Related papers: A multi-fidelity neural network surrogate sampling…

While generally considered computationally expensive, Uncertainty Quantification using Monte Carlo sampling remains beneficial for applications with uncertainties of high dimension. As an extension of the naive Monte Carlo method, the…

A vital stage in the mathematical modelling of real-world systems is to calibrate a model's parameters to observed data. Likelihood-free parameter inference methods, such as Approximate Bayesian Computation, build Monte Carlo samples of the…

Estimating the probability of failure for complex real-world systems using high-fidelity computational models is often prohibitively expensive, especially when the probability is small. Exploiting low-fidelity models can make this process…

A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…

Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…

This paper introduces a practical sampling method for training surrogate models in the context of uncertainty propagation. We propose a heuristic method to uniformly draw samples within highest density regions of the density given by the…

Variational inference is a powerful paradigm for approximate Bayesian inference with a number of appealing properties, including support for model learning and data subsampling. By contrast MCMC methods like Hamiltonian Monte Carlo do not…

We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the…

In this paper, we present an adaptive algorithm to construct response surface approximations of high-fidelity models using a hierarchy of lower fidelity models. Our algorithm is based on multi-index stochastic collocation and automatically…

Neural networks predictions are unreliable when the input sample is out of the training distribution or corrupted by noise. Being able to detect such failures automatically is fundamental to integrate deep learning algorithms into robotics.…

Machine learning surrogates are increasingly employed to replace expensive computational models for physics-based reliability analysis. However, their use introduces epistemic uncertainty from model approximation errors, which couples with…

We propose a novel training method based on nonlinear multilevel minimization techniques, commonly used for solving discretized large scale partial differential equations. Our multilevel training method constructs a multilevel hierarchy by…

We present a framework for automatically structuring and training fast, approximate, deep neural surrogates of stochastic simulators. Unlike traditional approaches to surrogate modeling, our surrogates retain the interpretable structure and…

Semi-supervised learning has made significant strides in the medical domain since it alleviates the heavy burden of collecting abundant pixel-wise annotated data for semantic segmentation tasks. Existing semi-supervised approaches enhance…

Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation involves resolving tails of probability distribution, and Monte Carlo sampling…

We present an approach for constructing a surrogate from ensembles of information sources of varying cost and accuracy. The multifidelity surrogate encodes connections between information sources as a directed acyclic graph, and is trained…

This paper introduces a novel and scalable framework for uncertainty estimation and separation with applications in data driven modeling in science and engineering tasks where reliable uncertainty quantification is critical. Leveraging an…

In this paper we introduce a novel way of estimating prediction uncertainty in deep networks through the use of uncertainty surrogates. These surrogates are features of the penultimate layer of a deep network that are forced to match…

Multilevel sampling methods, such as multilevel and multifidelity Monte Carlo, multilevel stochastic collocation, or delayed acceptance Markov chain Monte Carlo, have become standard uncertainty quantification (UQ) tools for a wide class of…

In this paper, we introduce a new technique that combines two popular methods to estimate uncertainty in object detection. Quantifying uncertainty is critical in real-world robotic applications. Traditional detection models can be ambiguous…