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We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms. A comparative analysis between…

In recent years, Physics-informed neural networks (PINNs) have been widely used to solve partial differential equations alongside numerical methods because PINNs can be trained without observations and deal with continuous-time problems…

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the…

Graph representation learning has become a crucial task in machine learning and data mining due to its potential for modeling complex structures such as social networks, chemical compounds, and biological systems. Spiking neural networks…

Simulating particle dynamics with high fidelity is crucial for solving real-world interaction and control tasks involving liquids in design, graphics, and robotics. Recently, data-driven approaches, particularly those based on graph neural…

The efficiency of modern machine intelligence depends on high accuracy with minimal computational cost. In spiking neural networks (SNNs), synaptic delays are crucial for encoding temporal structure, yet existing models treat them as fully…

We introduce a neural network (NN) strictly governed by Newton's Law, with the nature required basis functions derived from the fundamental classic mechanics. Then, by classifying the training model as a quick procedure of 'force pattern'…

Deep Learning is considered to be a quite young in the area of machine learning research, found its effectiveness in dealing complex yet high dimensional dataset that includes but limited to images, text and speech etc. with multiple levels…

We have trained a fully convolutional spatio-temporal model for fast and accurate representation learning in the challenging exemplar application area of fusion energy plasma science. The onset of major disruptions is a critically important…

Recurrent neural networks for language models like long short-term memory (LSTM) have been utilized as a tool for modeling and predicting long term dynamics of complex stochastic molecular systems. Recently successful examples on learning…

Singularly perturbed partial differential equations arise in many applications, including magnetohydrodynamic duct flows, chemical reaction transport systems, and Poisson Boltzmann electrostatics. These problems are characterized by sharp…

Low-latency deep spiking neural networks (SNNs) have become a promising alternative to conventional artificial neural networks (ANNs) because of their potential for increased energy efficiency on event-driven neuromorphic hardware. Neural…

The success of the current wave of artificial intelligence can be partly attributed to deep neural networks, which have proven to be very effective in learning complex patterns from large datasets with minimal human intervention. However,…

This paper presents a sequence of two approaches for the data-driven control-oriented modeling of networked systems, i.e., the systems that involve many interacting dynamical components. First, a novel deep learning approach named the weak…

Fluid-structure interaction is common in engineering and natural systems, where floating-body motion is governed by added mass, drag, and background flows. Modeling these dissipative dynamics is difficult: black-box neural models regress…

Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…

Spiking Neural Networks (SNNs) that operate in an event-driven manner and employ binary spike representation have recently emerged as promising candidates for energy-efficient computing. However, a cost bottleneck arises in obtaining…

Deep neural networks (DNNs) are so over-parametrized that recent research has found them to already contain a subnetwork with high accuracy at their randomly initialized state. Finding these subnetworks is a viable alternative training…

Physics-based models of dynamical systems are often used to study engineering and environmental systems. Despite their extensive use, these models have several well-known limitations due to simplified representations of the physical…

Seismic events, among many other natural hazards, reduce due functionality and exacerbate vulnerability of in-service buildings. Accurate modeling and prediction of building's response subjected to earthquakes makes possible to evaluate…