Related papers: A framework for the automation of generalised stab…
We develop a general framework unifying several gradient-based stochastic optimization methods for empirical risk minimization problems both in centralized and distributed scenarios. The framework hinges on the introduction of an augmented…
Stochastic gradient descent with momentum (SGDM) is one of the most widely used optimization algorithms in machine learning. While optimization properties of SGDM have been extensively studied in the literature, it remains insufficiently…
In this paper, we study the performance of a large family of SGD variants in the smooth nonconvex regime. To this end, we propose a generic and flexible assumption capable of accurate modeling of the second moment of the stochastic…
Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for…
The prediction of dynamical stability of power grids becomes more important and challenging with increasing shares of renewable energy sources due to their decentralized structure, reduced inertia and volatility. We investigate the…
We present an energy-stable scheme for simulating the incompressible Navier-Stokes equations based on the generalized Positive Auxiliary Variable (gPAV) framework. In the gPAV-reformulated system the original nonlinear term is replaced by a…
How to practically maintain the frequency stability of large-scale power systems by a decentralized way is a simple but non-trivial question. In other words, is it possible to design any local controller without understanding the other…
We investigate the stabilization of unstable multidimensional partially observed single-sensor and multi-sensor linear systems driven by unbounded noise and controlled over discrete noiseless channels under fixed-rate information…
Numerous theories of learning propose to prevent the gradient from exponential growth with depth or time, to stabilize and improve training. Typically, these analyses are conducted on feed-forward fully-connected neural networks or simple…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
This paper presents the construction of novel stabilized finite element methods in the convective-diffusive context that exhibit correct-energy behavior. Classical stabilized formulations can create unwanted artificial energy. Our…
The recent surge in 4D Gaussian Splatting (4DGS) has achieved impressive dynamic scene reconstruction. While these methods demonstrate remarkable performance, the specific drivers behind such gains remain less explored, making a systematic…
The finite-difference time-domain (FDTD) algorithm is a popular numerical method for solving electromagnetic problems. FDTD simulations can suffer from instability due to the explicit nature of the method. Stability enforcement can be…
In this paper the finite-time stabilization problem is solved for a linear time-varying system with unknown control direction by exploiting a modified version of the classical extremum seeking algorithm. We propose to use a suitable…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
Imitation learning presents an effective approach to alleviate the resource-intensive and time-consuming nature of policy learning from scratch in the solution space. Even though the resulting policy can mimic expert demonstrations…
The evolution of any complex dynamical system is described by its state derivative operators. However, the extraction of the exact N-order state derivative operators is often inaccurate and requires approximations. The open-source CFD code…
Formal control synthesis approaches over stochastic systems have received significant attention in the past few years, in view of their ability to provide provably correct controllers for complex logical specifications in an automated…
This paper aims to provide a methodology for generating autonomous and non-autonomous systems with a fixed-time stable equilibrium point where an Upper Bound of the Settling Time (UBST) is set a priori as a parameter of the system. In…
The problem of stopping stochastic gradient descent (SGD) in an online manner, based solely on the observed trajectory, is a challenging theoretical problem with significant consequences for applications. While SGD is routinely monitored as…