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This work explores the relationship between state space methods and Koopman operator-based methods for predicting the time-evolution of nonlinear dynamical systems. We demonstrate that extended dynamic mode decomposition with dictionary…

We propose a tensor neural network ($t$-NN) framework that offers an exciting new paradigm for designing neural networks with multidimensional (tensor) data. Our network architecture is based on the $t$-product (Kilmer and Martin, 2011), an…

We propose Fluid Logic, a paradigm in which modal logical reasoning, temporal, epistemic, doxastic, deontic, is lifted from discrete Kripke structures to continuous manifolds via Neural Stochastic Differential Equations (Neural SDEs). Each…

The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…

Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…

Despite many modern applications of Deep Neural Networks (DNNs), the large number of parameters in the hidden layers makes them unattractive for deployment on devices with storage capacity constraints. In this paper we propose a Data-Driven…

Ship roll motion in high sea states has large amplitudes and nonlinear dynamics, and its prediction is significant for operability, safety, and survivability. This paper presents a novel data-driven methodology to provide a multi-step…

To ensure frequency security in power systems, both the rate of change of frequency (RoCoF) and the frequency nadir (FN) must be explicitly accounted for in real-time frequency-constrained optimal power flow (FCOPF). However, accurately…

Deep neural networks (DNNs), especially physics-informed neural networks (PINNs), have recently become a new popular method for solving forward and inverse problems governed by partial differential equations (PDEs). However, these methods…

To fully learn the latent temporal dependencies from post-disturbance system dynamic trajectories, deep learning is utilized for short-term voltage stability (STVS) assessment of power systems in this paper. First of all, a semi-supervised…

Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been…

A properly designed controller can help improve the quality of experimental measurements or force a dynamical system to follow a completely new time-evolution path. Recent developments in deep reinforcement learning have made steep advances…

Recent progress in semantic segmentation has been driven by improving the spatial resolution under Fully Convolutional Networks (FCNs). To address this problem, we propose a Stacked Deconvolutional Network (SDN) for semantic segmentation.…

Sequence models based on linear state spaces (SSMs) have recently emerged as a promising choice of architecture for modeling long range dependencies across various modalities. However, they invariably rely on discretization of a continuous…

Spiking neural networks (SNNs) have closer dynamics to the brain than current deep neural networks. Their low power consumption and sample efficiency make these networks interesting. Recently, several deep convolutional spiking neural…

Model-based methods are the dominant paradigm for controlling robotic systems, though their efficacy depends heavily on the accuracy of the model used. Deep neural networks have been used to learn models of robot dynamics from data, but…

This paper deals with neural networks as dynamical systems governed by differential or difference equations. It shows that the introduction of skip connections into network architectures, such as residual networks and dense networks, turns…

Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly…

This paper considers the problem of controlling a dynamical system when the state cannot be directly measured and the control performance metrics are unknown or partially known. In particular, we focus on the design of data-driven…

Spiking neural network (SNN) is studied in multidisciplinary domains to (i) enable order-of-magnitudes energy-efficient AI inference and (ii) computationally simulate neuro-scientific mechanisms. The lack of discrete theory obstructs the…