Related papers: Runge-Kutta Random Feature Method for Solving Mult…
In this paper, we consider stochastic Runge-Kutta methods for stochastic Hamiltonian partial differential equations and present some sufficient conditions for multisymplecticity of stochastic Runge-Kutta methods of stochastic Hamiltonian…
Strong stability preserving (SSP) Runge-Kutta methods are desirable when evolving in time problems that have discontinuities or sharp gradients and require nonlinear non-inner-product stability properties to be satisfied. Unlike the case…
I give an overview of rare event simulation techniques to generate dynamical pathways across high free energy barriers. The methods on which I will concentrate are the reactive flux approach, transition path sampling, (replica-exchange)…
We introduce the Quantization Monte Carlo method to solve thermal radiative transport equations with possibly several collision regimes, ranging from few collisions to massive number of collisions per time unit. For each particle in a given…
Confluent cell monolayers and epithelia tissues show remarkable patterns and correlations in structural arrangements and actively-driven collective flows. We simulate these properties using multiphase field models. The models are based on…
Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the…
The family of PDE-constrained LDDMM methods is emerging as a particularly interesting approach for physically meaningful diffeomorphic transformations. The original combination of Gauss--Newton--Krylov optimization and Runge--Kutta…
In order to solve continuous-time optimal control problems, direct methods transcribe the infinite-dimensional problem to a nonlinear program (NLP) using numerical integration methods. In cases where the integration error can be manipulated…
In this paper, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-solution of numerical algorithms by exploiting the time periodicity inherent to many applications in science and engineering. The time-periodic…
Stochastic Hamiltonian partial differential equations, which possess the multi-symplectic conservation law, are an important and fairly large class of systems. The multi-symplectic methods inheriting the geometric features of stochastic…
This paper investigates, a new class of fractional order Runge-Kutta (FORK) methods for numerical approximation to the solution of fractional differential equations (FDEs). By using the Caputo generalizedTaylor formula and the total…
Sampling from a high-dimensional probability distribution is a fundamental algorithmic task arising in wide-ranging applications across multiple disciplines, including scientific computing, computational statistics and machine learning.…
The combined Continuous Time Random Walk (CTRW) in position and momentum space is introduced, in the form of two coupled integral equations that describe the evolution of the probability distribution for finding a particle at a certain…
Deriving analytical solutions of ordinary differential equations is usually restricted to a small subset of problems and numerical techniques are considered. Inevitably, a numerical simulation of a differential equation will then always be…
Runge-Kutta formulas are some of the workhorses of numerical solving of differential equations. However, they are extremely difficult to generate; the algebra involved can be very complicated indeed. It is now standard, following the work…
We introduce COT-FM, a general framework that reshapes the probability path in Flow Matching (FM) to achieve faster and more reliable generation. FM models often produce curved trajectories due to random or batchwise couplings, which…
An efficient third-order discrete unified gas kinetic scheme (DUGKS) with efficiency is presented in this work for simulating continuum and rarefied flows. By employing two-stage time-stepping scheme and the high-order DUGKS flux…
In this paper, we propose an efficient exponential integrator finite element method for solving a class of semilinear parabolic equations in rectangular domains. The proposed method first performs the spatial discretization of the model…
Computational modeling of cellular systems, where reactants are governed by biochemical equations and physical representations, requires extensive classical computing resources. These limitations significantly constrain the system size and…
In this paper we develop a class of Implicit-Explicit Runge-Kutta schemes for solving the multi-scale semiconductor Boltzmann equation. The relevant scale which characterizes this kind of problems is the diffusive scaling. This means that,…