Related papers: A deformation-based framework for learning solutio…

Recently, deep-learning-based approaches have been widely studied for deformable image registration task. However, most efforts directly map the composite image representation to spatial transformation through the convolutional neural…

We introduce and analyze a method of learning-informed parameter identification for partial differential equations (PDEs) in an all-at-once framework. The underlying PDE model is formulated in a rather general setting with three unknowns:…

Domain adaptation is a sub-field of machine learning that involves transferring knowledge from a source domain to perform the same task in the target domain. It is a typical challenge in machine learning that arises, e.g., when data is…

Shape correspondence from 3D deformation learning has attracted appealing academy interests recently. Nevertheless, current deep learning based methods require the supervision of dense annotations to learn per-point translations, which…

We introduce a new framework for learning dense correspondence between deformable 3D shapes. Existing learning based approaches model shape correspondence as a labelling problem, where each point of a query shape receives a label…

In this paper, we propose an end-to-end framework that jointly learns keypoint detection, descriptor representation and cross-frame matching for the task of image-based 3D localization. Prior art has tackled each of these components…

In scientific and engineering applications, solving partial differential equations (PDEs) across various parameters and domains normally relies on resource-intensive numerical methods. Neural operators based on deep learning offered a…

Multiparameter persistent homology has emerged as a powerful generalization of topological data analysis, capable of encoding multivariate filtrations. However, the algebraic complexity of multiparameter persistence modules, marked by wild…

Partial differential equations (PDEs) play a central role in describing many physical phenomena. Various scientific and engineering applications demand a versatile and differentiable PDE solver that can quickly generate solutions with…

We present ShapeFlow, a flow-based model for learning a deformation space for entire classes of 3D shapes with large intra-class variations. ShapeFlow allows learning a multi-template deformation space that is agnostic to shape topology,…

Deformable image registration poses a challenging problem where, unlike most deep learning tasks, a complex relationship between multiple coordinate systems has to be considered. Although data-driven methods have shown promising…

Density-equalizing map (DEM) serves as a powerful technique for creating shape deformations with the area changes reflecting an underlying density function. In recent decades, DEM has found widespread applications in fields such as data…

We develop a mathematically rigorous framework for multilayer neural networks in the mean field regime. As the network's widths increase, the network's learning trajectory is shown to be well captured by a meaningful and dynamically…

This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…

We present MeshODE, a scalable and robust framework for pairwise CAD model deformation without prespecified correspondences. Given a pair of shapes, our framework provides a novel shape feature-preserving mapping function that continuously…

In this paper, we present a framework for learning the solution map of a backward parabolic Cauchy problem. The solution depends continuously but nonlinearly on the final data, source, and force terms, all residing in Banach spaces of…

For domains that are easily represented by structured meshes, robust geometric multigrid solvers can quickly provide the numerical solution to many discretized elliptic PDEs. However, for complicated domains with unstructured meshes,…

Across numerous applications, forecasting relies on numerical solvers for partial differential equations (PDEs). Although the use of deep-learning techniques has been proposed, actual applications have been restricted by the fact the…

Neural operators aim to learn mappings between infinite-dimensional function spaces, but their performance often degrades on complex or irregular geometries due to the lack of geometry-aware representations. We propose the Finite Element…

Humans can robustly learn novel visual concepts even when images undergo various deformations and lose certain information. Mimicking the same behavior and synthesizing deformed instances of new concepts may help visual recognition systems…