Physics-Informed Neural Controlled Differential Equations for Scalable Long Horizon Multi-Agent Motion Forecasting

2025-09-30

AI Summary

To address the challenges of modeling nonlinear inter-agent interactions, severe error accumulation, and inadequate continuous-time dynamical representation in long-horizon motion prediction for multi-robot systems, this paper proposes PINCoDE—a Physics-Informed Neural Control Differential Equation framework. PINCoDE explicitly models continuous-time dynamics via Neural Controlled Differential Equations (Neural CDEs), incorporates physics-based constraints to ensure kinematically plausible motion, and integrates target-conditioned encoding with curriculum learning to enhance long-term stability. Crucially, the architecture scales to hundreds of agents without additional parameters. Experiments demonstrate that PINCoDE achieves an average displacement error (ADE) below 0.5 m over a 1-minute prediction horizon and reduces orientation error by 2.7× compared to analytical models at the 4-minute horizon. These results significantly improve both accuracy and generalization in long-horizon, multi-agent trajectory forecasting.

Technology Category

• Multiagent Systems: Adversarial Agents
• Intelligent Robots: Multi-Robot Systems
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Long-horizon motion forecasting for multiple autonomous robots is challenging due to non-linear agent interactions, compounding prediction errors, and continuous-time evolution of dynamics. Learned dynamics of such a system can be useful in various applications such as travel time prediction, prediction-guided planning and generative simulation. In this work, we aim to develop an efficient trajectory forecasting model conditioned on multi-agent goals. Motivated by the recent success of physics-guided deep learning for partially known dynamical systems, we develop a model based on neural Controlled Differential Equations (CDEs) for long-horizon motion forecasting. Unlike discrete-time methods such as RNNs and transformers, neural CDEs operate in continuous time, allowing us to combine physics-informed constraints and biases to jointly model multi-robot dynamics. Our approach, named PINCoDE (Physics-Informed Neural Controlled Differential Equations), learns differential equation parameters that can be used to predict the trajectories of a multi-agent system starting from an initial condition. PINCoDE is conditioned on future goals and enforces physics constraints for robot motion over extended periods of time. We adopt a strategy that scales our model from 10 robots to 100 robots without the need for additional model parameters, while producing predictions with an average ADE below 0.5 m for a 1-minute horizon. Furthermore, progressive training with curriculum learning for our PINCoDE model results in a 2.7X reduction of forecasted pose error over 4 minute horizons compared to analytical models.

Problem

• Forecasting long-horizon multi-agent trajectories with physics constraints
• Modeling continuous-time dynamics to reduce compounding prediction errors
• Scaling motion prediction from 10 to 100 agents efficiently

Innovation

• Physics-informed neural CDEs model multi-agent dynamics
• Continuous-time modeling with physics constraints for robots
• Scalable to 100 robots without extra parameters