Identifying physical properties of deformable objects by using particle filters

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Driven by the need for more efficient and seamless integration of physical models and data, physics -informed neural networks (PINNs) have seen a surge of interest in recent years. However, ensuring the reliability of their convergence and accuracy remains ...

Distributed learning is the key for enabling training of modern large-scale machine learning models, through parallelising the learning process. Collaborative learning is essential for learning from privacy-sensitive data that is distributed across various ...

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...

We consider the idealized setting of gradient flow on the population risk for infinitely wide two-layer ReLU neural networks (without bias), and study the effect of symmetries on the learned parameters and predictors. We first describe a general class of s ...

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

The Dirichlet-Neumann (DN) method has been extensively studied for linear partial differential equations, while little attention has been devoted to the nonlinear case. In this paper, we analyze the DN method both as a nonlinear iterative method and as a p ...

Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are ubiquitous in statistics, ...

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

We generalize and provide a linear algebra-based perspective on a finite element (FE) ho-mogenization scheme, pioneered by Schneider et al. (2017)[1] and Leuschner and Fritzen (2018)[2]. The efficiency of the scheme is based on a preconditioned, well-scale ...

Stabilized Runge???Kutta methods are especially efficient for the numerical solution of large systems of stiff nonlinear differential equations because they are fully explicit. For semi-discrete parabolic problems, for instance, stabilized Runge???Kutta me ...

The optimization of surface finish to improve performance, such as adhesion, friction, wear, fatigue life, or interfacial transport, occurs largely through trial and error, despite significant advancements in the relevant science. There are three central c ...

This paper considers the multi-agent linear least-squares problem in a server-agent network architecture. The system comprises multiple agents, each with a set of local data points. The agents are connected to a server, and there is no inter-agent communic ...

Two-level domain decomposition methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level preconditioner (or its corr ...

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

Sharpness-Aware Minimization (SAM) is a recent training method that relies on worst-case weight perturbations which significantly improves generalization in various settings. We argue that the existing justifications for the success of SAM which are based ...

We propose a stochastic conditional gradient method (CGM) for minimizing convex finitesum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or require carefully inc ...

Astrobots are robotic artifacts whose swarms are used in astrophysical studies to generate the map of the observable universe. These swarms have to be coordinated with respect to various desired observations. Such coordination\footnote{\z{A coordination sa ...

Modern manufacturing engineering is based on a ``design-through-analysis'' workflow. According to this paradigm, a prototype is first designed with Computer-aided-design (CAD) software and then finalized by simulating its physical behavior, which usually i ...

We study the performance of Stochastic Cubic Regularized Newton (SCRN) on a class of functions satisfying gradient dominance property with

1\le\alpha\le2

which holds in a wide range of applications in machine learning and signal processing. This conditio ...

Identifying physical properties of deformable objects by using particle filters

Chattez avec Graph Search

Residual-based attention in physics-informed neural networks

Optimization Algorithms for Decentralized, Distributed and Collaborative Machine Learning

Generalization of Scaled Deep ResNets in the Mean-Field Regime

On the symmetries in the dynamics of wide two-layer neural networks

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

On the nonlinear Dirichlet-Neumann method and preconditioner for Newton's method

Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution

Singular quadratic eigenvalue problems: linearization and weak condition numbers

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

An optimal preconditioned FFT-accelerated finite element solver for homogenization

Explicit Stabilized Multirate Method For Stiff Differential Equations

Contact.engineering-Create, analyze and publish digital surface twins from topography measurements across many scales

Iterative pre-conditioning for expediting the distributed gradient-descent method: The case of linear least-squares problem

Substructured Two-grid and Multi-grid Domain Decomposition Methods

TimeEvolver: A program for time evolution with improved error bound

Towards Understanding Sharpness-Aware Minimization

Faster One-Sample Stochastic Conditional Gradient Method for Composite Convex Minimization

Data-Driven Convergence Prediction of Astrobots Swarms

Stabilized isogeometric discretizations on trimmed and union geometries, and weak imposition of the boundary conditions for the Darcy flow

Stochastic Second-Order Methods Improve Best-Known Sample Complexity of SGD for Gradient-Dominated Function