Related papers: Long-time predictive modeling of nonlinear dynamic…

The use of deep neural network (DNN) models as surrogates for linear and nonlinear structural dynamical systems is explored. The goal is to develop DNN based surrogates to predict structural response, i.e., displacements and accelerations,…

After showing the efficiency of feedforward networks to estimate control in high dimension in the global optimization of some storages problems, we develop a modification of an algorithm based on some dynamic programming principle. We show…

Federated Learning (FL) has been successfully adopted for distributed training and inference of large-scale Deep Neural Networks (DNNs). However, DNNs are characterized by an extremely large number of parameters, thus, yielding significant…

Linear Quadratic Regulator (LQR) is often combined with feedback linearization (FBL) for nonlinear systems that have the nonlinearity additive to the input. Conventional approaches estimate and cancel the nonlinearity based on the first…

Deep neural networks are known to suffer from exploding or vanishing gradients as depth increases, a phenomenon closely tied to the spectral behavior of the input-output Jacobian. Prior work has identified critical initialization schemes…

Over the past two decades, the feedforward neural network (FNN) optimization has been a key interest among the researchers and practitioners of multiple disciplines. The FNN optimization is often viewed from the various perspectives: the…

The generalization error of deep neural networks via their classification margin is studied in this work. Our approach is based on the Jacobian matrix of a deep neural network and can be applied to networks with arbitrary non-linearities…

Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering…

Adversarial examples are crafted with imperceptible perturbations with the intent to fool neural networks. Against such attacks, adversarial training and its variants stand as the strongest defense to date. Previous studies have pointed out…

We introduce a new class of non-linear models for functional data based on neural networks. Deep learning has been very successful in non-linear modeling, but there has been little work done in the functional data setting. We propose two…

This paper proposes an adaptive neural network-based backstepping controller that uses rigid graph theory to address the distance-based formation control problem and target tracking for nonlinear multi-agent systems with bounded time-delay…

A promising trend in deep learning replaces traditional feedforward networks with implicit networks. Unlike traditional networks, implicit networks solve a fixed point equation to compute inferences. Solving for the fixed point varies in…

This work presents a novel resolution-invariant model order reduction strategy for multifidelity applications. We base our architecture on a novel neural network layer developed in this work, the graph feedforward network, which extends the…

Tracking performance of physical-model-based feedforward control for interventional X-ray systems is limited by hard-to-model parasitic nonlinear dynamics, such as cable forces and nonlinear friction. In this paper, these nonlinear dynamics…

Complex nonlinear dynamics are ubiquitous in many fields. Moreover, we rarely have access to all of the relevant state variables governing the dynamics. Delay embedding allows us, in principle, to account for unobserved state variables.…

The application of neural networks in modeling dynamic systems has become prominent due to their ability to estimate complex nonlinear functions. Despite their effectiveness, neural networks face challenges in long-term predictions, where…

The nonlinear propagation of ultrashort pulses in optical fiber depends sensitively on both input pulse and fiber parameters. As a result, optimizing propagation for specific applications generally requires time-consuming simulations based…

Recurrent neural networks (RNNs) are instrumental in modelling sequential and time-series data. Yet, when using RNNs to inform decision-making, predictions by themselves are not sufficient; we also need estimates of predictive uncertainty.…

Neural networks (NNs) inspired by the forward-backward algorithm (FBA) are used as equalizers for bandlimited channels with a memoryless nonlinearity. The NN-equalizers are combined with successive interference cancellation (SIC) to…

We introduce a new class of non-linear function-on-function regression models for functional data using neural networks. We propose a framework using a hidden layer consisting of continuous neurons, called a continuous hidden layer, for…