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In this study, a fast and stable machine-learned hybrid algorithm implemented in TensorFlow for the integration of stiff chemical kinetics is introduced. Numerical solutions to differential equations are at the core of computational fluid…
While the application of the Smoothed Particle Hydrodynamics (SPH) method for the modeling of welding processes has become increasingly popular in recent years, little is yet known about the quantitative predictive capability of this…
Multiple scattering of an electromagnetic wave as it passes through an object is a fundamental problem that limits the performance of current imaging systems. In this paper, we describe a new technique-called Series Expansion with…
Toward the goal of using Scientific Machine Learning (SciML) emulators to improve the numerical representation of aerosol processes in global atmospheric models, we explore the emulation of aerosol microphysics processes under cloud-free…
The aim of this study was to check how efficient can be smoothed finite element method (FEM) for solution of the linear fracture mechanics problems. Accuracy of stress intensity factor (SIF) computation were investigated using three types…
Stabilized explicit methods are particularly efficient for large systems of stiff stochastic differential equations (SDEs) due to their extended stability domain. However, they loose their efficiency when a severe stiffness is induced by…
As a concrete setting where stochastic partial differential equations (SPDEs) are able to model real phenomena, we propose a stochastic Meinhardt model for cell repolarisation and study how parameter estimation techniques developed for…
The modeling of solid-state transformations, such as polymorphic transitions and chemical reactions in molecular crystals, is vital for many applications including drug design or the development of new synthesis methods. However, a…
Processing high-volume, streaming data is increasingly common in modern statistics and machine learning, where batch-mode algorithms are often impractical because they require repeated passes over the full dataset. This has motivated…
This chapter provides a brief introduction to the theory and practice of spatial stochastic simulations. It begins with an overview of different methods available for biochemical simulations highlighting their strengths and limitations.…
State space models (SSMs) provide a flexible framework for modeling complex time series via a latent stochastic process. Inference for nonlinear, non-Gaussian SSMs is often tackled with particle methods that do not scale well to long time…
We propose a staggered mesh method for correlation energy calculations of periodic systems under the random phase approximation (RPA), which generalizes the recently developed staggered mesh method for periodic second order…
Simulating trajectories of multi-particle systems on complex energy landscapes is a central task in molecular dynamics (MD) and drug discovery, but remains challenging at scale due to computationally expensive and long simulations. Previous…
Simulating physical problems involving multi-time scale coupling is challenging due to the need of solving these multi-time scale processes simultaneously. In response to this challenge, this paper proposed an explicit multi-time step…
The reconstruction of low-textured areas is a prominent research focus in multi-view stereo (MVS). In recent years, traditional MVS methods have performed exceptionally well in reconstructing low-textured areas by constructing plane models.…
A novel Material Point Method (MPM) is introduced for addressing frictional contact problems. In contrast to the standard multi-velocity field approach, this method employs a penalty method to evaluate contact forces at the discretised…
This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness…
Mixture of Experts (MoE) architectures have emerged as pivotal for scaling Large Language Models (LLMs) efficiently. Fine-grained MoE approaches - utilizing more numerous, smaller experts - have demonstrated potential in improving model…
We introduce an efficient and accurate staggered-grid finite-difference (SGFD) method to solve the two-dimensional elastic wave equation. We use a coupled first-order stress-velocity formulation. In the standard implementation of SGFD…
The Heterogeneous Multiscale Finite Element Method (FE-HMM) is a two-scale FEM based on asymptotic homogenization for solving multiscale partial differential equations. It was introduced in [W. E and B. Engquist, \emph{Commun. Math. Sci.},…