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Dissipative Particle Dynamics (DPD) is a popular simulation model for investigating hydrodynamic behavior of systems with non-negligible equilibrium thermal fluctuations. DPD employs soft core repulsive interactions between the system…
Smoothed Dissipative Particle Dynamics (SDPD) is a mesoscopic method which allows to select the level of resolution at which a fluid is simulated. In this work, we study the consistency of the resulting thermodynamic properties as a…
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…
Parameter inference for stochastic differential equation mixed effects models (SDEMEMs) is a challenging problem. Analytical solutions for these models are rarely available, which means that the likelihood is also intractable. In this case,…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found,…
The main objective of a statistical mechanical calculation is drawing the phase diagram of a many-body system. In this respect, discrete systems offer the clear advantage over continuum systems of an easier enumeration of microstates,…
The Latent Stochastic Differential Equation (SDE) is a powerful tool for time series and sequence modeling. However, training Latent SDEs typically relies on adjoint sensitivity methods, which depend on simulation and backpropagation…
We present a nonlinear dynamical approximation method for time-dependent Partial Differential Equations (PDEs). The approach makes use of parametrized decoder functions, and provides a general, and principled way of understanding and…
Stochastic differential equation mixed-effects models (SDEMEMs) are flexible hierarchical models that are able to account for random variability inherent in the underlying time-dynamics, as well as the variability between experimental units…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
This article presents a comparison of various implementations of the Lattice Discrete Particle Model (LDPM) for the numerical simulation of concrete and other heterogeneous quasibrittle materials. The comparison involves the use of…
This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These…
Studying single-particle dynamics over many periods of oscillations is a well-understood problem solved using symplectic integration. Such integration schemes derive their update sequence from an approximate Hamiltonian, guaranteeing that…
We consider energy stable summation by parts finite difference methods (SBP-FD) for the homogeneous and piecewise homogeneous dynamic beam equation (DBE). Previously the constant coefficient problem has been solved with SBP-FD together with…
Dense image matching is a fundamental low-level problem in Computer Vision, which has received tremendous attention from both discrete and continuous optimization communities. The goal of this paper is to combine the advantages of discrete…
This paper proposes an unconditionally stable numerical method for solving a nonlinear Sobolev model with distributed delay. The proposed computational approach approximates the time derivative by interpolation technique whereas the spatial…
This paper studies explicit symplectic adapted exponential integrators for solving charged-particle dynamics in a strong and constant magnetic field. We first formulate the scheme of adapted exponential integrators and then derive its…
The stability of integrators dealing with high order Differential Algebraic Equations (DAEs) is a major issue. The usual procedures give rise to instabilities that are not predicted by the usual linear analysis, rendering the common checks…
The phase field method is an effective tool for modeling microstructure evolution in materials. Many efficient implicit numerical solvers have been proposed for phase field simulations under uniform and time-invariant model parameters. We…