Related papers: High-efficient machine learning projection method …
It is a critical challenge to simultaneously gain high interpretability and efficiency with the current schemes of deep machine learning (ML). Tensor network (TN), which is a well-established mathematical tool originating from quantum…
The development of next-generation autonomous control of fission systems, such as nuclear power plants, will require leveraging advancements in machine learning. For fission systems, accurate prediction of nuclear transport is important to…
This paper presents a probabilistic framework to obtain both reliable and fast uncertainty estimates for predictions with Deep Neural Networks (DNNs). Our main contribution is a practical and principled combination of DNNs with sparse…
The Variationally Mimetic Operator Network (VarMiON) approach is a machine learning technique, originally developed to predict the solution of elliptic differential problems, that combines operator networks with a structure inherited from…
In this paper, a pore-scale network modeling method, based on the flow continuity residual in conjunction with a Newton-Raphson non-linear iterative solving technique, is proposed and used to obtain the pressure and flow fields in a network…
Probabilistic inference is a fundamental task in modern machine learning. Recent advances in tensor network (TN) contraction algorithms have enabled the development of better exact inference methods. However, many common inference tasks in…
This paper presents a novel stabilized mixed material point method (MPM) designed for the unified modeling of free-surface and seepage flow. The unified formulation integrates the Navier-Stokes equation with the Darcy-Brinkman-Forchheimer…
Machine learning (ML) problems are often posed as highly nonlinear and nonconvex unconstrained optimization problems. Methods for solving ML problems based on stochastic gradient descent are easily scaled for very large problems but may…
We present an adaptive finite element method for the incompressible Navier--Stokes equations based on a standard splitting scheme (the incremental pressure correction scheme). The presented method combines the efficiency and simplicity of a…
Solving flow through porous media is a crucial step in the topology optimisation of cold plates, a key component in modern thermal management. Traditional computational fluid dynamics (CFD) methods, while accurate, are often prohibitively…
Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in…
Terrain elevation modeling for off-road navigation aims to accurately estimate changes in terrain geometry in real-time and quantify the corresponding uncertainties. Having precise estimations and uncertainties plays a crucial role in…
We introduce a collection of benchmark problems in 2D and 3D (geometry description and boundary conditions), including simple cases with known analytic solution, classical experimental setups, and complex geometries with fabricated…
Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a…
We present a strong form, meshless point collocation explicit solver for the numerical solution of the transient, incompressible, viscous Navier-Stokes (N-S) equations in two dimensions. We numerically solve the governing flow equations in…
Machine learning (ML) is rapidly transforming the way molecular dynamics simulations are performed and analyzed, from materials modeling to studies of protein folding and function. ML algorithms are often employed to learn low-dimensional…
In this work, by introducing the seismic impedance tensor we propose a new Rayleigh wave dispersion function in a homogeneous and layered medium of the Earth, which provides an efficient way to compute the dispersion curve -- a relation…
We aim to solve the incompressible Navier-Stokes equations within the complex microstructure of a porous material. Discretizing the equations on a fine grid using a staggered (e.g., marker-and-cell, mixed FEM) scheme results in a nonlinear…
We develop a Bayesian methodology for numerical solution of the incompressible Navier--Stokes equations with quantified uncertainty. The central idea is to treat discretized Navier--Stokes dynamics as a state-space model and to view…
Elliptic Partial Differential Equations (PDEs) play a central role in computing the equilibrium conditions of physical problems (heat, gravitation, electrostatics, etc.). Efficient solutions to elliptic PDEs are also relevant to computer…