Recent probabilistic methods for 3D triangular meshes capture diverse shapes by differentiable mesh connectivity, but face high computational costs with increased shape details. We introduce a new differentiable mesh processing method in 2D and 3D that addresses this challenge and efficiently handles meshes with intricate structures. Additionally, we present an algorithm that adapts the mesh resolution to local geometry in 2D for efficient representation. We demonstrate the effectiveness of our approach on 2D point cloud and 3D multi-view reconstruction tasks. Visit our project page (https://sonsang.github.io/dmesh2-project) for source code and supplementary material.

In this work, we introduce the Time-Aware World Model (TAWM), a model-based approach that explicitly incorporates temporal dynamics. By conditioning on the time-step size, $\Delta t$, and training over a diverse range of $\Delta t$ values – rather than sampling at a fixed time-step – TAWM learns both high- and low-frequency task dynamics across diverse control problems. Grounded in the information-theoretic insight that the optimal sampling rate depends on a system’s underlying dynamics, this time-aware formulation improves both performance and data efficiency. Empirical evaluations show that TAWM consistently outperforms conventional models across varying observation rates in a variety of control tasks, using the same number of training samples and iterations. Our code can be found online at: github.com/anh-nn01/Time-Aware-World-Model.

We present a parallelized differentiable traffic simulator based on the Intelligent Driver Model (IDM), a car-following framework that incorporates driver behavior as key variables. Our vehicle simulator efficiently models vehicle motion, generating trajectories that can be supervised to fit real-world data. By leveraging its differentiable nature, IDM parameters are optimized using gradient-based methods. With the capability to simulate up to 2 million vehicles in real time, the system is scalable for large-scale trajectory optimization. We show that we can use the simulator to filter noise in the input trajectories (trajectory filtering), reconstruct dense trajectories from sparse ones (trajectory reconstruction), and predict future trajectories (trajectory prediction), with all generated trajectories adhering to physical laws. We validate our simulator and algorithm on several datasets including NGSIM and Waymo Open Dataset. The code is publicly available at: https://github.com/SonSang/diffidm.

In trajectory forecasting tasks for traffic, future output trajectories can be computed by advancing the ego vehicle’s state with predicted actions according to a kinematics model. By unrolling predicted trajectories via time integration and models of kinematic dynamics, predicted trajectories should not only be kinematically feasible but also relate uncertainty from one timestep to the next. While current works in probabilistic prediction do incorporate kinematic priors for mean trajectory prediction, variance is often left as a learnable parameter, despite uncertainty in one time step being inextricably tied to uncertainty in the previous time step. In this paper, we show simple and differentiable analytical approximations describing the relationship between variance at one timestep and that at the next with the kinematic bicycle model. In our results, we find that encoding the relationship between variance across timesteps works especially well in unoptimal settings, such as with small or noisy datasets. We observe up to a 50% performance boost in partial dataset settings and up to an 8% performance boost in large-scale learning compared to previous kinematic prediction methods on SOTA trajectory forecasting architectures out-of-the-box, with no fine-tuning.

We present a differentiable representation, DMesh, for general 3D triangular meshes. DMesh considers both the geometry and connectivity information of a mesh. In our design, we first get a set of convex tetrahedra that compactly tessellates the domain based on Weighted Delaunay Triangulation (WDT), and select triangular faces on the tetrahedra to define the final mesh. We formulate probability of faces to exist on the actual surface in a differentiable manner based on the WDT. This enables DMesh to represent meshes of various topology in a differentiable way, and allows us to reconstruct the mesh under various observations, such as point clouds and multi-view images using gradient-based optimization. We publicize the source code and supplementary material at our project page (https://sonsang.github.io/dmesh-project).

While there have been advancements in autonomous driving control and traffic simulation, there have been little to no works exploring their unification with deep learning. Works in both areas seem to focus on entirely different exclusive problems, yet traffic and driving are inherently related in the real world. In this paper, we present Traffic-Aware Autonomous Driving (TrAAD), a generalizable distillation-style method for traffic-informed imitation learning that directly optimizes for faster traffic flow and lower energy consumption. TrAAD focuses on the supervision of speed control in imitation learning systems, as most driving research focuses on perception and steering. Moreover, our method addresses the lack of co-simulation between traffic and driving simulators and provides a basis for directly involving traffic simulation with autonomous driving in future work. Our results show that, with information from traffic simulation involved in the supervision of imitation learning methods, an autonomous vehicle can learn how to accelerate in a fashion that is beneficial for traffic flow and overall energy consumption for all nearby vehicles.

Place recognition plays an important role in multi-robot collaborative perception, such as aerial-ground search and rescue, in order to identify the same place they have visited. Recently, approaches based on semantics showed the promising performance to address cross-view and cross-modal challenges in place recognition, which can be further categorized as graph-based and geometric-based methods. However, both methods have shortcomings, including ignoring geometric cues and affecting by large non-overlapped regions between observations. In this paper, we introduce a novel approach that integrates semantic graph matching and distance fields (DF) matching for cross-view and cross-modal place recognition. Our method uses a graph representation to encode visual-spatial cues of semantics and uses a set of class-wise DFs to encode geometric cues of a scene. Then, we formulate place recognition as a two-step matching problem. We first perform semantic graph matching to identify the correspondence of semantic objects. Then, we estimate the overlapped regions based on the identified correspondences and further align these regions to compute their geometric-based DF similarity. Finally, we integrate graph-based similarity and geometry-based DF similarity to match places. We evaluate our approach over two public benchmark datasets, including KITTI and AirSim. Compared with the previous methods, our approach achieves around 10% improvement in ground-ground place recognition in KITTI and 35% improvement in aerial-ground place recognition in AirSim.

We introduce a novel policy learning method that integrates analytical gradients from differentiable environments with the Proximal Policy Optimization (PPO) algorithm. To incorporate analytical gradients into the PPO framework, we introduce the concept of an α-policy that stands as a locally superior policy. By adaptively modifying the α value, we can effectively manage the influence of analytical policy gradients during learning. To this end, we suggest metrics for assessing the variance and bias of analytical gradients, reducing dependence on these gradients when high variance or bias is detected. Our proposed approach outperforms baseline algorithms in various scenarios, such as function optimization, physics simulations, and traffic control environments. Our code can be found online: https://github.com/SonSang/gippo.

We introduce a novel differentiable hybrid traffic simulator , which simulates traffic using a hybrid model of both macroscopic and microscopic models and can be directly integrated into a neural network for traffic control and flow optimization. This is the first differentiable traffic simulator for macroscopic and hybrid models that can compute gradients for traffic states across time steps and inhomogeneous lanes. To compute the gradient flow between two types of traffic models in a hybrid framework, we present a novel intermediate conversion component that bridges the lanes in a differentiable manner as well. We also show that we can use analytical gradients to accelerate the overall process and enhance scalability. Thanks to these gradients, our simulator can provide more efficient and scalable solutions for complex learning and control problems posed in traffic engineering than other existing algorithms. Refer to https://sites.google.com/umd.edu/diff-hybrid-traffic-sim for our project.

Abstract We present a highly efficient algorithm for computing the minimum distance between two solids of revolution, each of which is defined by a planar cross‐section region and a rotation axis. The boundary profile curve for the cross‐section is first approximated by a bounding volume hierarchy (BVH) of fat arcs. By rotating the fat arcs around the axis, we generate the BVH of fat tori that bounds the surface of revolution. The minimum distance between two solids of revolution is then computed very efficiently using the distance between fat tori, which can be boiled down to the minimum distance computation for circles in the three‐dimensional space. Our circle‐based approach to the solids of revolution has distinctive features of geometric simplification. The main advantage is in the effectiveness of our approach in handling the complex cases where the minimum distance is obtained in non‐convex regions of the solids under consideration. Though we are dealing with a geometric problem for solids, the algorithm actually works in a computational style similar to that of handling planar curves. Compared with conventional BVH‐based methods, our algorithm demonstrates outperformance in computing speed, often 10–100 times faster. Moreover, the minimum distance can be computed very efficiently for the solids of revolution under deformation, where the dynamic reconstruction of fat arcs dominates the overall computation time and takes a few milliseconds.