Related papers: Regularized dynamical parametric approximation of …

Uniformly regular equilibrium problems are natural generalizations of abstract equilibrium prob lems and they are defined over the uniformly prox-regular nonconvex sets. Some new efficient implicit methods for solving uniformly regular…

Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…

Neural networks have emerged as promising tools for solving partial differential equations (PDEs), particularly through the application of neural operators. Training neural operators typically requires a large amount of training data to…

A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…

This paper details how to parameterize the posterior distribution of state-space systems to generate improved optimization problems for system identification using variational inference. Three different parameterizations of the assumed…

The parameters of a neural network are naturally organized in groups, some of which might not contribute to its overall performance. To prune out unimportant groups of parameters, we can include some non-differentiable penalty to the…

An ill-posed inverse problem of autoconvolution type is investigated. This inverse problem occurs in nonlinear optics in the context of ultrashort laser pulse characterization. The novelty of the mathematical model consists in a physically…

We introduce a new general framework for the approximation of evolution equations at low regularity and develop a new class of schemes for a wide range of equations under lower regularity assumptions than classical methods require. In…

Classical and new numerical schemes are generated using evolutionary computing. Differential Evolution is used to find the coefficients of finite difference approximations of function derivatives, and of single and multi-step integration…

We propose a numerical method based on physics-informed Random Projection Neural Networks for the solution of Initial Value Problems (IVPs) of Ordinary Differential Equations (ODEs) with a focus on stiff problems. We address an Extreme…

In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…

In this paper, we develop a regularized higher-order Taylor based method for solving composite (e.g., nonlinear least-squares) problems. At each iteration, we replace each smooth component of the objective function by a higher-order Taylor…

All discretized numerical models contain modelling errors - this reality is amplified when reduced-order models are used. The ability to accurately approximate modelling errors informs statistics on model confidence and improves…

Physics-informed neural networks have gained popularity as a deep-learning based parametric partial differential equation solver. Especially for engineering applications, this approach is promising because a single neural network could…

Data-driven methods have recently made great progress in the discovery of partial differential equations (PDEs) from spatial-temporal data. However, several challenges remain to be solved, including sparse noisy data, incomplete candidate…

Dynamical models identified from data are frequently employed in control system design. However, decoupling system identification from controller synthesis can result in situations where no suitable controller exists after a model has been…

There are many critical challenges in optimizing neural network models, including distributed computing, compression techniques, and efficient training, regardless of their application to specific tasks. Solving such problems is crucial…

The successful training of deep neural networks requires addressing challenges such as overfitting, numerical instabilities leading to divergence, and increasing variance in the residual stream. A common solution is to apply regularization…

Modern deep learning models generalize remarkably well in-distribution, despite being overparametrized and trained with little to no explicit regularization. Instead, current theory credits implicit regularization imposed by the choice of…

Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…