Related papers: Newton's Lantern: A Reinforcement Learning Framewo…

Newton-type methods enjoy fast local convergence and strong empirical performance, but achieving global guarantees comparable to first-order methods remains challenging. Even for simple strongly convex problems, no straightforward variant…

Machine learning algorithms, especially Neural Networks (NNs), are a valuable tool used to approximate non-linear relationships, like the AC-Optimal Power Flow (AC-OPF), with considerable accuracy -- and achieving a speedup of several…

With the increasing proportion of renewable energy in the generation side, it becomes more difficult to accurately predict the power generation and adapt to the large deviations between the optimal dispatch scheme and the day-ahead…

The objective of this publication is to reduce the sensitivity of iterative equation solvers on the initial value. To this end, at the hand of Newton's method, we exemplify how to reformulate the initial problem by means of a set of…

To address computational challenges associated with power flow nonconvexities, significant research efforts over the last decade have developed convex relaxations and approximations of optimal power flow (OPF) problems. However, benefits…

Newton-step approximations to pseudo maximum likelihood estimates of spatial autoregressive models with a large number of parameters are examined, in the sense that the parameter space grows slowly as a function of sample size. These have…

We present a linear cutting-plane relaxation approach that rapidly proves tight lower bounds for the Alternating Current Optimal Power Flow Problem (ACOPF). Our method leverages outer-envelope linear cuts for well-known second-order cone…

Power flow calculations for systems with a large number of buses, e.g. grids with multiple voltage levels, or time series based calculations result in a high computational effort. A common power flow solver for the efficient analysis of…

We propose a new method to efficiently compute load-flows (the steady-state of the power-grid for given productions, consumptions and grid topology), substituting conventional simulators based on differential equation solvers. We use a deep…

Reinforcement Learning offers a framework to learn to choose actions in order to achieve some goal. However, at the nano-scale, thermal fluctuations hamper the learning process. We analyze this regime using the general framework of Markov…

A new variant of Newton's method for empirical risk minimization is studied, where at each iteration of the optimization algorithm, the gradient and Hessian of the objective function are replaced by robust estimators taken from existing…

We propose, analyze, and test a nonlinear preconditioning technique to improve the Newton iteration for non-isothermal flow simulations. We prove that by first applying an Anderson accelerated Picard step, Newton becomes unconditionally…

Solving AC Optimal Power Flow (AC-OPF) is of central importance in electricity market operations, where interior-point methods (IPMs) such as IPOPT are the standard solvers. A growing body of work uses machine learning to predict primal…

Energy-efficient machine learning models that can run directly on edge devices are of great interest in IoT applications, as they can reduce network pressure and response latency, and improve privacy. An effective way to obtain…

As an effective emulator of ill-conditioned power flow, continuous Newton methods (CNMs) have been extensively investigated using explicit and implicit numerical integration algorithms. Explicit CNMs are prone to non-convergence issues due…

In emerging high-performance Network-on-Chip (NoC) architectures, efficient power management is crucial to minimize energy consumption. We propose a novel framework called CAFEEN that employs both heuristic-based fine-grained and machine…

The power flow is a non-linear problem that requires a Newton's method to be solved in dc microgrids with constant power terminals. This paper presents sufficient conditions for the quadratic convergence of the Newton's method in this type…

A standard approach to Collaborative Filtering (CF), i.e. prediction of user ratings on items, relies on Matrix Factorization techniques. Representations for both users and items are computed from the observed ratings and used for…

This paper studies the convergence difficulty of cohesive zone models in static analysis. It is shown that an inappropriate starting point of iterations in the Newton-Raphson method is responsible for the convergence difficulty. A simple,…

Recently, small models with latent recursion have obtained promising results on complex reasoning tasks. These results are typically explained by the theory that such recursion increases a networks depth, allowing it to compactly emulate…