# Calibrated Uncertainty for Informative Path Planning in Aquatic Environmental Monitoring

arXiv: https://arxiv.org/abs/2609.34577 · HTML: https://mlsanity.com/paper/2609.34577/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 18 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 7 of 7)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Deep Reinforcement Multi-agent Learning framework for Information Gathering with Local Gaussian Processes for Water Monitoring](https://mlsanity.com/paper/2401.04631/) (2024)
- [Censored Deep Reinforcement Patrolling with Information Criterion for Monitoring Large Water Resources using Autonomous Surface Vehicles](https://mlsanity.com/paper/2210.08115/) (2022)
- [Uncertainty Estimation for Deep Reconstruction in Actuatic Disaster Scenarios with Autonomous Vehicles](https://mlsanity.com/paper/2604.06387/) (2026)

## Abstract (arXiv)

Informative Path Planning for scalar field reconstruction uses predictive uncertainty to direct sensing vehicles toward maximally informative locations. Gaussian Processes provide this signal but their stationary isotropic kernels are misspecified for non-homogeneous phenomena such as oil spills, producing miscalibrated estimates that degrade planning. We investigate whether replacing the Gaussian Process with a well-calibrated Deep Ensemble improves path planning outcomes, and whether uncertainty quality interacts with the choice of planning algorithm. Five strategies (ε-Greedy, Value Greedy, Uncertainty Greedy, Monte Carlo Tree Search, and Receding Horizon Orienteering) share a common Deep Ensemble backbone trained on physics-based oil spill simulations. On held-out stochastic spill scenarios, the Deep Ensemble reduces normalised reconstruction error by 83% relative to the Gaussian Process baseline. Crucially, well-calibrated uncertainty amplifies the importance of the planning strategy: the performance gap between algorithms is negligible under miscalibrated models but becomes substantial under the ensemble, where multi-step lookahead planners outperform greedy selection by up to 32% in reconstruction error and achieve IoU above 0.85. Monte Carlo Tree Search is the recommended planner, matching Orienteering in reconstruction quality at an order-of-magnitude lower computational cost.