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Recurrent neural networks (RNNs) have gained a great deal of attention in solving sequential learning problems. The learning of long-term dependencies, however, remains challenging due to the problem of a vanishing or exploding hidden…

In this paper we address the importance and the impact of employing structure preserving neural networks as surrogate of the analytical physics-based models typically employed to describe the rheology of non-Newtonian fluids in Stokes…

This paper introduces a new Convolutional Neural Network (ConvNet) architecture inspired by a class of partial differential equations (PDEs) called quasi-linear hyperbolic systems. With comparable performance on the image classification…

In the recent application of scientific modeling, machine learning models are largely applied to facilitate computational simulations of fluid systems. Rotation symmetry is a general property for most symmetric fluid systems. However, in…

This is the third paper in a series in which we develop machine learning (ML) moment closure models for the radiative transfer equation (RTE). In our previous work \cite{huang2021gradient}, we proposed an approach to learn the gradient of…

This paper introduces an end-to-end residual network that operates entirely on the Poincar\'e ball model of hyperbolic space. Hyperbolic learning has recently shown great potential for visual understanding, but is currently only performed…

Hyperbolic space is quickly gaining traction as a promising geometry for hierarchical and robust representation learning. A core open challenge is the development of a mathematical formulation of hyperbolic neural networks that is both…

The infinite-depth paradigm pioneered by Neural ODEs has launched a renaissance in the search for novel dynamical system-inspired deep learning primitives; however, their utilization in problems of non-trivial size has often proved…

We introduce a new training paradigm that enforces interval constraints on neural network parameter space to control forgetting. Contemporary Continual Learning (CL) methods focus on training neural networks efficiently from a stream of…

By embedding physical intuition, network architectures enforce fundamental properties, such as energy conservation laws, leading to plausible predictions. Yet, scaling these models to intrinsically high-dimensional systems remains a…

Deep reinforcement learning (RL) is notoriously impractical to deploy due to sample inefficiency. Meta-RL directly addresses this sample inefficiency by learning to perform few-shot learning when a distribution of related tasks is available…

Deep learning methods, which exploit auto-differentiation to compute derivatives without dispersion or dissipation errors, have recently emerged as a compelling alternative to classical mesh-based numerical schemes for solving hyperbolic…

Models based on deep convolutional networks have dominated recent image interpretation tasks; we investigate whether models which are also recurrent, or "temporally deep", are effective for tasks involving sequences, visual and otherwise.…

Deploying accurate event detection on resource-constrained devices is challenged by the trade-off between performance and computational cost. While Early-Exit (EE) networks offer a solution through adaptive computation, they often fail to…

Spatio-temporal dynamics of physical processes are generally modeled using partial differential equations (PDEs). Though the core dynamics follows some principles of physics, real-world physical processes are often driven by unknown…

Learning complex network dynamics is fundamental for understanding, modeling, and controlling real-world complex systems. Though great efforts have been made to predict the future states of nodes on networks, the capability of capturing…

We introduce a deep residual recurrent neural network (DR-RNN) as an efficient model reduction technique for nonlinear dynamical systems. The developed DR-RNN is inspired by the iterative steps of line search methods in finding the residual…

We present GoRINNs: numerical analysis-informed (shallow) neural networks for the solution of inverse problems of non-linear systems of conservation laws. GoRINNs is a hybrid/blended machine learning scheme based on high-resolution Godunov…

A least-squares neural network (LSNN) method was introduced for solving scalar linear and nonlinear hyperbolic conservation laws (HCLs) in [7, 6]. This method is based on an equivalent least-squares (LS) formulation and uses ReLU neural…

In this work, we introduce a framework to design multidimensional Riemann solvers for nonlinear systems of hyperbolic conservation laws on general unstructured polygonal Voronoi-like tessellations. In this framework we propose two simple…