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We present a two-dimensional (2D) Particle-Particle-Particle-Mesh (P$^3$M) algorithm with an optimized Green function and adaptive softening length for gravitational lensing studies in N-Body simulations. The analytical form of the…
Standard Bayesian Optimization (BO) assumes uniform smoothness across the search space an assumption violated in multi-regime problems such as molecular conformation search through distinct energy basins or drug discovery across…
Variational approaches for the calculation of vibrational wave functions and energies are a natural route to obtain highly accurate results with controllable errors. However, the unfavorable scaling and the resulting high computational cost…
Gravitational instabilities naturally give rise to multi-scale structure, which is difficult for traditional Eulerian hydrodynamic methods to accurately evolve. This can be circumvented by adaptively adding resolution (in the form of…
We investigate uncertainties in the estimation of the Hubble constant ($H_0$) arising from Gaussian Process (GP) reconstruction, demonstrating that the choice of kernel introduces systematic variations comparable to those arising from…
Electromagnetic simulations of complex geologic settings are computationally expensive. One reason for this is the fact that a fine mesh is required to accurately discretize the electrical conductivity model of a given setting. This…
We have carried out numerical simulations of strongly gravitating systems based on the Einstein equations coupled to the relativistic hydrodynamic equations using adaptive mesh refinement (AMR) techniques. We show AMR simulations of NS…
High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial…
Numerical simulations in modified gravity have commonly been performed under the quasi-static approximation -- that is, by neglecting the effect of time derivatives in the equation of motion of the scalar field that governs the fifth force…
The distribution of galaxies provides an ideal laboratory to test for deviations from General Relativity. In particular, redshift-space distortions are commonly used to constrain modifications to the Poisson equation, which governs the…
We present a novel formulation of the vibrational density matrix renormalization group (vDMRG) algorithm tailored to strongly anharmonic molecules described by general high-dimensional model representations of potential energy surfaces. For…
Compressible Mooney-Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of soft tissues for biomedical tissues, undergoing large elastic deformations. We propose a…
The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamical…
We report on the development of a computational framework for the parallel, mesh-adaptive solution of systems of hyperbolic conservation laws like the time-dependent Euler equations in compressible gas dynamics or Magneto-Hydrodynamics…
We study the model space generated by the time-dependent operator coefficients in the effective field theory of the cosmological background evolution and perturbations of modified gravity and dark energy models. We identify three classes of…
We present here the first systematic treatment of the problems posed by the visualization and analysis of large-scale, parallel adaptive mesh refinement (AMR) simulations on an Eulerian grid. When compared to those obtained by constructing…
We test the convergence of fast simulations based on the COmoving Lagrangian Acceleration (COLA) method for predictions of the matter power spectrum, specialising our analysis in the redshift range $1 \le z \le 1.65$, relevant to…
A reconstruction of modified gravity is proposed by establishing a correspondence between the effective density of the modified gravity and the holographic density. The non-homogeneous term in the modified Friedmann equation, generated by…
We present a new massively parallel code for N-body and cosmological hydrodynamical simulations of modified gravity models. The code employs a multigrid-accelerated Newton-Gauss-Seidel relaxation solver on an adaptive mesh to efficiently…
The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and…