Related papers: Robust Matrix-Free Newton-Krylov Solvers via Autom…

This paper introduces significant advancements in fractional neural operators (FNOs) through the integration of adaptive hybrid kernels and stochastic multiscale analysis. We address several open problems in the existing literature by…

This paper proposes a deep neural network (DNN)-driven framework to address the longstanding generalization challenge in adaptive filtering (AF). In contrast to traditional AF frameworks that emphasize explicit cost function design, the…

Discontinuous Galerkin (DG) methods are promising high order discretizations for unsteady compressible flows. Here, we focus on Numerical Weather Prediction (NWP). These flows are characterized by a fine resolution in $z$-direction and low…

In this paper we present a refined Radial Basis Function-generated Finite Difference (RBF-FD) solution for a non-Newtonian fluid in a closed differentially heated cavity. The non-Newtonian behaviour is modelled with the Ostwald-de Waele…

The control of high-dimensional distributed parameter systems (DPS) remains a challenge when explicit coarse-grained equations are unavailable. Classical equation-free (EF) approaches rely on fine-scale simulators treated as black-box…

We study a semismooth Newton-type method for the nearest doubly stochastic matrix problem where both differentiability and nonsingularity of the Jacobian can fail. The optimality conditions for this problem are formulated as a system of…

We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include…

We present a general and scalable framework for the automated discovery of optimal meta-solvers for the solution of time-dependent nonlinear partial differential equations after appropriate discretization. By integrating classical numerical…

Neural network-based approaches have recently shown significant promise in solving partial differential equations (PDEs) in science and engineering, especially in scenarios featuring complex domains or incorporation of empirical data. One…

Recent developments have made it possible to overcome grid-based limitations of finite difference (FD) methods by adopting the kernel-based meshless framework using radial basis functions (RBFs). Such an approach provides a meshless…

This paper presents the Jump Markov Filtering Network (JMFNet), a novel model-based deep learning framework for real-time state-state estimation in jump Markov systems with unknown noise statistics and mode transition dynamics. A hybrid…

Dissipative estimator (observer) design for continuous time-delay systems poses a significant challenge when an unlimited number of pointwise and general distributed delays (DDs) are concerned. We propose an effective solution to this…

Two novel parallel Newton-Krylov Balancing Domain Decomposition by Constraints (BDDC) and Dual-Primal Finite Element Tearing and Interconnecting (FETI-DP) solvers are here constructed, analyzed and tested numerically for implicit time…

This paper presents a detailed discussion of the ``Newton's method'' algorithm for finding apparent horizons in 3+1 numerical relativity. We describe a method for computing the Jacobian matrix of the finite differenced $H(h)$ function by…

This paper develops a new class of Rosenbrock-type integrators based on a Krylov space solution of the linear systems. The new family, called Rosenbrock-Krylov (Rosenbrock-K), is well suited for solving large scale systems of ODEs or…

Feedforward computation, such as evaluating a neural network or sampling from an autoregressive model, is ubiquitous in machine learning. The sequential nature of feedforward computation, however, requires a strict order of execution and…

This contribution presents an improved low-order 3D finite element formulation with hourglass stabilization using automatic differentiation (AD). Here, the former Q1STc formulation is enhanced by an approximation-free computation of the…

A new penalty-free neural network method, PFNN-2, is presented for solving partial differential equations, which is a subsequent improvement of our previously proposed PFNN method [1]. PFNN-2 inherits all advantages of PFNN in handling the…

Automatic differentiation (AD), a technique for constructing new programs which compute the derivative of an original program, has become ubiquitous throughout scientific computing and deep learning due to the improved performance afforded…

Deep neural networks (DNNs) are known to be vulnerable to adversarial examples that are crafted with imperceptible perturbations, i.e., a small change in an input image can induce a mis-classification, and thus threatens the reliability of…