Related papers: The Augmented Fast Marching Method for Level Set R…

Reparameterization aims to improve the generalization of deep neural networks by transforming convolutional layers into equivalent multi-branched structures during training. However, there exists a gap in understanding how…

Quantization techniques have been applied in many challenging finance applications, including pricing claims with path dependence and early exercise features, stochastic optimal control, filtering problems and efficient calibration of large…

In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm (FMT*). The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional…

While backpropagation--reverse-mode automatic differentiation--has been extraordinarily successful in deep learning, it requires two passes (forward and backward) through the neural network and the storage of intermediate activations.…

We propose a new technique that boosts the convergence of training generative adversarial networks. Generally, the rate of training deep models reduces severely after multiple iterations. A key reason for this phenomenon is that a deep…

As deep learning models and datasets rapidly scale up, network training is extremely time-consuming and resource-costly. Instead of training on the entire dataset, learning with a small synthetic dataset becomes an efficient solution.…

We present careful numerical convergence studies, using parameterized curves to reach very high resolutions in two dimensions, of a level set method for multiphase curvature motion known as the Voronoi implicit interface method. Our tests…

We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…

Existing hybrid Level Set / Front Tracking methods have been developed for structured meshes and successfully used for efficient and accurate simulations of complex multiphase flows. This contribution extends the capability of hybrid Level…

We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…

Stokes flow equations have been implemented successfully in practice for simulating problems with moving interfaces. Though computational methods produce accurate solutions and numerical convergence can be demonstrated using a resolution…

Unsigned Distance Fields (UDFs) can be used to represent non-watertight surfaces. However, current approaches to converting them into explicit meshes tend to either be expensive or to degrade the accuracy. Here, we extend the marching cube…

Deep learning has revolutionized industries like computer vision, natural language processing, and speech recognition. However, back propagation, the main method for training deep neural networks, faces challenges like computational…

We propose a new methodology to design first-order methods for unconstrained strongly convex problems. Specifically, instead of tackling the original objective directly, we construct a shifted objective function that has the same minimizer…

We developed a sharp interface level-set approach for two-phase immiscible flow with moving contact lines. The Cox-Voinov model is used to describe the moving contact line. A piecewise linear interface method is used to construct the signed…

Federated learning faces critical challenges in balancing communication efficiency and model accuracy. One key issue lies in the approximation of update errors without incurring high computational costs. In this paper, we propose a…

We consider Trace finite element methods for the linear membrane problem on second order tetrahedral elements. To accomplish this, zero-level set reconstruction methods for second order tetrahedra are considered. For the higher order…

Federated learning (FL) is a novel machine learning setting that enables on-device intelligence via decentralized training and federated optimization. Deep neural networks' rapid development facilitates the learning techniques for modeling…

A simulation framework based on the level-set and the immersed boundary methods (LS-IBM) has been developed for reactive transport problems in porous media involving a moving solid-fluid interface. The interface movement due to surface…

We propose a novel method for reconstructing explicit parameterized surfaces from Signed Distance Fields (SDFs), a widely used implicit neural representation (INR) for 3D surfaces. While traditional reconstruction methods like Marching…