# PIETRA: Physics-Informed Evidential Learning for Traversing Out-of-Distribution Terrain

arXiv: https://arxiv.org/abs/2409.03005 · HTML: https://mlsanity.com/paper/2409.03005/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 52 references that are in the map.
- First posted on arXiv 4 Sep 2024.

## Builds on (most cited first, 30 of 35)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimation](https://mlsanity.com/paper/2110.03051/) (2021)
- [Squared Earth Mover's Distance-based Loss for Training Deep Neural Networks](https://mlsanity.com/paper/1611.05916/) (2016)
- [Fast Traversability Estimation for Wild Visual Navigation](https://mlsanity.com/paper/2305.08510/) (2023)
- [V-STRONG: Visual Self-Supervised Traversability Learning for Off-road Navigation](https://mlsanity.com/paper/2312.16016/) (2023)
- [TerrainNet: Visual Modeling of Complex Terrain for High-speed, Off-road Navigation](https://mlsanity.com/paper/2303.15771/) (2023)
- [STEP: Stochastic Traversability Evaluation and Planning for Risk-Aware Off-road Navigation](https://mlsanity.com/paper/2103.02828/) (2021)
- [Learning Off-Road Terrain Traversability with Self-Supervisions Only](https://mlsanity.com/paper/2305.18896/) (2023)
- [RoadRunner -- Learning Traversability Estimation for Autonomous Off-road Driving](https://mlsanity.com/paper/2402.19341/) (2024)
- [Self-Supervised Traversability Prediction by Learning to Reconstruct Safe Terrain](https://mlsanity.com/paper/2208.01329/) (2022)
- [EVORA: Deep Evidential Traversability Learning for Risk-Aware Off-Road Autonomy](https://mlsanity.com/paper/2311.06234/) (2023)
- [Risk-Aware Off-Road Navigation via a Learned Speed Distribution Map](https://mlsanity.com/paper/2203.13429/) (2022)
- [Toward Wheeled Mobility on Vertically Challenging Terrain: Platforms, Datasets, and Algorithms](https://mlsanity.com/paper/2303.00998/) (2023)
- [SEEK: Semantic Reasoning for Object Goal Navigation in Real World Inspection Tasks](https://mlsanity.com/paper/2405.09822/) (2024)
- [Visual Representation Learning for Preference-Aware Path Planning](https://mlsanity.com/paper/2109.08968/) (2021)
- [Physics-Inspired Temporal Learning of Quadrotor Dynamics for Accurate Model Predictive Trajectory Tracking](https://mlsanity.com/paper/2206.03305/) (2022)
- [Probabilistic Traversability Model for Risk-Aware Motion Planning in Off-Road Environments](https://mlsanity.com/paper/2210.00153/) (2022)
- [Learning to Model and Plan for Wheeled Mobility on Vertically Challenging Terrain](https://mlsanity.com/paper/2306.11611/) (2023)
- [MEM: Multi-Modal Elevation Mapping for Robotics and Learning](https://mlsanity.com/paper/2309.16818/) (2023)
- [RCA: Ride Comfort-Aware Visual Navigation via Self-Supervised Learning](https://mlsanity.com/paper/2207.14460/) (2022)
- [Pixel to Elevation: Learning to Predict Elevation Maps at Long Range using Images for Autonomous Offroad Navigation](https://mlsanity.com/paper/2401.17484/) (2024)
- [WayFASTER: a Self-Supervised Traversability Prediction for Increased Navigation Awareness](https://mlsanity.com/paper/2402.00683/) (2024)
- [Model Predictive Control for Aggressive Driving Over Uneven Terrain](https://mlsanity.com/paper/2311.12284/) (2023)
- [PIAug -- Physics Informed Augmentation for Learning Vehicle Dynamics for Off-Road Navigation](https://mlsanity.com/paper/2311.00815/) (2023)
- [Terrain-Attentive Learning for Efficient 6-DoF Kinodynamic Modeling on Vertically Challenging Terrain](https://mlsanity.com/paper/2403.16419/) (2024)
- [PhysORD: A Neuro-Symbolic Approach for Physics-infused Motion Prediction in Off-road Driving](https://mlsanity.com/paper/2404.01596/) (2024)

## Built on by (most cited first, 8 of 8)

- [PhysGS: Bayesian-Inferred Gaussian Splatting for Physical Property Estimation](https://mlsanity.com/paper/2511.18570/) (2025)
- [Watch Your STEPP: Semantic Traversability Estimation using Pose Projected Features](https://mlsanity.com/paper/2501.17594/) (2025)
- [Wheeled Lab: Modern Sim2Real for Low-cost, Open-source Wheeled Robotics](https://mlsanity.com/paper/2502.07380/) (2025)
- [T-CBF: Traversability-based Control Barrier Function to Navigate Vertically Challenging Terrain](https://mlsanity.com/paper/2503.06083/) (2025)
- [Anomalies by Synthesis: Anomaly Detection using Generative Diffusion Models for Off-Road Navigation](https://mlsanity.com/paper/2505.22805/) (2025)
- [ProTerrain: Probabilistic Physics-Informed Rough Terrain World Modeling](https://mlsanity.com/paper/2510.19364/) (2025)
- [SyNeT: Synthetic Negatives for Traversability Learning](https://mlsanity.com/paper/2602.00814/) (2026)
- [Continual Learning for Traversability Prediction with Uncertainty-Aware Adaptation](https://mlsanity.com/paper/2609.17141/) (2026)

## Abstract (arXiv)

Self-supervised learning is a powerful approach for developing traversability models for off-road navigation, but these models often struggle with inputs unseen during training. Existing methods utilize techniques like evidential deep learning to quantify model uncertainty, helping to identify and avoid out-of-distribution terrain. However, always avoiding out-of-distribution terrain can be overly conservative, e.g., when novel terrain can be effectively analyzed using a physics-based model. To overcome this challenge, we introduce Physics-Informed Evidential Traversability (PIETRA), a self-supervised learning framework that integrates physics priors directly into the mathematical formulation of evidential neural networks and introduces physics knowledge implicitly through an uncertainty-aware, physics-informed training loss. Our evidential network seamlessly transitions between learned and physics-based predictions for out-of-distribution inputs. Additionally, the physics-informed loss regularizes the learned model, ensuring better alignment with the physics model. Extensive simulations and hardware experiments demonstrate that PIETRA improves both learning accuracy and navigation performance in environments with significant distribution shifts.