Map Uncertainty

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5 papers in the last four weeks, against 1 the four weeks before. 0.1% of all new papers.

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Latest papers 18

Sep 30, 2026cs.AI

Belief-Aware Multi-Agent Path Finding under Map Uncertainty

Multi-Agent Path Finding (MAPF) aims to find collision-free paths for multiple agents in a shared environment. Classical MAPF assumes that all static obstacles are known in advance, but real-world environments can change unexpectedly due to fallen objects, spills, or other local disturbances. When such changes are spatially correlated, an observation can inform traversability estimates beyond the observed location. Prior approaches address uncertainty in traversability through contingent plans or replanning based on direct observations, but do not leverage this spatial dependence to infer the traversability of nearby unobserved locations. As a result, they cannot use one observation to anticipate nearby unobserved obstacles that may cause costly rerouting later. We focus on Belief-Aware MAPF, where map discrepancies are fixed during execution but initially unknown, and observations can be informative beyond the observed location. We propose Multi-Agent Gaussian belief Inference for Coordination (MAGIC), a framework that updates a shared belief about traversability online based on agents' observations. MAGIC uses a Gaussian Markov Random Field and Gaussian Belief Propagation to approximately infer traversability and construct detour-aware costs for standard MAPF planners. Our experiments on MAPF benchmarks show that MAGIC reduces the executed sum of costs compared to existing approaches on 96.3% of instances, across several planner families and teams of up to 800 agents, demonstrating its applicability to large-scale MAPF problems.

Viraj Parimi, Shao-Hung Chan, Han Zhang +2

Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 01239. · Symbotic Inc., Wilmington, MA 01887, USA

Multi-Agent Path Finding Path Planning Traversability Map Uncertainty Path

Sep 21, 2026cs.CV

Ev-YOLO: Uncertainty-Aware Object Detection via a Unified Evidential Formulation

Reliable uncertainty estimation is essential for deploying object detectors in autonomous systems operating in uncertain environments. Evidential Deep Learning (EDL) provides a principled framework for uncertainty-aware classification by representing network outputs as evidence and interpreting predictions through subjective logic. However, existing evidential object detectors typically combine evidential classification with regression uncertainty models that do not share the same theoretical foundation. In this work, we propose an evidential version of YOLOv8 in which both classification and bounding-box regression are formulated within a common evidential framework. Our approach exploits YOLOv8's distribution-based bounding-box representation, allowing the evidential formulation to be applied not only to classification but also to localisation. As a result, both tasks produce belief, uncertainty, and probability estimates that can be interpreted within the Dempster--Shafer framework. Experiments on KITTI, MUSES, and nuScenes show that the resulting detector remains broadly competitive with standard YOLOv8 in terms of detection accuracy while providing a localisation uncertainty that effectively discriminates between correct and erroneous detections. Moreover, this uncertainty becomes increasingly discriminative under domain shift.

Simon Barbarit-Gaboriau, Hind Laghmara, Rémi Boutteau +1

LITIS - STI, INSA Rouen Normandie · INSA Rouen Normandie, Univ Rouen Normandie, Univ Le Havre Normandie, Normandie Univ, LITIS UR 4108, F-76000 Rouen, France. · LITIS - STI +1

Yolo26 Uncertainty-Aware Classification Evidential Uncertainty Map Uncertainty Objects

Sep 15, 2026stat.ML

Bracketing Uncertainty in Clustering Under the Manifold Hypothesis

The manifold hypothesis suggests a natural criterion for clustering: partition data according to the manifold component from which each point is drawn. Whether two components are separable depends on a geometric tradeoff: the ambient separation between components versus the largest gap in sampling. In practice, this tradeoff is rarely assessed explicitly, leading standard methods to over-commit to a single clustering assignment even when the data do not support a unique answer. We formalize this tradeoff by combining intrinsic manifold geometry (volume growth and reach) with sample-level quantities (fill distance and density), yielding a threshold phenomenon for mutual-

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-nearest-neighbor graphs: when the offset-to-fill ratio exceeds a conservative upper threshold, component separation is preserved; below a lower threshold, components fuse. The gap between these thresholds defines a geometric uncertainty zone in which the number of clusters is not identifiable from the data. Nevertheless, conventional approaches still seek one: sweeping parameters (an engineering approach) or fitting a generative mixture model (a model-based approach). Rather than forcing a single estimate of the number of clusters, we propose Manifold-Based Clustering (MBC), which returns an explicit bracket interval to quantify the underlying data uncertainty. This bracket acts as an empirically calibrated diagnostic: it narrows when a single resolution is supported, widens when multiple resolutions coexist, and collapses to one when no separated structure is detectable. Empirically, we find that many real datasets lie within the uncertainty zone rather than admitting one clear answer. Our results suggest that ambiguity in cluster number is often intrinsic, and should be quantified rather than resolved.

Savik Kinger, Luciano Dyballa, Steven W. Zucker

Department of Computer Science Yale University · School of Science & Technology IE University · Depts. of Computer Science and Biomedical Engineering Wu Tsai Institute Yale University

Clustering Cluster Data Manifold Map Uncertainty Mixture Models Input Uncertainties+1

Sep 14, 2026cs.CV

SURE-Map: Self-Correcting Streaming Geometric Foundation Models

Streaming geometric foundation models are emerging as a compelling alternative to SLAM systems. Yet this streaming nature introduces a fundamental issue: each prediction is made from limited context, which is vulnerable to dynamic objects and weak textures. Small local errors accumulate into severe geometric distortion and long-horizon scale drift. We argue that reliable streaming reconstruction requires geometric foundation models to be not only predictive, but also self-correcting. We introduce SURE-Map, a self-correcting framework built upon two complementary principles. First, we explicitly model cross-view geometric uncertainty. Unlike conventional depth or point confidence, which primarily reflects the reliability of individual-view prediction, our uncertainty directly measures whether the jointly predicted pose and depth induce geometrically consistent cross-view pixel correspondences. Second, because local correction alone cannot eliminate slowly accumulating scale errors, we introduce multi-timescale self-correction: fast consecutive-frame inference preserves streaming efficiency, while sparse keyframe-window inference provides longer-range geometric evidence to periodically recalibrate the scale of recent trajectories. SURE-Map establishes new state-of-the-art performance for online feed-forward reconstruction across long-horizon benchmarks, reducing ATE-RMSE from 24.00 to 17.24 m on KITTI, 5.11 to 4.74 m on Oxford Spires, and 31.37 to 28.58 m on VBR, with further improvements to 15.17, 4.63, and 22.12 m when incorporating loop-closure refinement. Project page: https://mingkai-liu.github.io/projects/sure-map/.

Mingkai Liu, Hao Zhao, Xingxing Zuo

Mohamed bin Zayed University of Artificial Intelligence (MBZUAI), UAE. · Peking University, China. · Tsinghua University, China.

Simultaneous Localization And Mapping 3D Foundation Models Map Uncertainty Streaming

Sep 11, 2026cs.LG

Estimating Inconsistency Response Surfaces under Uncertainty in Cyber-Physical System Development

Cyber-Physical Systems (CPS) are commonly represented through multiple interconnected models. During development, CPS consistency requires that shared model elements remain compatible across these models. Uncertainty, for example, due to sensor noise or model abstraction, changes the admissible values of model elements and can introduce inconsistencies, i.e., situations in which models can no longer be jointly satisfied. While existing approaches can determine consistency for a given uncertainty configuration, they provide limited support for systematically exploring, analyzing, and explaining inconsistency across large uncertainty spaces. We address this challenge by reformulating inconsistency as an intervention response modeling problem. Using Saltelli sampling and multi-fidelity Monte Carlo estimation, we generate intervention-response datasets and train a surrogate model that directly predicts inconsistency from the propagated uncertainty geometry. Experiments on 48 scenarios and 10 CPS domains show that the surrogate matches Monte Carlo estimates while reducing evaluation time from milliseconds to microseconds, enabling orders-of-magnitude more response-surface evaluations within fixed computational budgets. Building on the learned response surfaces, we perform sensitivity analysis to identify dominant uncertainty drivers and introduce a gradient-based consistency recourse method to determine minimal uncertainty interventions that restore consistency. The results show that inconsistency under uncertainty can be effectively learned, analyzed, and repaired through response-surface modeling, providing a scalable foundation for uncertainty-aware consistency management in CPS development.

Johannes Mäkelburg, Tim Schwabe, Maribel Acosta

Technische Universität München Munich, Germany

Cyber-Physical System Map Uncertainty Uncertainty Responses

Sep 8, 2026physics.geo-ph

Bayesian deep learning integration of geophysical and drilling data for 3D prediction of copper mineralization and drill targeting: a case study from the Kogodai prospect, Rudny Altai

Exploration drill targeting in structurally complex terranes is hindered by sparse sampling, heterogeneous datasets, and the ambiguity of geophysical inversions. Here, we present an uncertainty-aware 3D workflow for the acceleration of time-to-discovery in brownfield explorations and apply it to the Kogodai prospect in the Rudny Altai metallogenic province. We jointly analyse existing drilling and geophysical data in a comprehensive approach, revealing hidden patterns in already available data. Drillholes and trenches were desurveyed to a common 3D reference frame, and assays were composited to a consistent spatial support to facilitate joint modelling with geophysical inputs. We develop Bayesian deep-learning models to predict 3D fields of Cu grade together with chargeability and apparent resistivity while quantifying epistemic uncertainty via Monte Carlo sampling. The original contribution of this work is to treat the problem not as pointwise regression between co-located observations, but as joint learning of spatially continuous 3D fields from sparse, heterogeneous exploration evidence. The resulting 3D predictions delineate a principal mineralized trend and several localized candidate zones that coincide with elevated induced polarization (IP) responses, while uncertainty mapping highlights where predictions are robust versus where additional drilling would be most informative. The continuous Cu-grade field can also be thresholded to produce binary prospectivity maps, allowing the sensitivity of target delineation to the chosen cutoff to be evaluated. The outputs are intended for qualitative interpretation and risk-aware drill targeting rather than resource estimation, and we discuss key limitations arising from incomplete provenance metadata for geophysical products and heterogeneity of historical sampling.

Margarita Veshchezerova, Egor Barashov, Evgenii Gusev +4

Terra Quantum AG, Kornhausstrasse 25, 9000, St. Gallen, Switzerland · Kogodai Joint Venture LLP, Gorky Street 46, 070004, Ust-Kamenogorsk, Kazakhstan

Lithology Classification Drilling Data Geological Semantic Understanding Map Uncertainty Cogadapt

Aug 12, 2026cs.CV

Evaluating and Calibrating Diffusion Model-derived Uncertainty for Quantitative MRI Mapping

Quantitative MRI (qMRI) provides standardised tissue parameter maps, but the reliability of deep learning-based qMRI mapping methods is often not explicitly characterised. In this work we systematically evaluate uncertainty maps for quantitative MRI derived from multiple inferences of a data-consistent diffusion model-based qMRI framework. Evaluation on synthetic test data assessed error-awareness, high-error detection, selective prediction, and Gaussian interval calibration. Diffusion model-derived uncertainty was positively associated with the mapping error, while risk-coverage analysis showed that excluding high-uncertainty voxels reduced the retained error. However, the raw uncertainty was poorly calibrated for quantitative interval interpretation. Calibration was substantially improved using a post-hoc procedure combining prediction-value-dependent bias correction with scalar uncertainty scaling. Qualitative evaluation on a healthy volunteer showed spatially meaningful uncertainty patterns. These results indicate that diffusion model-derived uncertainty is informative for reliability assessment and selective prediction, but requires calibration for quantitative interval interpretation.

Shishuai Wang, Stefan Klein, Juan A. Hernandez-Tamames +1

Department of Radiology and Nuclear Medicine, Erasmus MC, Rotterdam, The Netherlands · Department of Imaging Physics, TU Delft, Delft, The Netherlands

Map Uncertainty Magnetic Resonance Imaging Pixel-Level Prediction Tissue

Jun 16, 2026cs.LG

Geometry-Aware Post-Hoc Uncertainty Quantification in Operator Learning

Neural operators provide fast surrogates for PDEs but their deterministic predictions limit their use in tasks requiring uncertainty quantification (UQ), especially under geometric variability. Existing approaches primarily model uncertainty in network parameters, largely overlooking the geometry-aware representations learned by the operator itself. We propose REEF-GP (Residual on Embedded Features Gaussian Process), a post-hoc UQ framework that fits a GP to the residuals of a frozen neural operator whose internal embeddings define the kernel feature space. Rather than learning a separate feature map, REEF-GP adapts the operator's intrinsic coordinate-feature representations to construct geometry-aware uncertainties. To ensure stability and scalability on unstructured domains, REEF-GP incorporates spectral-normalized projections, heteroscedastic geometry-aware noise, and efficient subset-based training that avoids restrictive low-rank approximations. Across five PDE benchmarks with varying geometries, REEF-GP preserves predictive accuracy while achieving calibrated uncertainty estimates competitive with deep ensembles but at a fraction of their cost. Our approach remains robust under geometric distribution shift, with uncertainty concentrating in physically meaningful regions (e.g., shock fronts). Our results demonstrate that accurate and scalable post-hoc UQ for neural operators can be achieved directly in their learned feature space, offering a practical alternative to parameter-centric approaches.

Oriol Vendrell-Gallart, Nima Negarandeh, Ramin Bostanabad

Department of Mechanical and Aerospace Engineering University of California, Irvine Irvine, CA 92617

Neural Operators Uncertainty Quantification Map Uncertainty Gaussian Process Partial Differential Equations Post-Hoc

Jun 2, 2026cs.LG

Integrating Local and Global Entropy for Uncertainty Quantification in LLMs

Large language models hallucinate confidently, making uncertainty quantification (UQ) essential for reliable deployment. Existing methods rely predominantly on token-level signals, leaving the geometric structure of intermediate hidden states underused. In this paper, we take the geometric complexity of hidden-state matrices as a measure of the global uncertainty of LLMs, while treating token-level uncertainty estimation as a local metric. We show that hidden-state geometric entropy (global uncertainty) and token-level entropy (local uncertainty) are statistically near-orthogonal, capturing distinct failure regimes for reliability prediction. In particular, global geometry recovers the confident-but-wrong failure mode that local signals systematically miss. Building on this, we propose Global-Local Uncertainty (GLU), an unsupervised, single-pass score that fuses the two signals via a multiplicative gate. Across three model families and six benchmarks, GLU matches or outperforms all unsupervised baselines while requiring only a single forward pass and remaining length-normalized and architecture-agnostic.

Johanne Medina, Tianyi Zhou, Keivin Isufaj +2

Qatar Computing Research Institute, HBKU Doha, Qatar · KTH Royal Institute of Technology Stockholm, Sweden

Large Language Model Uncertainty Uncertainty Quantification Map Uncertainty Entropy Token-Level Uncertainty

May 24, 2026cs.CG

A Geometric Gaussian Mixture Representation of Plane Curves

We introduce a user defined probabilistic polygonal representation for plane curves. Given a curve, we select vertices on the curve and connect consecutive vertices by line segments to obtain a polygonal approximation. Each segment is equipped with a user defined uncertainty parameter in the normal direction. This yields a collection of thin probabilistic geometric primitives that retain the geometrz of the underlying curve while extending it beyond the idealized deterministic one dimensional formulation. For each segment, we define a Random Variable that is uniform distributed in the tangent direction of the segment and Gaussian distributed in the normal direction of the segment. By matching the first and the second central moments, this construction induces a Gaussian component whose mean lies at the segment midpoint and whose covariance encodes both tangential and normal uncertainty. Combining the segment wise components with appropriate weights yields a Gaussian Mixture Model (GMM) representation of the user defined probabilistic polygonal representation of the plane curve. The proposed framework provides an analytically tractable probabilistic model that preserves local geometry, and uncertainty in the normal direction. It applies to smooth, closed, open, non regular, and self intersecting plane curves, allows adaptive discretization and varying uncertainty in the normal direction, and as a result supports uncertainty aware geometric modeling. Experiments on a collection of canonical plane curves show that the resulting GMM capture local tangent, local normal, and local arc length; resulting in the global shape of the underlying curves to be truthfully captured as well. The representation is particularly relevant for applications in uncertainty aware CAD and digital twins, probabilistic obstacle modeling in robotics, and probabilistic trajectory planning.

Ali Darijani, Benedikt Stratmann, Jürgen Beyerer

Fraunhofer IOSB · KIT, IES

Map Uncertainty Curves Gaussian Primitives Uncertainty Mixtures

May 19, 2026cs.RO

Conflict-Aware Active Perception and Control in 3D Gaussian Splatting Fields via Control Barrier Functions

Active perception in uncertain environments requires robots to navigate safely while acquiring informative observations to reduce map uncertainty. These objectives inherently conflict, as informative viewpoints often lie near uncertain regions with higher collision risk. To address this challenge, we develop a conflict-aware active perception and control framework for robotic systems operating in environments represented by 3D Gaussian Splatting (3DGS). Safety is enforced using a Control Barrier Function (CBF) derived from an Average Value-at-Risk AV@R collision-risk metric that accounts for geometric uncertainty and guarantees forward invariance of a safe set. To improve perception, we propose a risk-aware Expected Information Gain (EIG) formulation for selecting the next-best-view and introduce perception barrier functions that align the camera orientation with the local information-ascent direction. To obtain a tractable formulation for these conflicting safety and perception objectives, we propose a unified safety-critical, perception-aware quadratic program that enforces safety as a hard constraint while relaxing perception constraints through slack variables. Simulation results demonstrate that the proposed method improves both safety and information acquisition compared to existing 3DGS-based approaches.

Amirhossein Mollaei Khass, Athanasios Cosse, Vivek Pandey +1

Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, 18015, USA

Viewpoint-Dependent Active Perception Control Barrier Functions Gaussian Splatting Simultaneous Localization And Mapping Systems 3D Perception Map Uncertainty Robotic Systems+1

May 19, 2026cs.CV

Trust It or Not: Evidential Uncertainty for Feed-Forward 3D Reconstruction with Trust3R

Geometric foundation models hold promise for unconstrained dense geometry prediction from uncalibrated images. However, in current feed-forward designs, their predicted confidence scores are heuristic, lack probabilistic interpretation, and often fail to indicate where and how much the predicted geometry can be trusted. To address this gap, we present Trust3R, a lightweight evidential uncertainty framework for feed-forward 3D reconstruction. Trust3R combines gated residual mean refinement with a Normal-Inverse-Wishart evidential head, yielding a closed-form multivariate Student-t distribution for per-point geometric uncertainty. This design provides probabilistically grounded pointmap uncertainty estimates while adding moderate inference overhead. We evaluate on diverse indoor and outdoor benchmarks and compare against MASt3R's built-in confidence map as well as common uncertainty-aware baselines spanning single-pass heteroscedastic regression and sampling-based methods such as MC dropout and deep ensembles. Experimental results show that Trust3R consistently improves risk-coverage and sparsification, and generally improves geometric accuracy. These gains are reflected in stronger uncertainty ranking across benchmarks, with 25% lower AURC and 41% lower AUSE on ScanNet++, providing a practical reliability signal for uncertainty-aware weighting in downstream geometry pipelines. The project page and code are available at https://trust3r-z.github.io/.

Zihao Zhu, Wenyuan Zhao, Nuo Chen +2

Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX, USA

Feed-Forward 3D Reconstruction Robust Geometric Model Estimation Map Uncertainty 3D Generation Evidential Uncertainty AI Trustworthiness

May 18, 2026cs.CV

Lost in the Folds: When Cross-Validation Is Not a Deep Ensemble for Uncertainty Estimation

Ensemble disagreement is widely used as a proxy for epistemic uncertainty in medical image segmentation. In practice, many studies form ensembles via K-fold cross-validation (CV), yet refer to them as ``deep ensembles'' (DE). Because CV members are trained on different data subsets, their disagreement mixes seed-driven variability with data-exposure effects, which can change how uncertainty should be interpreted. We audit recent segmentation uncertainty studies and find that terminology--implementation mismatches are common. We then compare a standard 5-fold CV ensemble to a 5-member DE (fixed training set, different random seeds) under otherwise identical configurations on three multi-rater segmentation datasets spanning three modalities. We evaluate uncertainty for calibration, failure detection, ambiguity modeling, and robustness under distribution shift. DE match segmentation accuracy while improving calibration and failure detection, whereas CV ensembles sometimes correlate more strongly with inter-rater variability on the studied datasets. Thus, ensemble construction should be chosen to match the research question: DE for reliability-oriented use (e.g., selective referral/failure detection) and CV ensembles as a proxy for ambiguity. We provide a lightweight nnU-Net modification enabling DE training within the default pipeline.

Tristan Kirscher, Markus Bujotzek, Yannick Kirchhoff +5

ICube, Institut Strauss, DKFZ · ICube Laboratory, CNRS UMR-7357, University of Strasbourg, Strasbourg, France · CLCC Institut-Strauss, Strasbourg, France +6

Cross Validation Ensemble Semi-Supervised Medical Image Segmentation Map Uncertainty Uncertainty Disagreement

Mar 24, 2026cs.RO

Variable-Resolution Virtual Maps for Autonomous Exploration with Unmanned Surface Vehicles (USVs)

Autonomous exploration by unmanned surface vehicles (USVs) in near-shore waters requires reliable localisation and consistent mapping over extended areas, but this is challenged by GNSS degradation, environment-induced localisation uncertainty, and limited on-board computation. Virtual map-based methods explicitly model localisation and mapping uncertainty by tightly coupling factor-graph SLAM with a map uncertainty criterion. However, their storage and computational costs scale poorly with fixed-resolution workspace discretisations, leading to inefficiency in large near-shore environments. Moreover, overvaluing feature-sparse open-water regions can increase the risk of SLAM failure as a result of imbalance between exploration and exploitation. To address these limitations, we propose a Variable-Resolution Virtual Map (VRVM), a computationally efficient method for representing map uncertainty using bivariate Gaussian virtual landmarks placed in the cells of an adaptive quadtree. The adaptive quadtree enables an area-weighted uncertainty representation that keeps coarse, far-field virtual landmarks deliberately uncertain while allocating higher resolution to information-dense regions, and reduces the sensitivity of the map valuation to local refinements of the tree. An expectation-maximisation (EM) planner is adopted to evaluate pose and map uncertainty along frontiers using the VRVM, balancing exploration and exploitation. We evaluate VRVM against several state-of-the-art exploration algorithms in the VRX Gazebo simulator, using a realistic marina environment across different testing scenarios with an increasing level of exploration difficulty. The results indicate that our method offers safer behaviour and better utilisation of on-board computation in GNSS-degraded near-shore environments.

Ye Li, Yewei Huang, Yongchang Xie +4

Department of Mechanical Engineering, University College London, London, UK · Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, NJ, USA · Department of Computer Science, Dartmouth College, Hanover, NH, USA

Simultaneous Localization And Mapping Autonomous Surface Vehicles Map Uncertainty Exploration

Sep 17, 2025cs.CL

Geometric Uncertainty for Detecting and Correcting Hallucinations in LLMs

Large language models are known to hallucinate, generating linguistically plausible but incorrect answers to questions. Uncertainty quantification has been proposed as a strategy to detect such behaviour, but existing methods lack a unified framework to assess reliability at both the prompt and answer level. We introduce a geometric framework which quantifies language model uncertainty at both levels by explicitly modelling a prompt-conditioned semantic distribution in answer embedding space. Our approach is black-box and sampling-based; we generate multiple answers per prompt, and use archetypal analysis to estimate a geometric support for the answer distribution. At the prompt level, we approximate the distribution entropy to quantify uncertainty; for each individual answer, we then use notions of atypicality to assess its reliability relative to the batch. We employ our framework to not only detect hallucinations but correct them, by selecting the batch example deemed most reliable. Experiments show that our framework performs comparably to or better than prior methods on short form question-answering datasets, and achieves superior results on medical datasets where hallucinations carry particularly critical risks. Beyond pure performance, we suggest the theoretical grounding of our work provides support for semantic distributions as useful objects of study for language model uncertainty.

Edward Phillips, Sean Wu, Soheila Molaei +3

Department of Engineering Science, University of Oxford · GlaxoSmithKline · Oxford Suzhou Centre for Advanced Research

Large Language Model Uncertainty Large Language Model Hallucination Hallucination Mitigation Map Uncertainty Uncertainty Quantification

Jul 31, 2025stat.ME

A General Approach to Visualizing Uncertainty in Statistical Graphics

We present a general approach to visualizing uncertainty in static 2-D statistical graphics. If we treat a visualization as a function of its underlying quantities, uncertainty in those quantities induces a distribution over images. We show how to aggregate these images into a single visualization that represents the uncertainty. The approach can be viewed as a generalization of sample-based approaches that use overlay. Notably, standard representations, such as confidence intervals and bands, emerge with their usual coverage guarantees without being explicitly quantified or visualized. As a proof of concept, we implement our approach in the IID setting using resampling, provided as an open-source Python library. Because the approach operates directly on images, the user needs only to supply the data and the code for visualizing the quantities of interest without uncertainty. Through several examples, we show how both familiar and novel forms of uncertainty visualization can be created. The implementation is not only a practical validation of the underlying theory but also an immediately usable tool that can complement existing uncertainty-visualization libraries.

Bernarda Petek, David Nabergoj, Erik Štrumbelj

Map Uncertainty Uncertainty Chart

Mar 11, 2025cs.LG

A Generative-AI Modeling Framework for Explainable Decision Support in Complex Geosteering Scenarios

The real-time process of directional changes while drilling, known as geosteering, is crucial for hydrocarbon extraction and emerging directional drilling applications such as geothermal energy, civil infrastructure, and CO2 storage. The geo-energy industry seeks an automatic geosteering workflow that continually updates subsurface uncertainties and captures the latest geological understanding, informed by real-time observations. We propose a real-time, AI-driven geosteering workflow that integrates Generative Adversarial Networks (GANs) for geological parameterization, ensemble methods for model updating, and global discrete dynamic programming (DDP) optimization for complex decision-making during directional drilling operations. Our framework relies on offline training of a GAN model to reproduce relevant geology realizations and a Forward Neural Network (FNN) to model the response of Logging-While-Drilling (LWD) tools for a given geomodel. This paper introduces a first-of-its-kind workflow that progressively reduces GAN-geomodel uncertainty around and ahead of the drilling bit and adjusts the well plan accordingly. The workflow automatically integrates real-time around-bit LWD, which, through learned geological correlations, reduces uncertainty in predicted geology ahead of drilling. A DDP-based decision support system leverages probabilistic look-ahead predictions to suggest better steering strategies. We test the workflow prototype on a small yet challenging low-net-to-gross drilling scenario with several possible targets. The results show that the workflow produces meaningful steering recommendations and, through its probabilistic updates, automatically maps formation boundaries along the drilled well.

Sergey Alyaev, Kristian Fossum, Hibat Errahmen Djecta +2

NORCE Norwegian Research Centre AS, Bergen, Norway. · University of Stavanger, Stavanger, Norway. · Heriot-Watt University, Edinburgh, United Kingdom.

Drilling Data Geological Semantic Understanding Map Uncertainty Generative Models Software Engineering Decision Support

Mar 27, 2013cs.AI

Estimating Uncertain Spatial Relationships in Robotics

In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map contains the estimates of relationships among objects in the map, and their uncertainties, given all the available information. The procedures provide a general solution to the problem of estimating uncertain relative spatial relationships. The estimates are probabilistic in nature, an advance over the previous, very conservative, worst-case approaches to the problem. Finally, the procedures are developed in the context of state-estimation and filtering theory, which provides a solid basis for numerous extensions.

Randall Smith, Matthew Self, Peter Cheeseman

SRI International 333 Ravenswood Avenue Menlo Park, California 94025 · General Motors Research Laboratories Warren, Michigan · UC Berkeley +1

State Estimation Map Uncertainty Spatial Intent Simultaneous Localization And Mapping Worst-Case