Related papers: RandNet-Parareal: a time-parallel PDE solver using…

Physics-Informed Neural Networks (PINNs) have recently emerged as a promising alternative for solving partial differential equations, offering a mesh-free framework that incorporates physical laws directly into the learning process. In this…

We present a method for fast and accurate physics-based predictions during non-prehensile manipulation planning and control. Given an initial state and a sequence of controls, the problem of predicting the resulting sequence of states is a…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

In this paper we proposed two new quasi-boundary value methods for regularizing the ill-posed backward heat conduction problems. With a standard finite difference discretization in space and time, the obtained all-at-once nonsymmetric…

To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a…

Asynchronous iterations are more and more investigated for both scaling and fault-resilience purpose on high performance computing platforms. While so far, they have been exclusively applied within space domain decomposition frameworks,…

A key component of many robotics model-based planning and control algorithms is physics predictions, that is, forecasting a sequence of states given an initial state and a sequence of controls. This process is slow and a major computational…

We consider using deep neural networks to solve time-dependent partial differential equations (PDEs), where multi-scale processing is crucial for modeling complex, time-evolving dynamics. While the U-Net architecture with skip connections…

A variant of the Parareal method for highly oscillatory systems of PDEs was proposed by Haut and Wingate (2014). In that work they proved superlinear conver- gence of the method in the limit of infinite time scale separation. Their coarse…

Residual neural networks (ResNets) are a promising class of deep neural networks that have shown excellent performance for a number of learning tasks, e.g., image classification and recognition. Mathematically, ResNet architectures can be…

In this paper, a physics-informed multiresolution wavelet neural network (PIMWNN) method is proposed for solving partial differential equations (PDEs). This method uses the multiresolution wavelet neural network (MWNN) to approximate…

In this contribution the usage of the Parareal method is proposed for the time-parallel solution of the eddy current problem. The method is adapted to the particular challenges of the problem that are related to the differential algebraic…

Surface partial differential equations arise in numerous scientific and engineering applications. Their numerical solution on static and evolving surfaces remains challenging due to geometric complexity and, for evolving geometries, the…

Physics-informed neural networks (PINNs) encode physical conservation laws and prior physical knowledge into the neural networks, ensuring the correct physics is represented accurately while alleviating the need for supervised learning to a…

This paper analyzes the SParareal algorithm for stochastic differential equations (SDEs). Compared to the classical Parareal algorithm, the SParareal algorithm accelerates convergence by introducing stochastic perturbations, achieving…

This work unifies pseudo-time and inexact regularization techniques for nonmonotone classes of partial differential equations, into a regularized pseudo-time framework. Convergence of the residual at the predicted rate is investigated…

We propose a method combining boundary integral equations and neural networks (BINet) to solve partial differential equations (PDEs) in both bounded and unbounded domains. Unlike existing solutions that directly operate over original PDEs,…

Recently, the ParaOpt algorithm was proposed as an extension of the time-parallel Parareal method to optimal control. ParaOpt uses quasi-Newton steps that each require solving a system of matching conditions iteratively. The…

Parareal is a widely studied parallel-in-time method that can achieve meaningful speedup on certain problems. However, it is well known that the method typically performs poorly on non-diffusive equations. This paper analyzes linear…

Time-parallel algorithms, such as Parareal, are well-understood for linear problems, but their convergence analysis for nonlinear, chaotic systems remains limited. This paper introduces a new theoretical framework for analysing…