Related papers: Statistical higher-order multi-scale method for no…
We present several improvements of the infinite matrix product state (iMPS) algorithm for finding ground states of one-dimensional quantum systems with long-range interactions. As a main new ingredient we introduce the superposed…
Numerical simulations are crucial for comprehending how engineering structures behave under extreme conditions, particularly when dealing with thermo-mechanically coupled issues compounded by damage-induced material softening. However, such…
The behavior of materials is influenced by a wide range of phenomena occurring across various time and length scales. To better understand the impact of microstructure on macroscopic response, multiscale modeling strategies are essential.…
The synchronized molecular dynamics simulation via macroscopic heat and momentum transfer is proposed for the non-isothermal flow behaviors of complex fluids. In this method, the molecular dynamics simulations are assigned to small fluid…
Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a…
We derived a number of numerical methods to treat biomolecular systems with multiple time scales. Based on the splitting of the operators associated with the slow-varying and fast-varying forces, new multiple time-stepping (MTS) methods are…
Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…
In this paper, we consider an unconstrained stochastic optimization problem where the objective function exhibits high-order smoothness. Specifically, we propose a new stochastic first-order method (SFOM) with multi-extrapolated momentum,…
In simulations of multiscale dynamical systems, not all relevant processes can be resolved explicitly. Taking the effect of the unresolved processes into account is important, which introduces the need for paramerizations. We present a…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
In this paper, Hamiltonian and energy preserving reduced-order models are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form with the state-dependent Poisson matrix. The high fidelity…
In this paper, we investigate projection-based intrusive and data-driven non-intrusive model order reduction methods in numerical simulation of rotating thermal shallow water equation (RTSWE) in parametric and non-parametric form.…
We introduce a new resource-efficient scheme for fault-tolerant quantum computation known as `macroscale multiplexing' (or simply `Macromux'), that utilizes scalable postselection to significantly improve the threshold of a given…
Mesoscale simulations of woven composites using parameterized analytical geometries offer a way to connect constituent material properties and their geometric arrangement to effective composite properties and performance. However, the…
This article reviews recent inverse statistical-mechanical methodologies that we have devised to optimize interaction potentials in soft matter systems that correspond to stable "target" structures. We are interested in finding the…
In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realized in the semi-discrete finite-volume framework and is based…
Thermospheric mass density is a major driver of satellite drag, the largest source of uncertainty in accurately predicting the orbit of satellites in low Earth orbit (LEO) pertinent to space situational awareness. Most existing models for…
The paper suggests a generalization of the Sign-Perturbed Sums (SPS) finite sample system identification method for the identification of closed-loop observable stochastic linear systems in state-space form. The solution builds on the…
An algorithm for non-stationary spatial modelling using multiple secondary variables is developed. It combines Geostatistics with Quantile Random Forests to give a new interpolation and stochastic simulation algorithm. This paper introduces…
We consider a class of relaxation problems mixing slow and fast variations which can describe population dynamics models or hyperbolic systems, with varying stiffness (from non-stiff to strongly dissipative), and develop a multi-scale…