Related papers: A fast neural hybrid Newton solver adapted to impl…

Finding roots of equations is at the heart of most computational science. A well-known and widely used iterative algorithm is the Newton's method. However, its convergence depends heavily on the initial guess, with poor choices often…

Neural surrogates for stiff differential-algebraic equations (DAEs) face two barriers: soft-constraint methods leave algebraic residuals that stiffness amplifies into errors, and hard-constraint methods require trajectory data from stiff…

First-order optimization methods, such as stochastic gradient descent (SGD) and its variants, are widely used in machine learning applications due to their simplicity and low per-iteration costs. However, they often require larger numbers…

In [1], the non-linear space-time Hasegawa-Mima plasma equation is formulated as a coupled system of two linear PDE's, a solution of which is a pair (u, w). The first equation is of hyperbolic type and the second of elliptic type.…

Implicit layer deep learning techniques, like Neural Differential Equations, have become an important modeling framework due to their ability to adapt to new problems automatically. Training a neural differential equation is effectively a…

In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…

Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…

Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…

We present in this paper algorithms for solving stiff PDEs on the unit sphere with spectral accuracy in space and fourth-order accuracy in time. These are based on a variant of the double Fourier sphere method in coefficient space with…

We propose several deep-learning accelerated optimization solvers with convergence guarantees. We use ideas from the analysis of accelerated forward-backward schemes like FISTA, but instead of the classical approach of proving convergence…

Classification problems using deep learning have been shown to have a high-curvature subspace in the loss landscape equal in dimension to the number of classes. Moreover, this subspace corresponds to the subspace spanned by the logit…

We present a neural network-based method for learning scalar hyperbolic conservation laws. Our method replaces the traditional numerical flux in finite volume schemes with a trainable neural network while preserving the conservative…

Fixed-point or Newton-methods are typically employed for the numerical solution of nonlinear systems arising from discretization of nonlinear magnetic field problems. We here discuss an alternative strategy which uses local Quasi-Newton…

Optimization-based solvers play a central role in a wide range of signal processing and communication tasks. However, their applicability in latency-sensitive systems is limited by the sequential nature of iterative methods and the high…

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…

In this study, a fast and stable machine-learned hybrid algorithm implemented in TensorFlow for the integration of stiff chemical kinetics is introduced. Numerical solutions to differential equations are at the core of computational fluid…

In this work, we propose a parallel-in-time solver for linear and nonlinear ordinary differential equations. The approach is based on an efficient multilevel solver of the Schur complement related to a multilevel time partition. For linear…

This paper develops a numerical procedure to accelerate the convergence of the Favre-averaged Non-Linear Harmonic (FNLH) method. The scheme provides a unified mathematical framework for solving the sparse linear systems formed by the mean…

We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…

Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called…