Related papers: Variable Step Size Multiscale Methods for Stiff an…
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…
We propose a hierarchy of multi-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
Implicit integration of the viscous term can significantly improve performance in computational fluid dynamics for highly viscous fluids such as lava. We show improvements over our previous proposal for semi-implicit viscous integration in…
In the formalism of constrained mechanics, such as that which underlies the SHAKE and RATTLE methods of molecular dynamics, we present an algorithm to convert any one-step integration method to a variational integrator of the same order.…
We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy…
In this paper we propose a numerical method to solve a 2D advection-diffusion equation, in the highly oscillatory regime. We use an efficient and robust integrator which leads to an accurate approximation of the solution without any time…
When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon…
The lifted Heston model is a stochastic volatility model emerging as a Markovian lift of the rough Heston model and the class of rough volatility processes. The model encodes the path dependency of volatility on a set of N square-root state…
Large time-stepping is important for efficient long-time simulations of deterministic and stochastic Hamiltonian dynamical systems. Conventional structure-preserving integrators, while being successful for generic systems, have limited…
In this work we introduce a new family of 14-steps linear multistep methods for the integration of the Schr\"odinger equation. The new methods are phase fitted but they are designed in order to improve the frequency tolerance. This is…
Symplectic integration algorithms have become popular in recent years in long-term orbital integrations because these algorithms enforce certain conservation laws that are intrinsic to Hamiltonian systems. For problems with large variations…
Multiple time scale molecular dynamics enhances computational efficiency by updating slow motions less frequently than fast motions. However, in practice the largest outer time step possible is limited not by the physical forces but by…
Physically interpretable models are essential for next-generation industrial systems, as these representations enable effective control, support design validation, and provide a foundation for monitoring strategies. The aim of this paper is…
We present a multilevel Monte Carlo simulation method for analysing multi-scale physical systems via a hierarchy of coarse-grained representations, to obtain numerically-exact results, at the most detailed level. We apply the method to a…
Quasi-periodic solutions with multiple base frequencies exhibit the feature of $2\pi$-periodicity with respect to each of the hyper-time variables. However, it remains a challenge work, due to the lack of effective solution methods, to…
The advantages of using Multi-Step corrections for simulations of lattice gauge theories with dynamical fermions will be discussed. This technique is suited for algorithms based on the Multi-Boson representation of the dynamical fermions as…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
This work focuses on the construction of a new class of fourth-order accurate methods for multirate time evolution of systems of ordinary differential equations. We base our work on the Recursive Flux Splitting Multirate (RFSMR) version of…
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…