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Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…

A promising approach to optimal control of nonlinear systems involves iteratively linearizing the system and solving an optimization problem at each time instant to determine the optimal control input. Since this approach relies on online…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

Recently, deep neural network (DNN) has been widely adopted in the design of intelligent communication systems thanks to its strong learning ability and low testing complexity. However, most current offline DNN-based methods still suffer…

We consider both discrete and continuous control problems constrained by a fixed budget of some resource, which may be renewed upon entering a preferred subset of the state space. In the discrete case, we consider both deterministic and…

In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…

We show that artificial neural networks with rectifier units as activation functions can exactly represent the piecewise affine function that results from the formulation of model predictive control of linear time-invariant systems. The…

We propose two new criteria to understand the advantage of deepening neural networks. It is important to know the expressivity of functions computable by deep neural networks in order to understand the advantage of deepening neural…

Neural ordinary differential equations (NODEs) -- parametrizations of differential equations using neural networks -- have shown tremendous promise in learning models of unknown continuous-time dynamical systems from data. However, every…

The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…

Optimization-based solvers play a central role in a wide range of signal processing and communication tasks. However, their applicability in latency-sensitive systems is limited by the sequential nature of iterative methods and the high…

We propose a novel approach to solving input- and state-constrained parametric mixed-integer optimal control problems using Differentiable Predictive Control (DPC). Our approach follows the differentiable programming paradigm by learning an…

Successful training of convolutional neural networks is often associated with sufficiently deep architectures composed of high amounts of features. These networks typically rely on a variety of regularization and pruning techniques to…

Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis.…

In the context of classification problems, Deep Learning (DL) approaches represent state of art. Many DL approaches are based on variations of standard multi-layer feed-forward neural networks. These are also referred to as deep networks.…

Implicit equilibrium models, i.e., deep neural networks (DNNs) defined by implicit equations, have been becoming more and more attractive recently. In this paper, we investigate an emerging question: can an implicit equilibrium model's…

Sophisticated multilayer neural networks have achieved state of the art results on multiple supervised tasks. However, successful applications of such multilayer networks to control have so far been limited largely to the perception portion…

Two aspects of neural networks that have been extensively studied in the recent literature are their function approximation properties and their training by gradient descent methods. The approximation problem seeks accurate approximations…

In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly…

Deep neural networks (DNNs) have achieved remarkable success in computer vision; however, training DNNs for satisfactory performance remains challenging and suffers from sensitivity to empirical selections of an optimization algorithm for…