# ProTerrain: Probabilistic Physics-Informed Rough Terrain World Modeling

arXiv: https://arxiv.org/abs/2510.19364 · HTML: https://mlsanity.com/paper/2510.19364/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in World models for navigation, one of 11 directions in World models.
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 22 Oct 2025.

## Placed in

- World models / [World models for navigation](https://mlsanity.com/wm/world-models-for-navigation/)

## Builds on (most cited first, 13 of 13)

- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Lift, Splat, Shoot: Encoding Images From Arbitrary Camera Rigs by Implicitly Unprojecting to 3D](https://mlsanity.com/paper/2008.05711/) (2020)
- [Calibrated Reliable Regression using Maximum Mean Discrepancy](https://mlsanity.com/paper/2006.10255/) (2020)
- [Locomotion Policy Guided Traversability Learning using Volumetric Representations of Complex Environments](https://mlsanity.com/paper/2203.15854/) (2022)
- [Multivariate Uncertainty in Deep Learning](https://mlsanity.com/paper/1910.14215/) (2019)
- [STEP: Stochastic Traversability Evaluation and Planning for Risk-Aware Off-road Navigation](https://mlsanity.com/paper/2103.02828/) (2021)
- [How Does It Feel? Self-Supervised Costmap Learning for Off-Road Vehicle Traversability](https://mlsanity.com/paper/2209.10788/) (2022)
- [Learning Risk-aware Costmaps for Traversability in Challenging Environments](https://mlsanity.com/paper/2107.11722/) (2021)
- [Traversability Analysis for Autonomous Driving in Complex Environment: A LiDAR-based Terrain Modeling Approach](https://mlsanity.com/paper/2307.02060/) (2023)
- [PIETRA: Physics-Informed Evidential Learning for Traversing Out-of-Distribution Terrain](https://mlsanity.com/paper/2409.03005/) (2024)
- [Real-time Neural Dense Elevation Mapping for Urban Terrain with Uncertainty Estimations](https://mlsanity.com/paper/2208.03467/) (2022)
- [UNRealNet: Learning Uncertainty-Aware Navigation Features from High-Fidelity Scans of Real Environments](https://mlsanity.com/paper/2407.08720/) (2024)
- [MonoForce: Self-supervised Learning of Physics-informed Model for Predicting Robot-terrain Interaction](https://mlsanity.com/paper/2309.09007/) (2023)

## Abstract (arXiv)

Uncertainty-aware robot motion prediction is crucial for downstream traversability estimation and safe autonomous navigation in unstructured, off-road environments, where terrain is heterogeneous and perceptual uncertainty is high. Most existing methods assume deterministic or spatially independent terrain uncertainties, ignoring the inherent local correlations of 3D spatial data and often producing unreliable predictions. In this work, we introduce an efficient probabilistic framework that explicitly models spatially correlated aleatoric uncertainty over terrain parameters as a probabilistic world model and propagates this uncertainty through a differentiable physics engine for probabilistic trajectory forecasting. By leveraging structured convolutional operators, our approach provides high-resolution multivariate predictions at manageable computational cost. Experimental evaluation on a publicly available dataset shows significantly improved uncertainty estimation and trajectory prediction accuracy over aleatoric uncertainty estimation baselines.