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Nonlinear model predictive control (MPC) is a flexible and increasingly popular framework used to synthesize feedback control strategies that can satisfy both state and control input constraints. In this framework, an optimization problem,…

Perimeter control maintains high traffic efficiency within protected regions by controlling transfer flows among regions to ensure that their traffic densities are below critical values. Existing approaches can be categorized as either…

Simulations of complex turbulent flow are part and parcel of the engineering design process. Eddy viscosity based turbulence models represent the workhorse for these simulations. The underlying simplifications in eddy viscosity models make…

Traditional theories of optimization cannot describe the dynamics of optimization in deep learning, even in the simple setting of deterministic training. The challenge is that optimizers typically operate in a complex, oscillatory regime…

This paper proposes a novel approach to improve the performance of distributed nonlinear control systems while preserving stability by leveraging Deep Neural Networks (DNNs). We build upon the Neural System Level Synthesis (Neur-SLS)…

High-dimensional datasets present substantial challenges in statistical modeling across various disciplines, necessitating effective dimensionality reduction methods. Deep learning approaches, notable for their capacity to distill essential…

A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of strategies that seek to restrict the range of possible…

We study the convergence of gradient flow for the training of deep neural networks. If Residual Neural Networks are a popular example of very deep architectures, their training constitutes a challenging optimization problem due notably to…

This paper investigates the problem of data-driven modeling of port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability properties. We propose a novel neural-network-based port-Hamiltonian modeling…

While deep learning has shown tremendous success in a wide range of domains, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training, and inference of such models. In this paper, we aim…

Despite their great success in practical applications, there is still a lack of theoretical and systematic methods to analyze deep neural networks. In this paper, we illustrate an advanced information theoretic methodology to understand the…

In this paper, we present a deep neural network (DNN) training approach called the "DeepMimic" training method. Enormous amounts of data are available nowadays for training usage. Yet, only a tiny portion of these data is manually labeled,…

This proposed work introduces a data-assimilation-assisted approach to train neural networks, aimed at effectively reducing epistemic uncertainty in state estimates of separated flows. This method, referred to as model-consistent training,…

Objective. Precise control of neural systems is essential to experimental investigations of how the brain controls behavior and holds the potential for therapeutic manipulations to correct aberrant network states. Model predictive control,…

Fine-scale simulation of complex systems governed by multiscale partial differential equations (PDEs) is computationally expensive and various multiscale methods have been developed for addressing such problems. In addition, it is…

We propose a novel training method that integrates rules into deep learning, in a way the strengths of the rules are controllable at inference. Deep Neural Networks with Controllable Rule Representations (DeepCTRL) incorporates a rule…

The vast majority of systems of practical interest are characterised by nonlinear dynamics. This renders the control and optimization of such systems a complex task due to their nonlinear behaviour. Additionally, standard methods such as…

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…

System identification has greatly benefited from deep learning techniques, particularly for modeling complex, nonlinear dynamical systems with partially unknown physics where traditional approaches may not be feasible. However, deep…

Multi-agent reinforcement learning methods have shown remarkable potential in solving complex multi-agent problems but mostly lack theoretical guarantees. Recently, mean field control and mean field games have been established as a…