Related papers: On the Reconstruction of Static and Dynamic Discre…
The problem of reconstructing the drift of a diffusion in $\erre^d$, $d\geq 2$, from the transition probability density observed outside a domain is considered. The solution of this problem also solves a new inverse problem for a class of…
Developments in dynamical systems theory provides new support for the discretisation of \pde{}s and other microscale systems. By systematically resolving subgrid microscale dynamics the new approach constructs asymptotically accurate,…
It is a significant challenge to predict the network topology from a small amount of dynamical observations. Different from the usual framework of the node-based reconstruction, two optimization approaches (i.e., the global and partitioned…
Molecular dynamics simulations are widely used across chemistry, physics, and biology, providing quantitative insight into complex processes with atomic detail. However, their limited timescale of a few microseconds is a significant…
Fast image reconstruction techniques are becoming important with the increasing number of scientific cases in high resolution micro and nano tomography. The processing of the large scale three-dimensional data demands new mathematical tools…
Reconstructing dense geometry for dynamic scenes from a monocular video is a critical yet challenging task. Recent memory-based methods enable efficient online reconstruction, but they fundamentally suffer from a Memory Demand Dilemma: The…
Nowadays massive amount of data are available for analysis in natural and social systems. Inferring system structures from the data, i.e., the inverse problem, has become one of the central issues in many disciplines and interdisciplinary…
Inverse design of slender elastic structures underlies a wide range of applications in computer graphics, flexible electronics, biomedical devices, and soft robotics. Traditional optimization-based approaches, however, are often orders of…
We analyze multi-bounce propagation of light in an unknown hidden volume and demonstrate that the reflected light contains sufficient information to recover the 3D structure of the hidden scene. We formulate the forward and inverse theory…
We consider inverse problems estimating distributed parameters from indirect noisy observations through discretization of continuum models described by partial differential or integral equations. It is well understood that the errors…
Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…
The field of structural engineering is vast, spanning areas from the design of new infrastructure to the assessment of existing infrastructure. From the onset, traditional entry-level university courses teach students to analyse structural…
Deep learning has been the most popular machine learning method in the last few years. In this chapter, we present the application of deep learning and physics-informed neural networks concerning structural mechanics and vibration problems.…
Nowadays, the field computed tomography (CT) encompasses a large variety of settings, ranging from nanoscale to meter-sized objects imaged by different kinds of radiation in various acquisition modes. This experimental diversity challenges…
We analyze the inverse scattering series for diffuse waves in random media. In previous work the inverse series was used to develop fast, direct image reconstruction algorithms in optical tomography. Here we characterize the convergence,…
Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…
This report extends our recent progress in tackling a challenging 3D inverse scattering problem governed by the Helmholtz equation. Our target application is to reconstruct dielectric constants, electric conductivities and shapes of front…
This article presents original work combining a NURBS-based inverse analysis with both kinematic and constitutive nonlinearities to recover the applied loads and deformations of thin shell structures. The inverse formulation is tackled by…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…