NVFi: Neural Velocity Fields for 3D Physics Learning from Dynamic Videos

In this paper, we aim to model 3D scene dynamics from multi-view videos. Unlike the majority of existing works which usually focus on the common task of novel view synthesis within the training time period, we propose to simultaneously learn the geometry, appearance, and physical velocity of 3D scenes only from video frames, such that multiple desirable applications can be supported, including future frame extrapolation, unsupervised 3D semantic scene decomposition, and dynamic motion transfer. Our method consists of three major components, 1) the keyframe dynamic radiance field, 2) the interframe velocity field, and 3) a joint keyframe and interframe optimization module which is the core of our framework to effectively train both networks. To validate our method, we further introduce two dynamic 3D datasets: 1) Dynamic Object dataset, and 2) Dynamic Indoor Scene dataset. We conduct extensive experiments on multiple datasets, demonstrating the superior performance of our method over all baselines, particularly in the critical tasks of future frame extrapolation and unsupervised 3D semantic scene decomposition.

Probabilistic Symmetry for Improved Trajectory Forecasting

Trajectory prediction is a core AI problem with broad applications in robotics and autonomous driving. While most existing works focus on deterministic prediction, producing probabilistic forecasts to quantify prediction uncertainty is critical for downstream decision-making tasks such as risk assessment, motion planning, and safety guarantees. We introduce a new metric, mean regional score (MRS), to evaluate the quality of probabilistic trajectory forecasts. We propose a novel probabilistic trajectory prediction model, Probabilistic Equivariant Continuous COnvolution (PECCO) and show that leveraging symmetry, specifically rotation equivariance, can improve the predictions' accuracy as well as coverage. On both vehicle and pedestrian datasets, PECCO shows state-of-the-art prediction performance and improved calibration compared to baselines.

Trajectory Prediction using Equivariant Continuous Convolution

Trajectory prediction is a critical part of many AI applications, for example, the safe operation of autonomous vehicles. However, current methods are prone to making inconsistent and physically unrealistic predictions. We leverage insights from fluid dynamics to overcome this limitation by considering internal symmetry in trajectories. We propose a novel model, Equivariant Continous COnvolution (ECCO) for improved trajectory prediction. ECCO uses rotationally-equivariant continuous convolutions to embed the symmetries of the system. On two real-world vehicle and pedestrian trajectory datasets, ECCO attains competitive accuracy with significantly fewer parameters. It is also more sample efficient, generalizing automatically from few data points in any orientation. Lastly, ECCO improves generalization with equivariance, resulting in more physically consistent predictions. Our method provides a fresh perspective towards increasing trust and transparency in deep learning models.