Related papers: Numerical Method for Modeling Nucleation and Growt…
Diffusion models have demonstrated powerful performance in generating high-quality images. A typical example is text-to-image generator like Stable Diffusion. However, their widespread use also poses potential privacy risks. A key concern…
Molecular dynamics (MD) has long been the de facto choice for simulating complex atomistic systems from first principles. Recently deep learning models become a popular way to accelerate MD. Notwithstanding, existing models depend on…
In the present chapter we focus on the fundamentals of non-grid-conforming numerical approaches to simulating particulate flows, implementation issues and grid convergence vs. available reference data. The main idea is to avoid adapting the…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations…
The infamous numerical sign problem poses a fundamental obstacle to particle-based stochastic Wigner simulations in high dimensional phase space. Although the existing particle annihilation via uniform mesh significantly alleviates the sign…
Crystallization processes at the mesoscopic scale, where faceted, dendritic growth, and multigrain formation can be observed, are of particular interest within materials science and metallurgy. These processes are highly nonlinear,…
We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…
A numerical approach to the problem of wave scattering by many small particles is developed under the assumptions k<<1, d>>a, where a is the size of the particles and d is the distance between the neighboring particles. On the wavelength…
We present a generative modeling framework for atomistic systems that combines score-based diffusion for atomic positions with a novel continuous-time discrete diffusion process for atomic types. This approach enables flexible and…
Diffusion models have been popular for point cloud generation tasks. Existing works utilize the forward diffusion process to convert the original point distribution into a noise distribution and then learn the reverse diffusion process to…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
A great many observables seen in intermediate energy heavy ion collisions can be explained on the basis of statistical equilibrium. Calculations based on statistical equilibrium can be implemented in microcanonical ensemble (energy and…
Denoising diffusion models have shown great potential in multiple research areas. Existing diffusion-based generative methods on de novo 3D molecule generation face two major challenges. Since majority heavy atoms in molecules allow…
Diffusion-based generative graph models have been proven effective in generating high-quality small graphs. However, they need to be more scalable for generating large graphs containing thousands of nodes desiring graph statistics. In this…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
We propose a novel formulation for parametric finite element methods to simulate surface diffusion of closed curves, which is also called as the curve diffusion. Several high-order temporal discretizations are proposed based on this new…
A statistical model for the calculation of the ionisation-cluster size distribution in nanodosimetry is proposed. It is based on a canonical ensemble and derives from the well-known nuclear droplet model. The model especially can be applied…
This work presents a probabilistic scheme for solving semilinear nonlocal diffusion equations with volume constraints and integrable kernels. The nonlocal model of interest is defined by a time-dependent semilinear partial…