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The graph-based variational autoencoder represents an architecture that can handle the uncertainty of different geological scenarios, such as depositional or structural, through the concept of a lowerdimensional latent space. The main…

In this paper, we present a hypergraph neural networks (HGNN) framework for data representation learning, which can encode high-order data correlation in a hypergraph structure. Confronting the challenges of learning representation for…

Recent work has constructed neural networks that are equivariant to continuous symmetry groups such as 2D and 3D rotations. This is accomplished using explicit Lie group representations to derive the equivariant kernels and nonlinearities.…

Many real-world optimization problems are not naturally homogeneous vectors but composite design objects with heterogeneous parameters: integers, real values, Booleans, categoricals, complex-valued descriptors, and embedding vectors.…

An important goal for the machine learning (ML) community is to create approaches that can learn solutions with human-level capability. One domain where humans have held a significant advantage is visual processing. A significant approach…

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…

Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures. These models aggregate signals over such…

Graph convolutional network (GCN) is an emerging neural network approach. It learns new representation of a node by aggregating feature vectors of all neighbors in the aggregation process without considering whether the neighbors or…

Despite the omnipresence of tensors and tensor operations in modern deep learning, the use of tensor mathematics to formally design and describe neural networks is still under-explored within the deep learning community. To this end, we…

In generative modeling, numerous successful approaches leverage a low-dimensional latent space, e.g., Stable Diffusion models the latent space induced by an encoder and generates images through a paired decoder. Although the selection of…

The geometry of three-dimensional (3D) graphs, consisting of nodes and edges, plays a crucial role in many important applications. An excellent example is molecular graphs, whose geometry influences important properties of a molecule…

Most existing feature learning methods optimize inflexible handcrafted features and the affinity matrix is constructed by shallow linear embedding methods. Different from these conventional methods, we pretrain a generative neural network…

Social and information networks are gaining huge popularity recently due to their various applications. Knowledge representation through graphs in the form of nodes and edges should preserve as many characteristics of the original data as…

We introduce the $\star_G$ tensor algebra, in which any finite group $G$ defines the multiplication rule, making equivariance an intrinsic algebraic property rather than an architectural constraint. The framework rests on three…

Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a…

We present a novel application of category theory for deep learning. We show how category theory can be used to understand and work with the linear layer functions of group equivariant neural networks whose layers are some tensor power…

In standard generative deep learning models, such as autoencoders or GANs, the size of the parameter set is proportional to the complexity of the generated data distribution. A significant challenge is to deploy resource-hungry deep…

Generative methods (Gen-AI) are reviewed with a particular goal of solving tasks in machine learning and Bayesian inference. Generative models require one to simulate a large training dataset and to use deep neural networks to solve a…

Scientific machine learning has enabled the extraction of physical insights and data-driven modeling of high-dimensional spatiotemporal data, yet achieving physically interpretable latent representations and computationally efficient…

Generative adversarial networks (GANs) are a powerful framework for generative tasks. However, they are difficult to train and tend to miss modes of the true data generation process. Although GANs can learn a rich representation of the…