Related papers: A New Re-redistribution Scheme for Weighted State …

State redistribution is an algorithm that stabilizes cut cells for embedded boundary grid methods. This work extends the earlier algorithm in several important ways. First, state redistribution is extended to three spatial dimensions.…

Berger & Giuliani (2024) developed a provably stable weighted state redistribution (SRD) algorithm for cut-cell meshes. A key limitation of their method is that, although flux redistribution naturally vanishes when updates are small, SRD…

In this paper we develop a new technique, called \textit{state redistribution}, that allows the use of explicit time stepping when approximating solutions to hyperbolic conservation laws on embedded boundary grids. State redistribution is a…

Cut meshes are a type of mesh that is formed by allowing embedded boundaries to "cut" a simple underlying mesh resulting in a hybrid mesh of cut and standard elements. While cut meshes can allow complex boundaries to be represented well…

We propose a practical finite volume method on cut cells using state redistribution. Our algorithm is provably monotone, total variation diminishing, and GKS stable in many situations, and shuts off continuously as the cut cell size…

We propose a state redistribution method for high order discontinuous Galerkin methods on curvilinear embedded boundary grids. State redistribution relaxes the overly restrictive CFL condition that results from arbitrarily small cut cells…

The representation of small scale barriers, such as sea-walls, in coastal flooding simulations is a common computational constraint that can be difficult to overcome due to the combination of the need for resolution and the CFL constraining…

This work aims to extend the residual distribution (RD) framework to stiff relaxation problems. The RD is a class of schemes which is used to solve hyperbolic system of partial differential equations. Up to our knowledge, it was used only…

Due to the lack of state dimension optimization methods, deep state space models (SSMs) have sacrificed model capacity, training search space, or stability to alleviate computational costs caused by high state dimensions. In this work, we…

In this paper, we develop a high order residual distribution (RD) method for solving steady state conservation laws in a novel Hermite weighted essentially non-oscillatory (HWENO) framework recently developed in [24]. In particular, we…

Limiting failures of machine learning systems is of paramount importance for safety-critical applications. In order to improve the robustness of machine learning systems, Distributionally Robust Optimization (DRO) has been proposed as a…

We propose an improved successive branch reduction (SBR) method to solve stochastic distribution network reconfiguration (SDNR), a mixed-integer program that is known to be computationally challenging. First, for a special distribution…

Large-scale finite element simulations of complex physical systems governed by partial differential equations (PDE) crucially depend on adaptive mesh refinement (AMR) to allocate computational budget to regions where higher resolution is…

This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks,…

We present a new state transfer method for geographic State Machine Replication (SMR) that dynamically allocates the state to be transferred among replicas according to changes in communication bandwidths. SMR is a method that improves…

Adaptive Mesh Refinement (AMR) enhances the Finite Element Method, an important technique for simulating complex problems in engineering, by dynamically refining mesh regions, enabling a favorable trade-off between computational speed and…

We present Re-weighted Gradient Descent (RGD), a novel optimization technique that improves the performance of deep neural networks through dynamic sample re-weighting. Leveraging insights from distributionally robust optimization (DRO)…

Random Reshuffling (RR), also known as Stochastic Gradient Descent (SGD) without replacement, is a popular and theoretically grounded method for finite-sum minimization. We propose two new algorithms: Proximal and Federated Random…

Random Reshuffling (RR), which is a variant of Stochastic Gradient Descent (SGD) employing sampling without replacement, is an immensely popular method for training supervised machine learning models via empirical risk minimization. Due to…

Finite element discretizations of problems in computational physics often rely on adaptive mesh refinement (AMR) to preferentially resolve regions containing important features during simulation. However, these spatial refinement strategies…