Related papers: Scalable Local Timestepping on Octree Grids
We present a variant of the immersed boundary method integrated with octree meshes for highly efficient and accurate Large-Eddy Simulations (LES) of flows around complex geometries. We demonstrate the scalability of the proposed method up…
The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length and timescales. Often, it is computationally intractable to resolve the finest features…
Accurately estimating spatiotemporal traffic states on freeways is a significant challenge due to limited sensor deployment and potential data corruption. In this study, we propose an efficient and robust low-rank model for precise…
The family of temporal difference (TD) methods span a spectrum from computationally frugal linear methods like TD({\lambda}) to data efficient least squares methods. Least square methods make the best use of available data directly…
Radiative transfer modelling is part of many astrophysical simulations and is used to make synthetic observations and to assist analysis of observations. We concentrate on the modelling of the radio lines emitted by the interstellar medium.…
This work presents a data-driven approach to the identification of spatial and temporal truncation errors for linear and nonlinear discretization schemes of Partial Differential Equations (PDEs). Motivated by the central role of truncation…
Synchronization overheads pose a major challenge as applications advance towards extreme scales. In current large-scale algorithms, synchronization as well as data communication delay the parallel computations at each time step in a…
Auto-regressive decoding in Large Language Models (LLMs) is inherently memory-bound: every generation step requires loading the model weights and intermediate results from memory (e.g., High-Bandwidth Memory (HBM) for GPU servers), making…
We develop new dynamically orthogonal tensor methods to approximate multivariate functions and the solution of high-dimensional time-dependent nonlinear partial differential equations (PDEs). The key idea relies on a hierarchical…
Stochastic programming can be applied to consider uncertainties in energy system optimization models for capacity expansion planning. However, these models become increasingly large and time-consuming to solve, even without considering…
Partial differential equations (PDEs) are typically used as models of physical processes but are also of great interest in PDE-based image processing. However, when it comes to their use in imaging, conventional numerical methods for…
Ordinary differential equations (ODEs) can provide mechanistic models of temporally local changes of processes, where parameters are often informed by external knowledge. While ODEs are popular in systems modeling, they are less established…
For low-dimensional data sets with a large amount of data points, standard kernel methods are usually not feasible for regression anymore. Besides simple linear models or involved heuristic deep learning models, grid-based discretizations…
In this paper, we address the issue of modeling and estimating changes in the state of the spatio-temporal dynamical systems based on a sequence of observations like video frames. Traditional numerical simulation systems depend largely on…
Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…
We have found provably optimal algorithms for full-domain discrete-ordinate transport sweeps on a class of grids in 2D and 3D Cartesian geometry that are regular at a coarse level but arbitrary within the coarse blocks. We describe these…
We consider the optimal control problem of a general nonlinear spatio-temporal system described by Partial Differential Equations (PDEs). Theory and algorithms for control of spatio-temporal systems are of rising interest among the…
We develop a multirate timestepper for semi-implicit solutions of the unsteady incompressible Navier-Stokes equations (INSE) based on a recently-developed multidomain spectral element method (SEM). For {\em incompressible} flows, multirate…
Many safety-critical systems must achieve high-level task specifications with guaranteed safety and correctness. Much recent progress towards this goal has been made through controller synthesis from signal temporal logic (STL)…
Effective and timely responses to unexpected contingencies are crucial for enhancing the resilience of power grids. Given the fast, complex process of cascading propagation, corrective actions such as optimal load shedding (OLS) are…