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The accurate quantum chemical calculation of excited states is a challenging task, often requiring computationally demanding methods. When entire ground and excited potential energy surfaces (PESs) are desired, e.g., to predict the…
The dynamics of energetic particle (EP) species, born from fusion reactions or plasma heating schemes, are critical for predicting the behavior of magnetic confinement fusion experiments and future fusion reactors. Because energetic…
Numerical resolution of high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by…
An improved Boris algorithm for simulating the motion of charged particles in electromagnetic fields has been developed. This enhancement addresses the issue of inaccurate fast-scale cyclotron phase calculations present in the original…
We introduce the so called DeepParticle method to learn and generate invariant measures of stochastic dynamical systems with physical parameters based on data computed from an interacting particle method (IPM). We utilize the expressiveness…
The quasi-neutral hybrid model with kinetic ions and fluid electrons is a promising approach for bridging the inherent multi-scale nature of many problems in space and laboratory plasmas. Here, a novel, implicit, particle-in-cell based…
We introduce a robust optimization method for flip-free distortion energies used, for example, in parametrization, deformation, and volume correspondence. This method can minimize a variety of distortion energies, such as the symmetric…
This dissertation makes three main contributions. First, We identify a new connection between policy gradient and dynamic programming in MMDPs and propose the Coordinate Ascent Dynamic Programming (CADP) algorithm to compute a Markov policy…
Efficient design and performance of electrically actuated MEMS devices necessitate accurate estimation of electrostatic forces on the MEMS structures. This in turn requires thorough study of the capacitance of the structures and finally the…
We investigate the convergence of quasi-particle energies for periodic systems to the thermodynamic limit using increasingly large simulation cells corresponding to increasingly dense integration meshes in reciprocal space. The…
The constant potential molecular dynamics simulation method proposed by Siepmann and Sprik and reformulated later by Reed (SR-CPM) has been widely employed to investigate the metallic electrolyte/electrode interfaces, especially for…
High-intensity laser plasma interactions create complex computational problems because they involve both fluid and kinetic regimes, which need models that maintain physical precision while keeping computational speed. The research…
Molecular dynamics simulations of biomolecules have been widely adopted in biomedical studies. As classical point-charge models continue to be used in routine biomolecular applications, there have been growing demands on developing…
Analyses in high energy physics aim to put the Standard Model---the commonly accepted theory---to test. For convincing conclusions, analysis methods are needed which offer an unambiguous comparison between data and theory while allowing…
In this work, we propose efficient and accurate numerical algorithms based on Difference Potentials Method for numerical solution of chemotaxis systems and related models in 3D. The developed algorithms handle 3D irregular geometry with the…
We present a new theory for partitioning simulations of periodic and solid-state systems into physically sound atomic contributions at the level of Kohn-Sham density functional theory. Our theory is based on spatially localized linear…
We consider partially observable Markov decision processes (POMDPs) with a set of target states and positive integer costs associated with every transition. The traditional optimization objective (stochastic shortest path) asks to minimize…
An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD) [J. Chem.…
Electron ptychography provides new opportunities to resolve atomic structures with deep sub-angstrom spatial resolution and studying electron-beam sensitive materials with high dose efficiency. In practice, obtaining accurate ptychography…
To minimise systematic errors in Monte Carlo simulations of charged particles, long range electrostatic interactions have to be calculated accurately and efficiently. Standard approaches, such as Ewald summation or the naive application of…