相关论文: Efficiency Gains from Time Refinement on AMR Meshe…

Group Theory techniques can aid greatly the determination of magnetic structures. The integration of their calculations into new and existing refinement programs is an ongoing development that will simplify and make more rigorous the…

We present a new refinement strategy for locally refined B-splines which ensures the local linear independence of the basis functions. The strategy also guarantees the spanning of the full spline space on the underlying locally refined…

The immense computational cost of traditional numerical weather and climate models has sparked the development of machine learning (ML) based emulators. Because ML methods benefit from long records of training data, it is common to use…

We argue that refining, coarse graining and entangling operators can be obtained from time evolution operators. This applies in particular to geometric theories, such as spin foams. We point out that this provides a construction principle…

This paper presents Space-Time MultiGrid (STMG) methods which are suitable for performing topology optimisation of transient heat conduction problems. The proposed methods use a pointwise smoother and uniform Cartesian space-time meshes.…

We formulate a general energy and method for segmentation that is designed to have preference for segmenting the coarse structure over the fine structure of the data, without smoothing across boundaries of regions. The energy is formulated…

Dynamic analysis of structures subjected to earthquake excitation is a time-consuming process, particularly in the case of extremely small time step required, or in the presence of high geometric and material nonlinearity. Performing…

Wave equation techniques have been an integral part of geophysical imaging workflows to investigate the Earth's subsurface. Least-squares reverse time migration (LSRTM) is a linearized inversion problem that iteratively minimizes a misfit…

Despite the advantageous subquadratic complexity of modern recurrent deep learning models -- such as state-space models (SSMs) -- recent studies have highlighted their potential shortcomings compared to transformers on reasoning and…

Current AMR simulations require algorithms that are highly parallelized and manage memory efficiently. As compute engines grow larger, AMR simulations will require algorithms that achieve new levels of efficient parallelization and memory…

An approach to utilizing adaptive mesh refinement algorithms for storm surge modeling is proposed. Currently numerical models exist that can resolve the details of coastal regions but are often too costly to be run in an ensemble…

We introduce a reinforcement learning (RL) based adaptive optimization algorithm for aerodynamic shape optimization focused on dimensionality reduction. The form in which RL is applied here is that of a surrogate-based, actor-critic policy…

Algorithm unrolling methods have proven powerful for solving the regularized least squares problem in computational magnetic resonance imaging (MRI). These approaches unfold an iterative algorithm with a fixed number of iterations,…

This research rigorously investigates the convergence of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in elastic solids. We specifically examine a novel Ambrosio-Tortorelli (AT1)…

Accurate prediction of energy and forces for 3D molecular systems is one of fundamental challenges at the core of AI for Science applications. Many powerful and data-efficient neural networks predict molecular energies and forces from…

We present an algorithm to perform trust-region-based optimization for nonlinear unconstrained problems. The method selectively uses function and gradient evaluations at different floating-point precisions to reduce the overall energy…

The local refinement of PHT-splines (polynomial splines over hierarchical T-meshes) is achieved by a simple cross insertion, which may introduce superfluous control points or coefficients. By allowing split-in-half in mesh refinement,…

Despite recent advances in subquadratic attention mechanisms or state-space models, processing long token sequences still imposes significant computational requirements. Token merging has emerged as a solution to increase computational…

Time reversal, that is prefiltering of transmitted signals with time reversed channel impulse responses, may be used in single user communications in order to move complexity from the receiver to the transmitter, and in multiuser…

Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to solve such structured convex optimization problems. Within…