Related papers: Flow with Nonlinear Potential in General Networks …
This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of)…
We propose a combination of machine learning and flux limiting for property-preserving subgrid scale modeling in the context of flux-limited finite volume methods for the one-dimensional shallow-water equations. The numerical fluxes of a…
Linear networks provide valuable insights into the workings of neural networks in general. This paper identifies conditions under which the gradient flow provably trains a linear network, in spite of the non-strict saddle points present in…
The optimal power flow (OPF) problem, which plays a central role in operating electrical networks is considered. The problem is nonconvex and is in fact NP hard. Therefore, designing efficient algorithms of practical relevance is crucial,…
This paper proposes a simple and flexible storage model for use in a variety of multi-period optimal power flow problems. The proposed model is designed for research use in a broad assortment of contexts enabled by the following key…
First we present an approach to formulate unbalanced three-phase power flow problems for general networks that explicitly separates device models and network models. A device model consists of (i) an internal model and (ii) a conversion…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
This paper considers distribution systems with a high penetration of distributed, renewable generation and addresses the problem of incorporating the associated uncertainty into the optimal operation of these networks. Joint chance…
Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder-Mead, Quasi-Newton, and Global) are investigated in conjunction with energy minimization principle to resolve the pressure and…
This paper describes new results linking constrained optimization theory and nonlinear contraction analysis. Generalizations of Lagrange parameters are derived based on projecting system dynamics on the tangent space of possibly…
We investigate the fundamental principles that drive the development of scalable algorithms for network optimization. Despite the significant amount of work on parallel and decentralized algorithms in the optimization community, the methods…
In this paper, we consider the network utility maximization problem with various user priorities via jointly optimizing user association, load distribution and power control in a load-coupled heterogeneous network. In order to tackle the…
The minimization of operation costs for natural gas transport networks is studied. Based on a recently developed model hierarchy ranging from detailed models of instationary partial differential equations with temperature dependence to…
Typical topology optimization methods require complex iterative calculations, which cannot meet the requirements of fast computing applications. The neural network is studied to reduce the time of computing the optimization result, however,…
Optimization is widely used to determine the physical and financial exchange of wholesale electricity in organized markets. Guarantees of solution optimality and feasibility rest largely on convexity, which is not in general a…
Deep neural networks (DNNs) are powerful machine learning models and have succeeded in various artificial intelligence tasks. Although various architectures and modules for the DNNs have been proposed, selecting and designing the…
This paper presents a general description of a parameter estimation inverse problem for systems governed by nonlinear differential equations. The inverse problem is presented using optimal control tools with state constraints, where the…
Stability of recurrent models is closely linked with trainability, generalizability and in some applications, safety. Methods that train stable recurrent neural networks, however, do so at a significant cost to expressibility. We propose an…
This paper introduces a framework to capture previously intractable optimization constraints and transform them to a mixed-integer linear program, through the use of neural networks. We encode the feasible space of optimization problems…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…