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Owing to their superior modeling capabilities, gated Recurrent Neural Networks, such as Gated Recurrent Units (GRUs) and Long Short-Term Memory networks (LSTMs), have become popular tools for learning dynamical systems. This paper aims to…

In our prior work [arXiv:2109.09316], neural network methods with inputs based on domain of dependence and a converging sequence were introduced for solving one dimensional conservation laws, in particular the Euler systems. To predict a…

Artificial neural networks with internal dynamics exhibit remarkable capability in processing information. Reservoir computing (RC) is a canonical example that features rich computing expressivity and compatibility with physical…

We present Linear Diffusion Networks (LDNs), a novel architecture that reinterprets sequential data processing as a unified diffusion process. Our model integrates adaptive diffusion modules with localized nonlinear updates and a…

The proliferation of mission-critical latency-sensitive services has intensified the demand for next-generation cloud-integrated networks to guarantee both reliable and resilient service delivery. While reliability imposes timely-throughput…

We propose a deep learning-based LiDAR odometry estimation method called LoRCoN-LO that utilizes the long-term recurrent convolutional network (LRCN) structure. The LRCN layer is a structure that can process spatial and temporal information…

Conventional fluid simulations can be time consuming and energy intensive. We researched the viability of a neural network for simulating incompressible fluids in a randomized obstacle-heavy environment, as an alternative to the numerical…

Recurrent Neural Networks (RNNs) are used to learn representations in partially observable environments. For agents that learn online and continually interact with the environment, it is desirable to train RNNs with real-time recurrent…

Deep neural networks have been applied in many computer vision tasks and achieved state-of-the-art performance. However, misclassification will occur when DNN predicts adversarial examples which add human-imperceptible adversarial noise to…

Autonomous vehicles are expected to emerge as a main trend in vehicle development over the next decade. To support autonomous vehicles, ultra-reliable low-latency communications (URLLC) is required between autonomous vehicles and…

Irregularly measured time series are common in many of the applied settings in which time series modelling is a key statistical tool, including medicine. This provides challenges in model choice, often necessitating imputation or similar…

Recurrent neural networks (RNNs) with continuous-time hidden states are a natural fit for modeling irregularly-sampled time series. These models, however, face difficulties when the input data possess long-term dependencies. We prove that…

We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…

We examine a reduced membrane model of liquid crystal polymer networks (LCNs) via asymptotics and computation. This model requires solving a minimization problem for a non-convex stretching energy. We show a formal asymptotic derivation of…

Reservoir computing (RC), a particular form of recurrent neural network, is under explosive development due to its exceptional efficacy and high performance in reconstruction or/and prediction of complex physical systems. However, the…

Modeling and simulation of complex fluid flows with dynamics that span multiple spatio-temporal scales is a fundamental challenge in many scientific and engineering domains. Full-scale resolving simulations for systems such as highly…

Neural Ordinary Differential Equations (Neural ODEs) construct the continuous dynamics of hidden units using ordinary differential equations specified by a neural network, demonstrating promising results on many tasks. However, Neural ODEs…

Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…

As deep neural network (NN) methods have matured, there has been increasing interest in deploying NN solutions to "edge computing" platforms such as mobile phones or embedded controllers. These platforms are often resource-constrained,…

Recurrent Neural Networks (RNNs) with sophisticated units that implement a gating mechanism have emerged as powerful technique for modeling sequential signals such as speech or electroencephalography (EEG). The latter is the focus on this…