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We cast shape matching as metric learning with convolutional networks. We break the end-to-end process of image representation into two parts. Firstly, well established efficient methods are chosen to turn the images into edge maps.…

Given a dataset of images containing different objects with different features such as shape, size, rotation, and x-y position; and a Variational Autoencoder (VAE); creating a disentangled encoding of these features in the hidden space…

State-of-the-art fully intrinsic networks for non-rigid shape matching often struggle to disambiguate the symmetries of the shapes leading to unstable correspondence predictions. Meanwhile, recent advances in the functional map framework…

We present a unified framework for solving partial differential equations (PDEs) using video-inpainting diffusion transformer models. Unlike existing methods that devise specialized strategies for either forward or inverse problems under…

Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…

Inverse problems involving partial differential equations (PDEs) with discontinuous coefficients are fundamental challenges in modeling complex spatiotemporal systems with heterogeneous structures and uncertain dynamics. Traditional…

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…

Recent advances in feature learning have shown that self-supervised vision foundation models can capture semantic correspondences but often lack awareness of underlying 3D geometry. GECO addresses this gap by producing geometrically…

Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…

We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…

In this work, we address the lack of 3D understanding of generative neural networks by introducing a persistent 3D feature embedding for view synthesis. To this end, we propose DeepVoxels, a learned representation that encodes the…

We present a new convolution layer for deep learning architectures which we call QuadConv -- an approximation to continuous convolution via quadrature. Our operator is developed explicitly for use on non-uniform, mesh-based data, and…

Given a collection of images, humans are able to discover landmarks by modeling the shared geometric structure across instances. This idea of geometric equivariance has been widely used for the unsupervised discovery of object landmark…

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…

We propose a multi-layer variational autoencoder method, we call HR-VQVAE, that learns hierarchical discrete representations of the data. By utilizing a novel objective function, each layer in HR-VQVAE learns a discrete representation of…

In this paper, we propose a novel supervised learning method that is called Deep Embedding Kernel (DEK). DEK combines the advantages of deep learning and kernel methods in a unified framework. More specifically, DEK is a learnable kernel…

We propose a new class of implicit networks, the multiscale deep equilibrium model (MDEQ), suited to large-scale and highly hierarchical pattern recognition domains. An MDEQ directly solves for and backpropagates through the equilibrium…

ADCME is a novel computational framework to solve inverse problems involving physical simulations and deep neural networks (DNNs). This paper benchmarks its capability to learn spatially-varying physical fields using DNNs. We demonstrate…

Spatial representation learning is essential for GeoAI applications such as urban analytics, enabling the encoding of shapes, locations, and spatial relationships (topological and distance-based) of geo-entities like points, polylines, and…

Deep learning is a kind of feature learning method with strong nonliear feature transformation and becomes more and more important in many fields of artificial intelligence. Deep autoencoder is one representative method of the deep learning…