相关论文: Parareal in time 3D numerical solver for the LWR B…

This paper presents a numerical framework for the low-rank approximation of the solution to three-dimensional parabolic problems. The key contribution of this work is the tensorization process based on a tensor-train reformulation of the…

Recently, generative diffusion priors have made huge strides as inverse problem solvers, including the ability to be adapted for inference on out-of-distribution data. Concurrently, implicit neural representations (INRs) have emerged as…

The parareal algorithm is known to allow for a significant reduction in wall clock time for accurate numerical solutions by parallelising across the time dimension. We present and test a micro-macro version of parareal, in which the fine…

The present research proposes a new memory-efficient method using diffusion models to inject turbulent inflow conditions into Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) for various flow problems. A guided diffusion…

Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation.…

We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has…

Recently, the ParaOpt algorithm was proposed as an extension of the time-parallel Parareal method to optimal control. ParaOpt uses quasi-Newton steps that each require solving a system of matching conditions iteratively. The…

Several Lagrangian methodologies have been proposed in recent years to simulate advection-dispersion of solutes in fluids as a mass exchange between numerical particles carrying the fluid. In this paper, we unify these methodologies,…

Neutron interactions in a fusion power plant play a pivotal role in determining critical design parameters such as coil-plasma distance and breeding blanket composition. Fast predictive neutronic capabilities are therefore crucial for an…

The diffusive-viscous wave equation is an advancement in wave equation theory, as it accounts for both diffusion and viscosity effects. This has a wide range of applications in geophysics, such as the attenuation of seismic waves in…

In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration…

This study introduces a novel point-wise diffusion model that processes spatio-temporal points independently to efficiently predict complex physical systems with shape variations. This methodological contribution lies in applying forward…

In High Energy Physics simulations play a crucial role in unraveling the complexities of particle collision experiments within CERN's Large Hadron Collider. Machine learning simulation methods have garnered attention as promising…

We present a numerical method for the solution of diffusion problems in unbounded planar regions with complex geometries of absorbing and reflecting bodies. Our numerical method applies the Laplace transform to the parabolic problem,…

We present and analyse an implicit-explicit timestepping procedure with finite element spatial approximation for a semilinear reaction-diffusion systems on evolving domains arising from biological models, such as Schnakenberg's (1979). We…

The conditional diffusion model has been demonstrated as an efficient tool for learning robot policies, owing to its advancement to accurately model the conditional distribution of policies. The intricate nature of real-world scenarios,…

Transformers and linear state space models can be evaluated in parallel on modern hardware, but evaluating nonlinear RNNs appears to be an inherently sequential problem. Recently, however, Lim et al. '24 developed an approach called DEER,…

Simulating long-term mass diffusion kinetics with atomic precision is important to predict chemical and mechanical properties of alloys over time scales of engineering interest in applications, including (but not limited to) alloy heat…

In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…