The estimation of model parameters with uncertainties from observed data is a ubiquitous inverse problem in science and engineering. In this paper, we suggest an inexpensive and easy to implement parameter estimation technique that uses a heteroscedastic Bayesian Neural Network trained using anchored ensembling. The heteroscedastic aleatoric error of the network models the irreducible uncertainty due to parameter degeneracies in our inverse problem, while the epistemic uncertainty of the Bayesian model captures uncertainties which may arise from an input observation's out-of-distribution nature. We use this tool to perform real-time parameter inference in a 6 parameter G-equation model of a ducted, premixed flame from observations of acoustically excited flames. We train our networks on a library of 2.1 million simulated flame videos. Results on the test dataset of simulated flames show that the network recovers flame model parameters, with the correlation coefficient between predicted and true parameters ranging from 0.97 to 0.99, and well-calibrated uncertainty estimates. The trained neural networks are then used to infer model parameters from real videos of a premixed Bunsen flame captured using a high-speed camera in our lab. Re-simulation using inferred parameters shows excellent agreement between the real and simulated flames. Compared to Ensemble Kalman Filter-based tools that have been proposed for this problem in the combustion literature, our neural network ensemble achieves better data-efficiency and our sub-millisecond inference times represent a savings on computational costs by several orders of magnitude. This allows us to calibrate our reduced-order flame model in real-time and predict the thermoacoustic instability behaviour of the flame more accurately.
This paper proposes a Bayesian data-driven machine learning method for the online inference of the parameters of a G-equation model of a ducted, premixed flame. Heteroscedastic Bayesian neural network ensembles are trained on a library of 1.7 million flame fronts simulated in LSGEN2D, a G-equation solver, to learn the Bayesian posterior distribution of the model parameters given observations. The ensembles are then used to infer the parameters of Bunsen flame experiments so that the dynamics of these can be simulated in LSGEN2D. This allows the surface area variation of the flame edge, a proxy…
University at Buffalo（布法罗大学）；Data Intensive Studies Center（数据密集型研究中心）；Tufts University（塔夫茨大学）
Complete computation of turbulent combustion flow involves two separate steps: mapping reaction kinetics to low-dimensional manifolds and looking-up this approximate manifold during CFD run-time to estimate the thermo-chemical state variables. In our previous work, we showed that using a deep architecture to learn the two steps jointly, instead of separately, is 73% more accurate at estimating the source energy, a key state variable, compared to benchmarks and can be integrated within a DNS turbulent combustion framework. In their natural form, such deep architectures do not allow for uncertai…
Fully Heteroscedastic Count Regression with Deep Double Poisson Networks
Brigham Young University, Department of Computer Science（Brigham Young 大学计算机科学系）；Arizona State University, School of Computing and Augmented Intelligence（亚利桑那州立大学计算与增强智能学院）；Ohio State University, Department of Marketing（俄亥俄州立大学市场营销系）
University of Cambridge（剑桥大学）；Lancaster University（兰卡斯特大学）；British Antarctic Survey（英国南极调查局）
Ensembles of geophysical models improve projection accuracy and express uncertainties. We develop a novel data-driven ensembling strategy for combining geophysical models using Bayesian Neural Networks, which infers spatiotemporally varying model weights and bias while accounting for heteroscedastic uncertainties in the observations. This produces more accurate and uncertainty-aware projections without sacrificing interpretability. Applied to the prediction of total column ozone from an ensemble of 15 chemistry-climate models, we find that the Bayesian neural network ensemble (BayNNE) outperfo…
Massachusetts Institute of Technology（麻省理工学院）；BITS Pilani Goa Campus（BITS Pilani果阿校区）
Understanding and quantifying uncertainty in black box Neural Networks (NNs) is critical when deployed in real-world settings such as healthcare. Recent works using Bayesian and non-Bayesian methods have shown how a unified predictive uncertainty can be modelled for NNs. Decomposing this uncertainty to disentangle the granular sources of heteroscedasticity in data provides rich information about its underlying causes. We propose a conceptually simple non-Bayesian approach, deep split ensemble, to disentangle the predictive uncertainties using a multivariate Gaussian mixture model. The NNs are …
A simple approach to obtaining uncertainty-aware neural networks for regression is to do Bayesian linear regression (BLR) on the representation from the last hidden layer. Recent work [Riquelme et al., 2018, Azizzadenesheli et al., 2018] indicates that the method is promising, though it has been limited to homoscedastic noise. In this paper, we propose a novel variation that enables the method to flexibly model heteroscedastic noise. The method is benchmarked against two prominent alternative methods on a set of standard datasets, and finally evaluated as an uncertainty-aware model in model-ba…
University of Cambridge（剑桥大学）；Technical University of Munich（慕尼黑工业大学）
Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous learning algorithm for state and parameter estimation with level-set methods. A Bayesian approach based on data assimilation is introduced. Data assimilation is enabled by the ensemble Kalman filter and smoother, which are used in their probabilistic formulations. The level-set data assimilation framework is verified in onedimensional and two-dimensional test c…
UiT The Arctic University of Norway（挪威北极大学）；Kongsberg Satellite Services（康斯伯格卫星服务公司）；NORCE Norwegian Research Centre（挪威NORCE研究中心）
This paper presents a novel probabilistic forecasting method called ensemble conformalized quantile regression (EnCQR). EnCQR constructs distribution-free and approximately marginally valid prediction intervals (PIs), which are suitable for nonstationary and heteroscedastic time series data. EnCQR can be applied on top of a generic forecasting model, including deep learning architectures. EnCQR exploits a bootstrap ensemble estimator, which enables the use of conformal predictors for time series by removing the requirement of data exchangeability. The ensemble learners are implemented as gener…
ONERA（法国国家航空航天研究院）；Université de Toulouse（图卢兹大学）；Zurich University of Applied Sciences（苏黎世应用科学大学）
Reliable uncertainty quantification on RUL prediction is crucial for informative decision-making in predictive maintenance. In this context, we assess some of the latest developments in the field of uncertainty quantification for prognostics deep learning. This includes the state-of-the-art variational inference algorithms for Bayesian neural networks (BNN) as well as popular alternatives such as Monte Carlo Dropout (MCD), deep ensembles (DE) and heteroscedastic neural networks (HNN). All the inference techniques share the same inception deep learning architecture as a functional model. We per…
Overcoming "Physics Shock" in Earth Observation A Heteroscedastic Uncertainty Framework for PINN-based Flood Inference
Built Environment Department, College of Science and Technology, North Carolina A&T State University（北卡罗来纳A&T州立大学科学与技术学院建筑环境系）；United Nations University Institute for Water, Environment and Health（联合国大学水、环境与健康研究所）
Mila - Quebec Institute of Artificial Intelligence（米拉 - 魁北克人工智能研究所）；Université de Montréal（蒙特利尔大学）
In model-free deep reinforcement learning (RL) algorithms, using noisy value estimates to supervise policy evaluation and optimization is detrimental to the sample efficiency. As this noise is heteroscedastic, its effects can be mitigated using uncertainty-based weights in the optimization process. Previous methods rely on sampled ensembles, which do not capture all aspects of uncertainty. We provide a systematic analysis of the sources of uncertainty in the noisy supervision that occurs in RL, and introduce inverse-variance RL, a Bayesian framework which combines probabilistic ensembles and B…
A Tale of Two Variances: When Single-Seed Benchmarks Fail in Bayesian Deep Learning
Department of Mathematical and Statistical Sciences（数学与统计科学系）；Marquette University（马凯特大学）；Cornell Ann S. Bowers College of Computing and Information Science（康奈尔大学安·S·博斯计算与信息科学学院）；Cornell University（康奈尔大学）；Physics Science and Engineering（物理科学与工程）；Tongji University（同济大学）；School of Computing and Information Systems（计算与信息科学学院）；The University of Melbourne（墨尔本大学）；Siebel School of Computing and Data Science（希贝尔计算与数据科学学院）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
BITS Pilani, K K Birla Goa Campus（比拉理工学院皮拉尼校区果阿分校）；Harvard Medical School（哈佛医学院）
Reliability of machine learning (ML) systems is crucial in safety-critical applications such as healthcare, and uncertainty estimation is a widely researched method to highlight the confidence of ML systems in deployment. Sequential and parallel ensemble techniques have shown improved performance of ML systems in multi-modal settings by leveraging the feature sets together. We propose an uncertainty-aware boosting technique for multi-modal ensembling in order to focus on the data points with higher associated uncertainty estimates, rather than the ones with higher loss values. We evaluate this…
Massachusetts Institute of Technology（麻省理工学院）；BITS Pilani Goa Campus（贝拉理工学院皮拉尼果阿校区）
Reliability in Neural Networks (NNs) is crucial in safety-critical applications like healthcare, and uncertainty estimation is a widely researched method to highlight the confidence of NNs in deployment. In this work, we propose an uncertainty-aware boosting technique for multi-modal ensembling to predict Alzheimer's Dementia Severity. The propagation of uncertainty across acoustic, cognitive, and linguistic features produces an ensemble system robust to heteroscedasticity in the data. Weighing the different modalities based on the uncertainty estimates, we experiment on the benchmark ADReSS d…
