# Gradient-based Trajectory Optimization with Parallelized Differentiable Traffic Simulation

arXiv: https://arxiv.org/abs/2412.16750 · HTML: https://mlsanity.com/paper/2412.16750/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 59 references that are in the map.
- First posted on arXiv 21 Dec 2024.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [CARLA: An Open Urban Driving Simulator](https://mlsanity.com/paper/1711.03938/) (2017)
- [Large Scale Interactive Motion Forecasting for Autonomous Driving : The Waymo Open Motion Dataset](https://mlsanity.com/paper/2104.10133/) (2021)
- [Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulation](https://mlsanity.com/paper/2106.13281/) (2021)
- [Wayformer: Motion Forecasting via Simple & Efficient Attention Networks](https://mlsanity.com/paper/2207.05844/) (2022)
- [Motion Transformer with Global Intention Localization and Local Movement Refinement](https://mlsanity.com/paper/2209.13508/) (2022)
- [MultiPath++: Efficient Information Fusion and Trajectory Aggregation for Behavior Prediction](https://mlsanity.com/paper/2111.14973/) (2021)
- [Waymax: An Accelerated, Data-Driven Simulator for Large-Scale Autonomous Driving Research](https://mlsanity.com/paper/2310.08710/) (2023)
- [MotionLM: Multi-Agent Motion Forecasting as Language Modeling](https://mlsanity.com/paper/2309.16534/) (2023)
- [MTR++: Multi-Agent Motion Prediction with Symmetric Scene Modeling and Guided Intention Querying](https://mlsanity.com/paper/2306.17770/) (2023)
- [CityFlow: A City-Scale Benchmark for Multi-Target Multi-Camera Vehicle Tracking and Re-Identification](https://mlsanity.com/paper/1903.09254/) (2019)
- [A Differentiable Physics Engine for Deep Learning in Robotics](https://mlsanity.com/paper/1611.01652/) (2016)
- [Accelerated Policy Learning with Parallel Differentiable Simulation](https://mlsanity.com/paper/2204.07137/) (2022)
- [Scalable Differentiable Physics for Learning and Control](https://mlsanity.com/paper/2007.02168/) (2020)
- [GPUDrive: Data-driven, multi-agent driving simulation at 1 million FPS](https://mlsanity.com/paper/2408.01584/) (2024)
- [Efficient Differentiable Simulation of Articulated Bodies](https://mlsanity.com/paper/2109.07719/) (2021)
- [Imagining The Road Ahead: Multi-Agent Trajectory Prediction via Differentiable Simulation](https://mlsanity.com/paper/2104.11212/) (2021)
- [Machine Learning for Autonomous Vehicle's Trajectory Prediction: A comprehensive survey, Challenges, and Future Research Directions](https://mlsanity.com/paper/2307.07527/) (2023)
- [EDA: Evolving and Distinct Anchors for Multimodal Motion Prediction](https://mlsanity.com/paper/2312.09501/) (2023)
- [ControlMTR: Control-Guided Motion Transformer with Scene-Compliant Intention Points for Feasible Motion Prediction](https://mlsanity.com/paper/2404.10295/) (2024)
- [Differentiable Agent-Based Simulation for Gradient-Guided Simulation-Based Optimization](https://mlsanity.com/paper/2103.12476/) (2021)
- [Differentiable Hybrid Traffic Simulation](https://mlsanity.com/paper/2210.08046/) (2022)
- [Gradient Informed Proximal Policy Optimization](https://mlsanity.com/paper/2312.08710/) (2023)
- [Scaling Motion Forecasting Models with Ensemble Distillation](https://mlsanity.com/paper/2404.03843/) (2024)
- [MOSS: A Large-scale Open Microscopic Traffic Simulation System](https://mlsanity.com/paper/2405.12520/) (2024)
- [Traffic-Aware Autonomous Driving with Differentiable Traffic Simulation](https://mlsanity.com/paper/2210.03772/) (2022)

## Built on by (most cited first, 2 of 2)

- [Quantifying and Modeling Driving Styles in Trajectory Forecasting](https://mlsanity.com/paper/2503.04994/) (2025)
- [Ultra-fast Traffic Nowcasting and Control via Differentiable Agent-based Simulation](https://mlsanity.com/paper/2603.25068/) (2026)

## Abstract (arXiv)

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.