steps. These results, together with an ablation study and tests involving friction-velocity slopes, long-time integration and loss weights, illustrate the computational accuracy and support the broad applicability of the proposed framework.
Related
- Parameter Estimation in Machining Dynamics with Regenerative Delay and Nonsmooth Friction using Physics-Informed Neural Networks
- Passage of particles through matter and the effective straggling-function: High-fidelity accelerated simulation via Physics-Informed Machine Learning
- The Magnusian generator for dissipative systems and application to leading 2.5PN radiation-reaction dynamics
- Efficient Simulation of Hybrid Continuous- and Discrete-Variable Quantum Circuits via Gaussian Decompositions
- Efficient Quantum Simulation of Variable-Coefficient Transport with Continuous Source Injection
BibTeX
@misc{li2026mixed,
title = {{A mixed leading variable physics-informed neural network for nonsmooth dynamics simulation in contact systems}},
author = {Xinyuan Li and Zilin Li and Hongtao Wei and Ronghan Wei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26495},
eprint = {2610.26495},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26495},
}
RIS
TY - UNPB
TI - A mixed leading variable physics-informed neural network for nonsmooth dynamics simulation in contact systems
AU - Xinyuan Li
AU - Zilin Li
AU - Hongtao Wei
AU - Ronghan Wei
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26495
UR - https://arxiv.org/abs/2610.26495
AB - High-accuracy computation of nonsmooth dynamics is a challenging problem in systems with multiple frictional contacts. This study proposes a general physics-informed neural network framework, termed the mixed leading variable physics-informed neural network (MLV-PINN). By using the governing equations and contact-friction laws as physical constraints, this framework provides common solution approaches for computing nonsmooth dynamics not only in discrete systems but also in continuum systems. Specifically, the network represents accelerations, normal contact forces and friction margins as independent outputs and determines them simultaneously, without first reducing the dynamics to discrete velocity-impulse complementary subproblems. A composite physics-informed loss is constructed from the equations of motion in their original form, contact-friction complementary conditions and a friction-margin consistency relation. To improve stick-slip state identification during PINN optimisation, a mixed leading variable combining relative tangential velocity and acceleration is introduced to reformulate the tangential complementary conditions. Four benchmark simulations cover one-dimensional (1-D) nonsmooth dynamics involving single-contact stick-slip, 1-D nonsmooth dynamics involving multi-contact stick-slip, two-dimensional (2-D) nonsmooth dynamics with coupled normal contact-separation and tangential stick-slip, and 2-D nonsmooth dynamics in a continuum system involving moving contact on an elastic beam. Benchmark comparisons show substantial reductions in displacement and velocity errors relative to the corresponding conventional methods at large time steps. These results, together with an ablation study and tests involving friction-velocity slopes, long-time integration and loss weights, illustrate the computational accuracy and support the broad applicability of the proposed framework.
ER -