Related papers: Projective Integration Schemes for Hyperbolic Mome…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
Nonlinear systems arising from time integrators like Backward Euler can sometimes be reformulated as optimization problems, known as incremental potentials. We show through a comprehensive experimental analysis that the widely used…
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…
We develop a convergence theory for non-monotone approximation schemes for fully nonlinear parabolic partial differential equations. Modern computational methods such as kernel-based collocation, spectral methods, physics-informed neural…
We propose a fast integrator to a class of dynamical systems with several temporal scales. The proposed method is developed as an extension of the variable step size Heterogeneous Multiscale Method (VSHMM), which is a two-scale integrator…
Stochastic differential equations projected onto manifolds occur in physics, chemistry, biology, engineering, nanotechnology and optimization, with interdisciplinary applications. Intrinsic coordinate stochastic equations on the manifold…
This paper addresses the trajectory planning problem for automated vehicle on-ramp highway merging. To tackle this challenge, we extend our previous work on trajectory planning at unsignalized intersections using Partially Observable Markov…
This article describes methods for the deterministic simulation of the collisional Boltzmann equation. It presumes that the transport and collision parts of the equation are to be simulated separately in the time domain. Time stepping…
In this paper, a fast synthetic iterative scheme is developed to accelerate convergence for the implicit DOM based on the stationary phonon BTE. The key innovative point of the present scheme is the introduction of the macroscopic synthetic…
We investigate the feasibility of modelling turbulence via numeric functional integration. By transforming the Burgers' equation into a functional integral we are able to calculate equal-time spatial correlation of system variables using…
We introduce a hyperbolic closure for the Grad moment expansion of the Bhatnagar-Gross-Krook's (BGK) kinetic model using a neural network (NN) trained on BGK's moment data. This closure is motivated by the exact closure for the free…
We consider the development of high order asymptotic-preserving linear multistep methods for kinetic equations and related problems. The methods are first developed for BGK-like kinetic models and then extended to the case of the full…
Convergence acceleration of flow simulations to their steady states at lower Mach numbers can be achieved via preconditioning the lattice Boltzmann (LB) schemes that alleviate the associated numerical stiffness, which have so far been…
We consider the problem of efficiently performing simulation and inference for stochastic kinetic models. Whilst it is possible to work directly with the resulting Markov jump process, computational cost can be prohibitive for networks of…
This paper introduces generalized Bregman projection algorithms for solving nonlinear split feasibility problems (SF P s) in infinitedimensional Hilbert spaces. The methods integrate Bregman projections, proximal gradient steps, and…
This article proposes a novel high-performance computing approach for the prediction of the temperature field in powder bed fusion (PBF) additive manufacturing processes. In contrast to many existing approaches to part-scale simulations,…
Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain…
Probabilistic Latent Variable Models (LVMs) excel at modeling complex, high-dimensional data through lower-dimensional representations. Recent advances show that equipping these latent representations with a Riemannian metric unlocks…
Deterministic solutions of the Boltzmann equation represent a real challenge due to the enormous computational effort which is required to produce such simulations and often stochastic methods such as Direct Simulation Monte Carlo (DSMC)…
Simulating hypersonic flow around a space vehicle is challenging because of the multiscale and nonequilibrium nature inherent in these flows. To effectively deal with such flows, a novel particle particle hybrid scheme combining the…