相关论文: An implicit numerical algorithm general relativist…

Geometric Hydrodynamics has flourished ever since the celebrated 1966 paper of V. Arnold. In this paper we present a collection of open problems along with several new constructions in fluid dynamics and a concise survey of recent…

Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the…

We introduce models and algorithmic foundations for graph watermarking. Our frameworks include security definitions and proofs, as well as characterizations when graph watermarking is algorithmically feasible, in spite of the fact that the…

We derive the special and general relativistic hydrodynamic equations of motion for ideal fluids from a variational principle. Our approach allows to find approximate solutions, whenever physically motivated trial functions can be used.…

It is shown how the dimension of any arbitrary over-determined system of differential equations can be reduced, which makes the system suitable for numerical solution modeling. Specifically, over-determined equations of hydrodynamics are…

We consider models of relativistic matter containing sharp interfaces across which the matter model changes. These models will be relevant for neutron stars with crusts, phase transitions, or for viscous boundaries where the length scale is…

This paper is devoted to the derivation of a digital quantum algorithm for the Cauchy problem for symmetric first order linear hyperbolic systems, thanks to the reservoir technique. The reservoir technique is a method designed to avoid…

Methods to solve the relativistic hydrodynamic equations are a key computational kernel in a large number of astrophysics simulations and are crucial to understanding the electromagnetic signals that originate from the merger of…

We present a generalized form of open boundary conditions, and an associated numerical algorithm, for simulating incompressible flows involving open or outflow boundaries. The generalized form represents a family of open boundary…

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We report on our numerical implementation of fully relativistic hydrodynamics coupled to Einstein's field equations in three spatial dimensions. We briefly review several steps in our code development, including our recasting of Einstein's…

This article surveys computational methods for posterior inference with intractable likelihoods, that is where the likelihood function is unavailable in closed form, or where evaluation of the likelihood is infeasible. We review recent…

Employing a kinetic framework, we calculate all transport coefficients for relativistic dissipative (second-order) hydrodynamics for arbitrary particle masses in the 14-moment approximation. Taking the non-relativistic limit, it is shown…

Implicit particle filters for data assimilation generate high-probability samples by representing each particle location as a separate function of a common reference variable. This representation requires that a certain underdetermined…

This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based…

We present a reduced basis technique for long-time integration of parametrized incompressible turbulent flows. The new contributions are threefold. First, we propose a constrained Galerkin formulation that corrects the standard Galerkin…

Simulating and predicting dynamics of quantum many-body systems is extremely challenging, even for state-of-the-art computational methods, due to the spread of entanglement across the system. However, in the long-wavelength limit, quantum…

In this article, we investigate the artificial viscosity and hourglass control algorithms for high-order staggered Lagrangian hydrodynamics(SGH), as proposed in~\cite[Sun et al., 2025]{Sun2025High}. Inspired by the subzonal pressure method…

We report on recent upgrades to our general relativistic radiation-magnetohydrodynamics code, Cosmos++, which expands the two-moment, $\bf{M}_1$, radiation treatment from grey to multi-frequency transport, including Doppler and…

In this paper we review recent progress on relativistic hydrodynamics in (2 + 1)-dimensions with an external magnetic field. We discuss the formalism allowing for momentum loss due to the explicit and spontaneous breaking of translation…