Related papers: Learning and correcting non-Gaussian model errors

Incorporating prior information into inverse problems, e.g. via maximum-a-posteriori estimation, is an important technique for facilitating robust inverse problem solutions. In this paper, we devise two novel approaches for linear inverse…

Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…

Euler's elastica is a classical model of flexible slender structures, relevant in many industrial applications. Static equilibrium equations can be derived via a variational principle. The accurate approximation of solutions of this problem…

Deep neural networks have been applied successfully to a wide variety of inverse problems arising in computational imaging. These networks are typically trained using a forward model that describes the measurement process to be inverted,…

Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…

We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…

We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…

Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the datagenerating process of variables.…

We explore unique considerations involved in fitting ML models to data with very high precision, as is often required for science applications. We empirically compare various function approximation methods and study how they scale with…

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…

Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…

We show how to treat systematic uncertainties using Bayesian deep networks for regression. First, we analyze how these networks separately trace statistical and systematic uncertainties on the momenta of boosted top quarks forming fat jets.…

Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the data-generating process of variables.…

Rapid development in numerical modelling of materials and the complexity of new models increases quickly together with their computational demands. Despite the growing performance of modern computers and clusters, calibration of such models…

This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…

In ultrasound tomography, the speed of sound inside an object is estimated based on acoustic measurements carried out by sensors surrounding the object. An accurate forward model is a prominent factor for high-quality image reconstruction,…

This work explores the search for heterogeneous approximate multiplier configurations for neural networks that produce high accuracy and low energy consumption. We discuss the validity of additive Gaussian noise added to accurate neural…

Neural networks work remarkably well in practice and theoretically they can be universal approximators. However, they still make mistakes and a specific type of them called adversarial errors seem inexcusable to humans. In this work, we…

A novel artificial neural network method is proposed for solving Cauchy inverse problems. It allows multiple hidden layers with arbitrary width and depth, which theoretically yields better approximations to the inverse problems. In this…

Safety-critical technical systems operating in unknown environments require the ability to quickly adapt their behavior, which can be achieved in control by inferring a model online from the data stream generated during operation. Gaussian…