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We propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly…

Diffusion models (DMs) have revolutionized generative learning. They utilize a diffusion process to encode data into a simple Gaussian distribution. However, encoding a complex, potentially multimodal data distribution into a single…

Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of these networks was pioneered by Mallat, 2012. Specifically, Mallat considered so-called…

We consider the ill-posed inverse problem of identifying a nonlinearity in a time-dependent PDE model. The nonlinearity is approximated by a neural network, and needs to be determined alongside other unknown physical parameters and the…

Data-driven depth estimation methods struggle with the generalization outside their training scenes due to the immense variability of the real-world scenes. This problem can be partially addressed by utilising synthetically generated…

Conventional machine learning algorithms have traditionally been designed under the assumption that input data follows a vector-based format, with an emphasis on vector-centric paradigms. However, as the demand for tasks involving set-based…

We develop a new and general encode-approximate-reconstruct operator learning model that leverages learned neural representations of bases for input and output function distributions. We introduce the concepts of \textit{numerical operator…

Deep neural networks are representation learning techniques. During training, a deep net is capable of generating a descriptive language of unprecedented size and detail in machine learning. Extracting the descriptive language coded within…

One of the key problems in computer vision is adaptation: models are too rigid to follow the variability of the inputs. The canonical computation that explains adaptation in sensory neuroscience is divisive normalization, and it has…

Accurate image segmentation remains challenging, particularly in generating sharp, confident boundaries. While modern architectures have advanced the field, many of them still rely on standard loss functions like Cross-Entropy and Dice,…

In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two…

In the presence of large sets of labeled data, Deep Learning (DL) has accomplished extraordinary triumphs in the avenue of computer vision, particularly in object classification and recognition tasks. However, DL cannot always perform well…

Diversity is a concept of prime importance in almost all disciplines based on information processing. In telecommunications, for example, spatial, temporal, and frequency diversity, as well as redundant coding, are fundamental concepts that…

Recent data-driven approaches to scene interpretation predominantly pose inference as an end-to-end black-box mapping, commonly performed by a Convolutional Neural Network (CNN). However, decades of work on perceptual organization in both…

Traditional computer graphics rendering pipeline is designed for procedurally generating 2D quality images from 3D shapes with high performance. The non-differentiability due to discrete operations such as visibility computation makes it…

Multimodal learning robust to missing modality has attracted increasing attention due to its practicality. Existing methods tend to address it by learning a common subspace representation for different modality combinations. However, we…

While much of the work in the design of convolutional networks over the last five years has revolved around the empirical investigation of the importance of depth, filter sizes, and number of feature channels, recent studies have shown that…

In this work we propose a deep learning network for deformable image registration (DIRNet). The DIRNet consists of a convolutional neural network (ConvNet) regressor, a spatial transformer, and a resampler. The ConvNet analyzes a pair of…

Many types of data from fields including natural language processing, computer vision, and bioinformatics, are well represented by discrete, compositional structures such as trees, sequences, or matchings. Latent structure models are a…

Deep neural networks (DNNs) have revolutionized artificial intelligence but often lack performance when faced with out-of-distribution (OOD) data, a common scenario due to the inevitable domain shifts in real-world applications. This…