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

2025-08-29

AI Summary

To address the low long-term prediction accuracy and high computational cost in data-driven modeling of constrained multibody systems, this paper proposes the FNODE framework. Instead of end-to-end trajectory integration via conventional Neural ODEs, FNODE directly learns the acceleration vector field under explicit supervision. It introduces a Flow-Matching mechanism to construct differentiable acceleration targets and integrates Fast Fourier Transform (FFT) with finite-difference methods for efficient, numerically stable target acceleration estimation. This design circumvents the numerical bottlenecks associated with ODE solver backpropagation, significantly improving training efficiency and generalization. Evaluated on multiple standard multibody dynamics benchmarks, FNODE outperforms MBD-NODE, LSTM, and FCNN in prediction accuracy, long-term stability, and inference speed. The framework establishes a new, efficient, and physically interpretable paradigm for physics-informed neural modeling.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Intelligent Robots: Multimodal Perception & Sensor Fusion
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Data-driven modeling of constrained multibody systems faces two persistent challenges: high computational cost and limited long-term prediction accuracy. To address these issues, we introduce the Flow-Matching Neural Ordinary Differential Equation (FNODE), a framework that learns acceleration vector fields directly from trajectory data. By reformulating the training objective to supervise accelerations rather than integrated states, FNODE eliminates the need for backpropagation through an ODE solver, which represents a bottleneck in traditional Neural ODEs. Acceleration targets are computed efficiently using numerical differentiation techniques, including a hybrid Fast Fourier Transform (FFT) and Finite Difference (FD) scheme. We evaluate FNODE on a diverse set of benchmarks, including the single and triple mass-spring-damper systems, double pendulum, slider-crank, and cart-pole. Across all cases, FNODE consistently outperforms existing approaches such as Multi-Body Dynamic Neural ODE (MBD-NODE), Long Short-Term Memory (LSTM) networks, and Fully Connected Neural Networks (FCNN), demonstrating good accuracy, generalization, and computational efficiency.

Problem

• Reduces computational cost in constrained multibody systems
• Improves long-term prediction accuracy from trajectory data
• Eliminates backpropagation bottleneck in Neural ODE training

Innovation

• Flow-Matching Neural ODE learns acceleration fields
• Uses numerical differentiation with FFT/FD scheme
• Eliminates backpropagation through ODE solver