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

• URL: http://arxiv.org/abs/2510.00401v1
• Date: Wed, 01 Oct 2025 01:27:07 GMT
• Title: Physics-Informed Neural Controlled Differential Equations for Scalable Long Horizon Multi-Agent Motion Forecasting
• Authors: Shounak Sural, Charles Kekeh, Wenliang Liu, Federico Pecora, Mouhacine Benosman,
• Abstract summary: Long-horizon motion forecasting for multiple autonomous robots is challenging due to non-linear agent interactions.<n>We develop a model based on neural Controlled Differential Equations (CDEs) for long-horizon motion forecasting.<n> PINCoDE is conditioned on future goals and enforces physics constraints for robot motion over extended periods of time.
• Score: 3.795837769531959
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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