Related papers: Sparse Grids based Adaptive Noise Reduction strate…
Grid cells in medial entorhinal cortex are believed to play a key role in path integration. However, the relation between path integration and the grid-like arrangement of their firing field remains unclear. We provide theoretical evidence…
This paper is concerned with developing an efficient numerical algorithm for fast implementation of the sparse grid method for computing the $d$-dimensional integral of a given function. The new algorithm, called the MDI-SG ({\em multilevel…
This article presents two novel adaptive-sparse polynomial dimensional decomposition (PDD) methods for solving high-dimensional uncertainty quantification problems in computational science and engineering. The methods entail global…
We develop a weak-form sparse identification method for interacting particle systems (IPS) with the primary goals of reducing computational complexity for large particle number $N$ and offering robustness to either intrinsic or extrinsic…
Particle Swarm Optimization (PSO) is a stochastic technique for solving the optimization problem. Attempts have been made to shorten the computation times of PSO based algorithms with massive threads on GPUs (graphic processing units),…
Recurrent neural networks (RNNs) are valued for their computational efficiency and reduced memory requirements on tasks involving long sequence lengths but require high memory-processor bandwidth to train. Checkpointing techniques can…
This research presents the development of an innovative algorithm tailored for the adaptive sampling of residual points within the framework of Physics-Informed Neural Networks (PINNs). By addressing the limitations inherent in existing…
The simulation of problems in kinetic plasma physics are often challenging due to strongly coupled phenomena across multiple scales. In this work, we propose a wavelet-based coarse-grained numerical scheme, based on the framework of…
Fully finetuning foundation language models (LMs) with billions of parameters is often impractical due to high computational costs, memory requirements, and the risk of overfitting. Although methods like low-rank adapters help address these…
Deep neural networks often suffer from poor generalization due to complex and non-convex loss landscapes. Sharpness-Aware Minimization (SAM) is a popular solution that smooths the loss landscape by minimizing the maximized change of…
Exploiting intrinsic structures in sparse signals underpins the recent progress in compressive sensing (CS). The key for exploiting such structures is to achieve two desirable properties: generality (\ie, the ability to fit a wide range of…
In this work, we present a high-fidelity and efficient point-particle direct numerical simulation framework based on a multi-block overset curvilinear grid system, enabling large-scale Lagrangian particle tracking in complex geometries with…
Particle-in-Cell (PIC) simulations are fundamental to plasma physics but often suffer from limited scalability due to particle-grid interaction bottlenecks and particle redistribution costs. Specifically, the particle-grid interaction…
We propose and study a Particle-In-Cell (PIC) method based on the Crank-Nicolson time discretization for the Vlasov-Poisson system with a strong and inhomogeneous external magnetic field with fixed direction, where we focus on the motion of…
Spiking Neural Networks (SNNs) are more biologically plausible and computationally efficient. Therefore, SNNs have the natural advantage of drawing the sparse structural plasticity of brain development to alleviate the energy problems of…
The numerical noise inherent to particle-in-cell simulation of 3D high intensity bunched beams is studied with the TRACEWIN code and compared with an analytical model by Struckmeier. The latter assumes that entropy growth can be related to…
The recently developed energy conserving semi-implicit method (ECsim) for PIC simulation is applied to multiple scale problems where the electron-scale physics needs to be only partially retained and the interest is on the macroscopic or…
In solving partial differential equations (PDEs), machine learning utilizing physical laws has received considerable attention owing to advantages such as mesh-free solutions, unsupervised learning, and feasibility for solving…
This paper considers sequential adaptive estimation of sparse signals under a constraint on the total sensing effort. The advantage of adaptivity in this context is the ability to focus more resources on regions of space where signal…
The stability of AC power grids relies on ancillary services that mitigate frequency fluctuations. The electromechanical inertia of large synchronous generators is currently the only resource to absorb frequency disturbances on sub-second…