Daniele Bigoni

Daniele Bigoni
Massachusetts Institute of Technology | MIT · Department of Aeronautics and Astronautics

PhD in Applied Mathematics and Computer Science

About

18
Publications
6,150
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288
Citations
Introduction
Daniele Bigoni currently works at the Department of Aeronautics and Astronautics, Massachusetts Institute of Technology. Daniele does research in uncertainty quantification, stochastic modeling and inference.
Additional affiliations
June 2015 - present
Massachusetts Institute of Technology
Position
  • PostDoc Position
February 2015 - May 2015
Technical University of Denmark
Position
  • Research Assistant
June 2013 - December 2013
Massachusetts Institute of Technology
Position
  • Visiting PhD student

Publications

Publications (18)
Preprint
Full-text available
We introduce a method for the nonlinear dimension reduction of a high-dimensional function $u:\mathbb{R}^d\rightarrow\mathbb{R}$, $d\gg1$. Our objective is to identify a nonlinear feature map $g:\mathbb{R}^d\rightarrow\mathbb{R}^m$, with a prescribed intermediate dimension $m\ll d$, so that $u$ can be well approximated by $f\circ g$ for some profil...
Article
Full-text available
2020 IOP Publishing Ltd. This paper suggests a framework for the learning of discretizations of expensive forward models in Bayesian inverse problems. The main idea is to incorporate the parameters governing the discretization as part of the unknown to be estimated within the Bayesian machinery. We numerically show that in a variety of inverse prob...
Preprint
Full-text available
This paper suggests a framework for the learning of discretizations of expensive forward models in Bayesian inverse problems. The main idea is to incorporate the parameters governing the discretization as part of the unknown to be estimated within the Bayesian machinery. We numerically show that in a variety of inverse problems arising in mechanica...
Preprint
Full-text available
We propose a framework for the greedy approximation of high-dimensional Bayesian inference problems, through the composition of multiple \emph{low-dimensional} transport maps or flows. Our framework operates recursively on a sequence of ``residual'' distributions, given by pulling back the posterior through the previously computed transport maps. T...
Article
Full-text available
Integration against an intractable probability measure is among the fundamental challenges of statistical inference, particularly in the Bayesian setting. A principled approach to this problem seeks a deterministic coupling of the measure of interest with a tractable "reference" measure (e.g., a standard Gaussian). This coupling is induced by a tra...
Article
Full-text available
A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a formulation of a fully nonlinear and dispersive potential flow water wave model with random inputs for the probabilistic description of the evolution of waves. The model is analyzed usi...
Conference Paper
Full-text available
We introduce a new stabilized high-order and unstructured numerical model for modeling fully nonlinear and dispersive water waves. The model is based on a nodal spectral element method of arbitrary order in space and a σ-transformed formulation due to Cai, Langtangen, Nielsen and Tveito (1998). In the present paper we use a single layer of quadrati...
Article
Full-text available
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al (1998), although the numerical implementation differs greatly. Features of...
Thesis
Full-text available
The systematic quantification of the uncertainties affecting dynamical systems and the characterization of the uncertainty of their outcomes is critical for engineering design and analysis, where risks must be reduced as much as possible. Uncertainties stem naturally from our limitations in measurements, predictions and manufacturing, and we can sa...
Conference Paper
Full-text available
This work addresses the problem of the reliability of simulations for realistic nonlinear systems, by using efficient techniques for the analysis of the propagation of the uncertainties of the model parameters through the dynamics of the system. We present the sensitivity analysis of the critical speed of a railway vehicle with respect to its suspe...
Article
Full-text available
The approximation of high-dimensional functions with surrogates is of key importance for the advance of uncertainty quantification and inference. We propose the construction of surrogate functions using a novel spectral extension of tensor-train decomposition and we provide error estimates for surrogate functions based on projection and interpolati...
Article
Full-text available
We present an approach to global sensitivity analysis aiming at the reduction of its computational cost without compromising the results. The method is based on sampling methods, cubature rules, high-dimensional model representation and total sensitivity indices. It is applied to a half car with a two-axle Cooperrider bogie, in order to study the s...
Article
Full-text available
The paper contains a report of the experiences with numerical analyses of railway vehicle dynamical systems, which all are nonlinear, non-smooth and stiff high-dimensional systems. Some results are shown, but the emphasis is on the numerical methods of solution and lessons learned. But for two examples the dynamical problems are formulated as syste...
Conference Paper
Full-text available
This paper describes the results of the application of Uncertainty Quantification methods to a simple railroad vehicle dynamical example. Uncertainty Quantification methods take the probability distribution of the system parameters that stems from the parameter tolerances into account in the result. In this paper the methods are applied to a low-di...
Article
Full-text available
The paper describes the results of the application of "Uncertainty Quantification" methods in railway vehicle dynamics. The system parameters are given by probability distributions. The results of the application of the Monte-Carlo and generalized Polynomial Chaos methods to a simple bogie model will be discussed.
Conference Paper
Full-text available
We present an approach to global sensitivity analysis aiming at the reduction of its computational cost without compromising the results. The method is based on sampling methods, cubature rules, High-Dimensional Model Representation and Total Sensitivity Indices. The approach has a general applicability in many engineering fields and does not requi...
Article
The paper describes the results of the application of "Uncertainty Quantification" methods in railway vehicle dynamics. The system parameters are given by probability distributions. The results of the application of the Monte-Carlo and generalized Polynomial Chaos methods to a simple bogie model will be discussed.
Conference Paper
Full-text available
This paper describes the results of the application of Uncertainty Quantification methods to a railway vehicle dynamical example. Uncertainty Quantification methods take the probability distribution of the system parameters that stems from the parameter tolerances into account in the result. In this paper the methods are applied to a low-dimensiona...

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Projects

Projects (3)
Project
Collaborative research that focus on researching, improving, developing and applying robust, fast and accurate spectral element methodologies with adaptive mesh capabilities for weakly and fully nonlinear and dispersive free surface wave modelling models, fixed and moving wave-body methods for marine offshore engineering applications.
Project
The systematic quantification of the uncertainties affecting dynamical systems and the characterization of the uncertainty of their outcomes is critical for engineering design and analysis, where risks must be reduced as much as possible. Uncertainties stem naturally from our limitations in measurements, predictions and manufacturing, and we can say that any dynamical system used in engineering is subject to some of these uncertainties.
Project
A collaborative open source project to research, improve and develop robust, fast and accurate open source methodologies based on flexible-order finite difference methods for large-scale fully nonlinear and dispersive free surface modelling and nonlinear wave-structure methods for marine offshore engineering applications that takes into account bathymetry. The project has been developed and hosted since 2008 at Department of Applied Mathematics and Computer Science, Technical University of Denmark (DTU). See also the website http://www2.compute.dtu.dk/~apek/OceanWave3D/. Next to this project, a more recent project MarineSEM focus on unstructured Spectral Element Methods for nonlinear wave propagation, nonlinear wave-structure and nonlinear wave-body modelling. See the new MarineSEM project : https://www.researchgate.net/project/Spectral-Element-Methods-for-Nonlinear-Waves-Wave-Structure-and-Wave-Body-modelling