相关论文: Momentum-Accelerated Richardson(m) and Their Multi…

Two major momentum-based techniques that have achieved tremendous success in optimization are Polyak's heavy ball method and Nesterov's accelerated gradient. A crucial step in all momentum-based methods is the choice of the momentum…

In this work, we extend and generalize our solving strategy, first introduced in [1], based on a greedy optimization algorithm and the alternating direction method (ADM) for nonlinear systems computed with multiple load steps. In…

We study optimization for losses that admit a variance-mean scale-mixture representation. Under this representation, each EM iteration is a weighted least squares update in which latent variables determine observation and parameter weights;…

Advancing the dynamics inference of power electronic systems (PES) to the real-time edge-side holds transform-ative potential for testing, control, and monitoring. How-ever, efficiently inferring the inherent hybrid continu-ous-discrete…

Multigrid solvers face multiple challenges on parallel computers. Two fundamental ones read as follows: Multiplicative solvers issue coarse grid solves which exhibit low concurrency and many multigrid implementations suffer from an…

Two algorithms are proposed, analyzed, and tested for solving continuous optimization problems with nonlinear equality constraints. Each is an extension of a stochastic momentum-based method from the unconstrained setting to the setting of…

We leverage physics-embedded differentiable graph network simulators (GNS) to accelerate particulate and fluid simulations to solve forward and inverse problems. GNS represents the domain as a graph with particles as nodes and learned…

We propose a Newton-based scheme, initialized by neural operator predictions, to accelerate the parametric solution of nonlinear problems in computational solid mechanics. First, a physics informed conditional neural field is trained to…

Iterative methods are widely used for solving partial differential equations (PDEs). However, the difficulty in eliminating global low-frequency errors significantly limits their convergence speed. In recent years, neural networks have…

Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…

This paper presents Mechanistic Neural Networks, a neural network design for machine learning applications in the sciences. It incorporates a new Mechanistic Block in standard architectures to explicitly learn governing differential…

We consider the convergence of iterative solvers for problems of nonlinear magnetostatics. Using the equivalence to an underlying minimization problem, we can establish global linear convergence of a large class of methods, including the…

We present a scalable strategy for development of mesh-free hybrid neuro-symbolic partial differential equation solvers based on existing mesh-based numerical discretization methods. Particularly, this strategy can be used to efficiently…

Fast multipole methods (FMM) were originally developed for accelerating $N$-body problems for particle-based methods. FMM is more than an $N$-body solver, however. Recent efforts to view the FMM as an elliptic Partial Differential Equation…

In the present work, a multi-scale framework for neural network enhanced methods is proposed for approximation of function and solution of partial differential equations (PDEs). By introducing the multi-scale concept, the total solution of…

Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization…

The demand for substantial increases in the spatial resolution of global weather- and climate- prediction models makes it necessary to use numerically efficient and highly scalable algorithms to solve the equations of large scale…

Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…

This paper presents a class of efficient manifold optimization algorithms for computing the ground state solutions of a semilinear elliptic system, which are unstable saddle points of the variational functional. Variational arguments show…

Fully connected multilayer perceptrons are used for obtaining numerical solutions of partial differential equations in various dimensions. Independent variables are fed into the input layer, and the output is considered as solution's value.…