Related papers: Towards Unstructured Mesh Generation Using the Inv…
In this paper, we effectively solve the inverse source problem of the fractional Poisson equation using MC-fPINNs. We construct two neural networks $ u_{NN}(x;\theta )$ and $f_{NN}(x;\psi)$ to approximate the solution $u^{*}(x)$ and the…
Image generation has been heavily investigated in computer vision, where one core research challenge is to generate images from arbitrarily complex distributions with little supervision. Generative Adversarial Networks (GANs) as an implicit…
A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…
Correcting measured detector-level distributions to particle-level is essential to make data usable outside the experimental collaborations. The term unfolding is used to describe this procedure. A new method of unfolding data using a…
Molecular conformation generation, a critical aspect of computational chemistry, involves producing the three-dimensional conformer geometry for a given molecule. Generating molecular conformation via diffusion requires learning to reverse…
We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and construct optimal sparse grids for scattered data…
We show that any polyhedron forming a topological ball with an even number of quadrilateral sides can be partitioned into O(n) topological cubes, meeting face to face. The result generalizes to non-simply-connected polyhedra satisfying an…
In this paper, we study the stability of the non symmetric version of the Nitsche's method without penalty for domain decomposition. The Poisson problem is considered as a model problem. The computational domain is divided into two…
The inverse design of metasurfaces faces inherent challenges due to the nonlinear and highly complex relationship between geometric configurations and their electromagnetic behavior. Traditional optimization approaches often suffer from…
Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following…
In this paper, we propose a discrete circular distribution obtained by extending the wrapped Poisson distribution. This new distribution, the Invariant Wrapped Poisson (IWP), enjoys numerous advantages: simple tractable density,…
When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often…
Partitioning an image into superpixels based on the similarity of pixels with respect to features such as colour or spatial location can significantly reduce data complexity and improve subsequent image processing tasks. Initial algorithms…
We propose conformal generative modeling, a framework for generative modeling on 2D surfaces approximated by discrete triangle meshes. Our approach leverages advances in discrete conformal geometry to develop a map from a source triangle…
This paper presents a method of reconstruction a primary structure of a protein that folds into a given geometrical shape. This method predicts the primary structure of a protein and restores its linear sequence of amino acids in the…
An algorithm for the generation of non-uniform unstructured grids on ellipsoidal geometries is described. This technique is designed to generate high quality triangular and polygonal meshes appropriate for general circulation modelling on…
A refined a priori error analysis of the lowest order (linear) Virtual Element Method (VEM) is developed for approximating a model two dimensional Poisson problem. A set of new geometric assumptions is proposed on shape regularity of…
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…
Deriving relationships between images and tracing back their history of modifications are at the core of Multimedia Phylogeny solutions, which aim to combat misinformation through doctored visual media. Nonetheless, most recent image…
For solving linear inverse problems, particularly of the type that appears in tomographic imaging and compressive sensing, this paper develops two new approaches. The first approach is an iterative algorithm that minimizes a regularized…