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An artificial neural network is presented based on the idea of connections between units that are only active for a specific range of input values and zero outside that range (and so are not evaluated outside the active range). The…

This paper focuses on finding reinforcement learning policies for control systems with hard state and action constraints. Despite its success in many domains, reinforcement learning is challenging to apply to problems with hard constraints,…

We analyze the topological properties of the set of functions that can be implemented by neural networks of a fixed size. Surprisingly, this set has many undesirable properties. It is highly non-convex, except possibly for a few exotic…

The fully connected (FC) layer, one of the most fundamental modules in artificial neural networks (ANN), is often considered difficult and inefficient to train due to issues including the risk of overfitting caused by its large amount of…

We propose a two-scale neural network method for optimal control problems governed by convection-dominated convection-diffusion-reaction equations. Building on two-scale architectures developed for singularly perturbed forward problems, we…

Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an…

Data-driven machine learning approaches have recently been proposed to facilitate wireless network optimization by learning latent knowledge from historical optimization instances. However, existing methods do not well handle the topology…

CoVariance Neural Networks (VNNs) perform convolutions on the graph determined by the covariance matrix of the data, which enables expressive and stable covariance-based learning. However, covariance matrices are typically dense, fail to…

The contribution of this paper is a framework for training and evaluation of Model Predictive Control (MPC) implemented using constrained neural networks. Recent studies have proposed to use neural networks with differentiable convex…

We contribute to a better understanding of the class of functions that can be represented by a neural network with ReLU activations and a given architecture. Using techniques from mixed-integer optimization, polyhedral theory, and tropical…

In this paper, we investigate a constrained formulation of neural networks where the output is a convex function of the input. We show that the convexity constraints can be enforced on both fully connected and convolutional layers, making…

We study the family of functions that are represented by a linear convolutional neural network (LCN). These functions form a semi-algebraic subset of the set of linear maps from input space to output space. In contrast, the families of…

The recent impressive results of deep learning-based methods on computer vision applications brought fresh air to the research and industrial community. This success is mainly due to the process that allows those methods to learn…

Neural networks (NN) have achieved state-of-the-art performance in various applications. Unfortunately in applications where training data is insufficient, they are often prone to overfitting. One effective way to alleviate this problem is…

Recently, over-parameterized neural networks have been extensively analyzed in the literature. However, the previous studies cannot satisfactorily explain why fully trained neural networks are successful in practice. In this paper, we…

Effective power flow modeling critically affects the ability to efficiently solve large-scale grid optimization problems, especially those with topology-related decision variables. In this work, we put forth a generative modeling approach…

Mathematical optimization is widely used in various research fields. With a carefully-designed objective function, mathematical optimization can be quite helpful in solving many problems. However, objective functions are usually…

Graph Neural Networks (GNNs) have achieved remarkable success across diverse applications, yet they remain limited by oversmoothing and poor performance on heterophilic graphs. To address these challenges, we introduce a novel framework…

Representations of multivariate functions with low-dimensional functions that depend on subsets of original coordinates (corresponding of different orders of coupling) are useful in quantum dynamics and other applications, especially where…

The control of large buildings encounters challenges in computational efficiency due to their size and nonlinear components. To address these issues, this paper proposes a Piecewise Affine (PWA)-based distributed scheme for Model Predictive…