This paper presents a safe, efficient, and agile ground vehicle navigation algorithm for 3D off-road terrain environments. Off-road navigation is subject to uncertain vehicle-terrain interactions caused by different terrain conditions on top of 3D terrain topology. The existing works are limited to adopt overly simplified vehicle-terrain models. The proposed algorithm learns the terrain-induced uncertainties from driving data and encodes the learned uncertainty distribution into the traversability cost for path evaluation. The navigation path is then designed to optimize the uncertainty-aware traversability cost, resulting in a safe and agile vehicle maneuver. Assuring real-time execution, the algorithm is further implemented within parallel computation architecture running on Graphics Processing Units (GPU).
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Current graph neural networks (GNNs) that tackle node classification on graphs tend to only focus on nodewise scores and are solely evaluated by nodewise metrics. This limits uncertainty estimation on graphs since nodewise marginals do not fully characterize the joint distribution given the graph structure. In this work, we propose novel edgewise metrics, namely the edgewise expected calibration error (ECE) and the agree/disagree ECEs, which provide criteria for uncertainty estimation on graphs beyond the nodewise setting. Our experiments demonstrate that the proposed edgewise metrics can complement the nodewise results and yield additional insights. Moreover, we show that GNN models which consider the structured prediction problem on graphs tend to have better uncertainty estimations, which illustrates the benefit of going beyond the nodewise setting.
The real-time interpretation of the logging-while-drilling data allows us to estimate the positions and properties of the geological layers in an anisotropic subsurface environment. Robust real-time estimations capturing uncertainty can be very useful for efficient geosteering operations. However, the model errors in the prior conceptual geological models and forward simulation of the measurements can be significant factors in the unreliable estimations of the profiles of the geological layers. The model errors are specifically pronounced when using a deep-neural-network (DNN) approximation which we use to accelerate and parallelize the simulation of the measurements. This paper presents a practical workflow consisting of offline and online phases. The offline phase includes DNN training and building of an uncertain prior near-well geo-model. The online phase uses the flexible iterative ensemble smoother (FlexIES) to perform real-time assimilation of extra-deep electromagnetic data accounting for the model errors in the approximate DNN model. We demonstrate the proposed workflow on a case study for a historic well in the Goliat Field (Barents Sea). The median of our probabilistic estimation is on-par with proprietary inversion despite the approximate DNN model and regardless of the number of layers in the chosen prior. By estimating the model errors, FlexIES automatically quantifies the uncertainty in the layers' boundaries and resistivities, which is not standard for proprietary inversion.
Despite the successes in many fields, it is found that neural networks are difficult to be both accurate and robust, i.e., high accuracy networks are often vulnerable. Various empirical and analytic studies have substantiated that there is more or less a trade-off between the accuracy and robustness of neural networks. If the property is inherent, applications based on the neural networks are vulnerable with untrustworthy predictions. To more deeply explore and understand this issue, in this study we show that the accuracy-robustness trade-off is an intrinsic property whose underlying mechanism is closely related to the uncertainty principle in quantum mechanics. By relating the loss function in neural networks to the wave function in quantum mechanics, we show that the inputs and their conjugates cannot be resolved by a neural network simultaneously. This work thus provides an insightful explanation for the inevitability of the accuracy-robustness dilemma for general deep networks from an entirely new perspective, and furthermore, reveals a potential possibility to study various properties of neural networks with the mature mathematical tools in quantum physics.
Nowadays, Deep Learning (DL) methods often overcome the limitations of traditional signal processing approaches. Nevertheless, DL methods are barely applied in real-life applications. This is mainly due to limited robustness and distributional shift between training and test data. To this end, recent work has proposed uncertainty mechanisms to increase their reliability. Besides, meta-learning aims at improving the generalization capability of DL models. By taking advantage of that, this paper proposes an uncertainty-based Meta-Reinforcement Learning (Meta-RL) approach with Out-of-Distribution (OOD) detection. The presented method performs a given task in unseen environments and provides information about its complexity. This is done by determining first and second-order statistics on the estimated reward. Using information about its complexity, the proposed algorithm is able to point out when tracking is reliable. To evaluate the proposed method, we benchmark it on a radar-tracking dataset. There, we show that our method outperforms related Meta-RL approaches on unseen tracking scenarios in peak performance by 16% and the baseline by 35% while detecting OOD data with an F1-Score of 72%. This shows that our method is robust to environmental changes and reliably detects OOD scenarios.
$T_{1\rho}$ mapping is a promising quantitative MRI technique for the non-invasive assessment of tissue properties. Learning-based approaches can map $T_{1\rho}$ from a reduced number of $T_{1\rho}$ weighted images, but requires significant amounts of high quality training data. Moreover, existing methods do not provide the confidence level of the $T_{1\rho}$ estimation. To address these problems, we proposed a self-supervised learning neural network that learns a $T_{1\rho}$ mapping using the relaxation constraint in the learning process. Epistemic uncertainty and aleatoric uncertainty are modelled for the $T_{1\rho}$ quantification network to provide a Bayesian confidence estimation of the $T_{1\rho}$ mapping. The uncertainty estimation can also regularize the model to prevent it from learning imperfect data. We conducted experiments on $T_{1\rho}$ data collected from 52 patients with non-alcoholic fatty liver disease. The results showed that our method outperformed the existing methods for $T_{1\rho}$ quantification of the liver using as few as two $T_{1\rho}$-weighted images. Our uncertainty estimation provided a feasible way of modelling the confidence of the self-supervised learning based $T_{1\rho}$ estimation, which is consistent with the reality in liver $T_{1\rho}$ imaging.
Transformers have recently been utilized to perform object detection and tracking in the context of autonomous driving. One unique characteristic of these models is that attention weights are computed in each forward pass, giving insights into the model's interior, in particular, which part of the input data it deemed interesting for the given task. Such an attention matrix with the input grid is available for each detected (or tracked) object in every transformer decoder layer. In this work, we investigate the distribution of these attention weights: How do they change through the decoder layers and through the lifetime of a track? Can they be used to infer additional information about an object, such as a detection uncertainty? Especially in unstructured environments, or environments that were not common during training, a reliable measure of detection uncertainty is crucial to decide whether the system can still be trusted or not.
The core numbers of vertices in a graph are one of the most well-studied cohesive subgraph models because of the linear running time. In practice, many data graphs are dynamic graphs that are continuously changing by inserting or removing edges. The core numbers are updated in dynamic graphs with edge insertions and deletions, which is called core maintenance. When a burst of a large number of inserted or removed edges come in, we have to handle these edges on time to keep up with the data stream. There are two main sequential algorithms for core maintenance, \textsc{Traversal} and \textsc{Order}. It is proved that the \textsc{Order} algorithm significantly outperforms the \alg{Traversal} algorithm over all tested graphs with up to 2,083 times speedups. To the best of our knowledge, all existing parallel approaches are based on the \alg{Traversal} algorithm; also, their parallelism exists only for affected vertices with different core numbers, which will reduce to sequential when all vertices have the same core numbers. In this paper, we propose a new parallel core maintenance algorithm based on the \alg{Order} algorithm. Importantly, our new approach always has parallelism, even for the graphs where all vertices have the same core numbers. Extensive experiments are conducted over real-world, temporal, and synthetic graphs on a 64-core machine. The results show that for inserting and removing 100,000 edges using 16-worker, our method achieves up to 289x and 10x times speedups compared with the most efficient existing method, respectively.
Current person image retrieval methods have achieved great improvements in accuracy metrics. However, they rarely describe the reliability of the prediction. In this paper, we propose an Uncertainty-Aware Learning (UAL) method to remedy this issue. UAL aims at providing reliability-aware predictions by considering data uncertainty and model uncertainty simultaneously. Data uncertainty captures the ``noise" inherent in the sample, while model uncertainty depicts the model's confidence in the sample's prediction. Specifically, in UAL, (1) we propose a sampling-free data uncertainty learning method to adaptively assign weights to different samples during training, down-weighting the low-quality ambiguous samples. (2) we leverage the Bayesian framework to model the model uncertainty by assuming the parameters of the network follow a Bernoulli distribution. (3) the data uncertainty and the model uncertainty are jointly learned in a unified network, and they serve as two fundamental criteria for the reliability assessment: if a probe is high-quality (low data uncertainty) and the model is confident in the prediction of the probe (low model uncertainty), the final ranking will be assessed as reliable. Experiments under the risk-controlled settings and the multi-query settings show the proposed reliability assessment is effective. Our method also shows superior performance on three challenging benchmarks under the vanilla single query settings.
Model-based control requires an accurate model of the system dynamics for precisely and safely controlling the robot in complex and dynamic environments. Moreover, in presence of variations in the operating conditions, the model should be continuously refined to compensate for dynamics changes. In this paper, we propose a self-supervised learning approach to actively model robot discrete-time dynamics. We combine offline learning from past experience and online learning from present robot interaction with the unknown environment. These two ingredients enable highly sample-efficient and adaptive learning for accurate inference of the model dynamics in real-time even in operating regimes significantly different from the training distribution. Moreover, we design an uncertainty-aware model predictive controller that is conditioned to the aleatoric (data) uncertainty of the learned dynamics. The controller actively selects the optimal control actions that (i) optimize the control performance and (ii) boost the online learning sample efficiency. We apply the proposed method to a quadrotor system in multiple challenging real-world experiments. Our approach exhibits high flexibility and generalization capabilities by consistently adapting to unseen flight conditions, while it significantly outperforms classical and adaptive control baselines.
In this paper, we propose new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher order accuracy in space and time. As a model problem, the convection-diffusion problem on a moving domain is studied. For geometrically higher order accuracy, we apply a parametric mapping on a background space-time tensor-product mesh. Concerning discretisation in time, we consider discontinuous Galerkin, as well as related continuous (Petrov-)Galerkin and Galerkin collocation methods. For stabilisation with respect to bad cut configurations and as an extension mechanism that is required for the latter two schemes, a ghost penalty stabilisation is employed. The article puts an emphasis on the techniques that allow to achieve a robust but higher order geometry handling for smooth domains. We investigate the computational properties of the respective methods in a series of numerical experiments. These include studies in different dimensions for different polynomial degrees in space and time, validating the higher order accuracy in both variables.
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