FNODE: Flow-Matching for data-driven simulation of constrained multibody systems

2025/08/29 by Hongyu Wang, Jingquan Wang, Wang, Hongyu +3
Engineering · Physics and Astronomy · #Dynamics and Control of Mechanical Systems #FOS: Computer and information sciences #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Vehicle Dynamics and Control Systems

paper · pdf · doi:10.48550/arxiv.2509.00183

openalex publication_date 2025/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Data-driven modeling of constrained multibody dynamics remains challenged by (i) the training cost of Neural ODEs, which typically require backpropagation through an ODE solver, and (ii) error accumulation in rollout predictions. We introduce a Flow-Matching Neural ODE (FNODE) framework that learns the acceleration mapping directly from trajectory data by supervising accelerations rather than integrated states, turning training into a supervised regression problem and eliminating the ODE-adjoint/solver backpropagation bottleneck. Acceleration targets are obtained efficiently via numerical differentiation using a hybrid fast Fourier transform (FFT) and finite-difference (FD) scheme. Kinematic constraints are enforced through coordinate partitioning: FNODE learns accelerations only for the independent generalized coordinates, while the dependent coordinates are recovered by solving the position-level constraint equations. We evaluate FNODE on single and triple mass-spring-damper systems, a double pendulum, a slider crank with and without friction, a vehicle model, and a cart-pole, and compare against MBD-NODE, LSTM, and fully connected baselines. Across these benchmarks, FNODE achieves improved prediction accuracy and training/runtime efficiency, while maintaining constraint satisfaction through the partitioning procedure. Our code and scripts are released as open source to support reproducibility and follow-on research.

Citations

• Flow Matching in the Low-Noise Regime: Pathologies and a Contrastive Remedy
• Nonlinear dynamics design for in-space assembly motion of manipulators on flexible base structures
• Simulation-Free Training of Neural ODEs on Paired Data
• Learning Dynamics of LLM Finetuning
• MBD-NODE: Physics-informed data-driven modeling and simulation of constrained multibody systems
• Improving the Training of Rectified Flows
• From Fourier to Neural ODEs: Flow Matching for Modeling Complex Systems
• Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraints
• Improving and generalizing flow-based generative models with minibatch optimal transport
• Flow Matching for Generative Modeling
• Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow
• On Numerical Integration in Neural Ordinary Differential Equations
• Physics-informed machine learning
• Neural ODE Processes
• ChemNODE: A Neural Ordinary Differential Equations Approach for Chemical Kinetics Solvers
• Fourier Neural Operator for Parametric Partial Differential Equations
• Neural Rough Differential Equations for Long Time Series
• Discovering Symbolic Models from Deep Learning with Inductive Biases
• Learning Physical Constraints with Neural Projections
• Neural Controlled Differential Equations for Irregular Time Series
• Lagrangian Neural Networks
• Learning to Simulate Complex Physics with Graph Networks
• SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems
• DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
• Hamiltonian Neural Networks
• ANODE: Unconditionally Accurate Memory-Efficient Gradients for Neural ODEs
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Neural Ordinary Differential Equations
• Adam: A Method for Stochastic Optimization
• OpenSim: Open-Source Software to Create and Analyze Dynamic Simulations of Movement
• Long Short-Term Memory

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