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Efficient nonlinearity compensation in fiber-optic communication systems is considered a key element to go beyond the "capacity crunch''. One guiding principle for previous work on the design of practical nonlinearity compensation schemes…

We present an approach that uses a deep learning model, in particular, a MultiLayer Perceptron (MLP), for estimating the missing values of a variable in multivariate time series data. We focus on filling a long continuous gap (e.g.,…

This paper presents a nonlinear model reduction method for systems of equations using a structured neural network. The neural network takes the form of a "three-layer" network with the first layer constrained to lie on the Grassmann…

Recent years have witnessed the great success of deep neural networks in many research areas. The fundamental idea behind the design of most neural networks is to learn similarity patterns from data for prediction and inference, which lacks…

Many machine learning methods operate by inverting a neural network at inference time, which has become a popular technique for solving inverse problems in computer vision, robotics, and graphics. However, these methods often involve…

This paper focuses on developing a method to obtain an uncertain linear fractional transformation (LFT) system that adequately captures the dynamics of a nonlinear time-invariant system over some desired envelope. First, the nonlinear…

Low-rank recurrent neural networks (lrRNNs) are a class of models that uncover low-dimensional latent dynamics underlying neural population activity. Although their functional connectivity is low-rank, it lacks disentanglement…

Many scientific and geometric problems exhibit general linear symmetries, yet most equivariant neural networks are built for compact groups or simple vector features, limiting their reuse on matrix-valued data such as covariances, inertias,…

Recent empirical evidence has demonstrated that the training dynamics of large-scale deep neural networks occur within low-dimensional subspaces. While this has inspired new research into low-rank training, compression, and adaptation,…

We propose a novel class of separable multilayer network models to capture cross-layer dependencies in multilayer networks, enabling the analysis of how interactions in one or more layers may influence interactions in other layers. Our…

Data-driven approaches are increasingly popular for identifying dynamical systems due to improved accuracy and availability of sensor data. However, relying solely on data for identification does not guarantee that the identified systems…

With the rapid development of geometric deep learning techniques, many mesh-based convolutional operators have been proposed to bridge irregular mesh structures and popular backbone networks. In this paper, we show that while convolutions…

Accurate and reliable prediction of individual travel mode choices is crucial for developing multi-mode urban transportation systems, conducting transportation planning and formulating traffic demand management strategies. Traditional…

In multi-task learning (MTL), we improve the performance of key machine learning algorithms by training various tasks jointly. When the number of tasks is large, modeling task structure can further refine the task relationship model. For…

A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new…

The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…

We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…

Model-based Reinforcement Learning (RL) is a popular learning paradigm due to its potential sample efficiency compared to model-free RL. However, existing empirical model-based RL approaches lack the ability to explore. This work studies a…

Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear…

Random cost simulations were introduced as a method to investigate optimization problems in systems with conflicting constraints. Here I study the approach in connection with the training of a feed-forward multilayer perceptron, as used in…