Related papers: The Tensor-Train Stochastic Finite Volume Method f…
This paper presents a computational framework for the robust stiffness design of hyperelastic structures at finite deformations subject to various uncertain sources. In particular, the loading, material properties, and geometry…
We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately…
The convergence of many numerical optimization techniques is highly dependent on the initial guess given to the solver. To address this issue, we propose a novel approach that utilizes tensor methods to initialize existing optimization…
We introduce and analyze a new mixed finite element method with reduced symmetry for the standard linear model in viscoelasticity. Following a previous approach employed for linear elastodynamics, the present problem is formulated as a…
In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with…
We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
We develop new more efficient A-WENO schemes for both hyperbolic systems of conservation laws and nonconservative hyperbolic systems. The new schemes are a very simple modification of the existing A-WENO schemes: They are obtained by a more…
In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochastic Galerkin and collocation methods. Based on the BGK-type…
Entropy conditions play a crucial role in the extraction of a physically relevant solution for systems of conservation laws, thus motivating the construction of entropy stable schemes that satisfy a discrete analogue of such conditions.…
We study polynomial optimization problems whose objective has a composition or tensor train structure. These polynomials can be evaluated as a sequence of maps, giving rise to intermediate variables (``states'') of dimension lower than the…
This paper investigates the exact controllability problem for multi-dimensional stochastic first-order symmetric hyperbolic systems with control inputs acting in two distinct ways: an internal control applied to the diffusion term and a…
We propose a hybrid stochastic method for the tensor renormalization group (TRG) approach. TRG is known as a powerful tool to study the many-body systems and quantum field theory on the lattice. It is based on a low-rank approximation of…
Discrete-time stochastic systems with continuous spaces are hard to verify and control, even with MDP abstractions due to the curse of dimensionality. We propose an abstraction-based framework with robust dynamic programming mappings that…
We present a new high-order finite volume reconstruction method for hyperbolic conservation laws. The method is based on a piecewise cubic polynomial which provides its solutions a fifth-order accuracy in space. The spatially reconstructed…
A new adaptive weighted essentially non-oscillatory WENO-$\theta$ scheme in the context of finite difference is proposed. Depending on the smoothness of the large stencil used in the reconstruction of the numerical flux, a parameter…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
We study general linear transport-reaction systems on an arbitrary dimensional hypercube with periodic boundary conditions. Transport-reaction systems are often used to model the finite speed movement and interaction of particles, bacteria…
High order fast sweeping methods for efficiently solving steady state solutions of hyperbolic PDEs were not available yet on unstructured meshes. In this paper, we extend high order fast sweeping methods to unstructured triangular meshes by…
In this paper, we aim at the problem of tensor data completion. Tensor-train decomposition is adopted because of its powerful representation ability and linear scalability to tensor order. We propose an algorithm named Sparse Tensor-train…