Related papers: Model calibration using a parallel differential ev…
Accurate prediction of machining deformation in structural components is essential for ensuring dimensional precision and reliability. Such deformation often originates from residual stress fields, whose distribution and influence vary…
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…
In this work we analyze strategies for convolutional neural network scaling; that is, the process of scaling a base convolutional network to endow it with greater computational complexity and consequently representational power. Example…
Among many evolutionary algorithms, differential evolution (DE) has received much attention over the last two decades. DE is a simple yet powerful evolutionary algorithm that has been used successfully to optimize various real-world…
We introduce two a posteriori error estimators for N\'ed\'elec finite element discretizations of the curl-curl problem. These estimators pertain to a new Prager-Synge identity and an associated equilibration procedure. They are reliable and…
Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically…
Many parallel and distributed computing research results are obtained in simulation, using simulators that mimic real-world executions on some target system. Each such simulator is configured by picking values for parameters that define the…
This study presents incremental correction methods for refining neural network parameters or control functions entering into a continuous-time dynamic system to achieve improved solution accuracy in satisfying the interim point constraints…
Failure probability estimation problem is an crucial task in engineering. In this work we consider this problem in the situation that the underlying computer models are extremely expensive, which often arises in the practice, and in this…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
In this paper we propose a method to generate suitably refined finite element meshes using neural networks. As a model problem we consider a linear elasticity problem on a planar domain (possibly with holes) having a polygonal boundary. We…
Computer simulation models are widely used to study complex physical systems. A related fundamental topic is the inverse problem, also called calibration, which aims at learning about the values of parameters in the model based on…
Unrolling training trajectories over time strongly influences the inference accuracy of neural network-augmented physics simulators. We analyze this in three variants of training neural time-steppers. In addition to one-step setups and…
Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which a function has the steepest rate of change. The main problem with basic…
Big science initiatives are trying to reconstruct and model the brain by attempting to simulate brain tissue at larger scales and with increasingly more biological detail than previously thought possible. The exponential growth of parallel…
A deep neural network (DNN) that can reliably model muscle responses from corresponding brain stimulation has the potential to increase knowledge of coordinated motor control for numerous basic science and applied use cases. Such cases…
Data-driven surrogate modeling has emerged as a promising approach for reducing computational expenses of multiscale simulations. Recurrent Neural Network (RNN) is a common choice for modeling of path-dependent behavior. However, previous…
The increasing use of deep neural networks (DNNs) in safety-critical systems has raised concerns about their potential for exhibiting ill-behaviors. While DNN verification and testing provide post hoc conclusions regarding unexpected…
Simulating collisions of deformable objects is a fundamental yet challenging task due to the complexity of modeling solid mechanics and multi-body interactions. Existing data-driven methods often suffer from lack of equivariance to physical…
Over 15 million epilepsy patients worldwide do not respond to drugs and require surgical treatment. Successful surgical treatment requires complete removal, or disconnection of the epileptogenic zone (EZ), but without a prospective…