相关论文: Non-intrusive and structure preserving multiscale …

The performance of flow matching and diffusion models can be greatly improved at inference time using reward alignment algorithms, yet efficiency remains a major limitation. While several algorithms were proposed, we demonstrate that a…

Models in cardiac electrophysiology are coupled systems of reaction diffusion PDE and of ODE. The ODE system displays a very stiff behavior. It is non linear and its upgrade at each time step is a preponderant load in the computational…

We introduce a family of implicit probabilistic integrators for initial value problems (IVPs), taking as a starting point the multistep Adams-Moulton method. The implicit construction allows for dynamic feedback from the forthcoming…

Neural ordinary differential equations (NODEs) are an effective approach for data-driven modeling of dynamical systems arising from simulations and experiments. One of the major shortcomings of NODEs, especially when coupled with explicit…

We design a novel, exactly energy-conserving implicit non-symplectic integration method for an eight-dimensional Hamiltonian system with four degrees of freedom. In our algorithm, each partial derivative of the Hamiltonian with respect to…

We propose and rigorously analyze a novel family of explicit low-regularity exponential integrators for the nonlinear Schr\"odinger (NLS) equation, based on a time-relaxation framework. The methods combine a resonance-based scheme for the…

Multiscale dynamical systems characterized by interacting fast and slow processes are ubiquitous across scientific domains, from climate dynamics to fluid mechanics. Accurate modeling of such systems requires capturing both the long-term…

Inferring the number of distinct components contributing to an observation, while simultaneously estimating their parameters, remains a long-standing challenge across signal processing, astrophysics, and neuroscience. Classical…

Non-linear statistical inverse problems pose major challenges both for statistical analysis and computation. Likelihood-based estimators typically lead to non-convex and possibly multimodal optimization landscapes, and Markov chain Monte…

For trigonometric and modified trigonometric integrators applied to oscillatory Hamiltonian differential equations with one or several constant high frequencies, near-conservation of the total and oscillatory energies are shown over time…

We present a new class of numerical methods for solving stochastic differential equations with additive noise on general Riemannian manifolds with high weak order of accuracy. In opposition to the popular approach with projection methods,…

We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are…

We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in…

Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and which forces are exerted on the…

Including the effect of thermal fluctuations in traditional computational fluid dynamics requires developing numerical techniques for solving the stochastic partial differential equations of fluctuating hydrodynamics. These Langevin…

In this work, we study long-time numerical integration of Hamiltonian systems subject to linear perturbations. By introducing an energy-induced metric, we establish a straightforward, coordinate-free criterion for dissipativity that ensures…

A class of trigonometric integrator is proposed for the constrained ring polymer Hamiltonian dynamics, arising from the path integral molecular dynamics. The integrator is formulated by the composition of flows, thereby integrating the…

In this paper, we study the convergence analysis for a robust stochastic structure-preserving Lagrangian numerical scheme in computing effective diffusivity of time-dependent chaotic flows, which are modeled by stochastic differential…

We present a new linearly implicit exponential integrator that preserves the polynomial first integrals or Lyapunov functions for the conservative and dissipative stiff equations, respectively. The method is tested by both oscillated…

In this paper we propose a novel way to integrate time-evolving partial differential equations that contain nonlinear advection and stiff linear operators, combining exponential integration techniques and semi-Lagrangian methods. The…