Computational Physics
In recent years, Physics-Informed Neural Networks (PINNs) have become a representative method for solving partial differential equations (PDEs) with neural networks. PINNs provide a novel approach to solving PDEs through optimization…
The implementation of adaptive genetic algorithms (AGA) for optimization problems has proven to be superior than many other methods due to its nature of producing more robust and high quality solutions. Considering the complexity involved…
Molecular Dynamics (MD) simulations are a powerful tool for studying matter at the atomic scale. However, to simulate solids, an initial atomic structure is crucial for the successful execution of MD simulations, but can be difficult to…
Nested sampling (NS) is a stochastic method for computing the log-evidence of a Bayesian problem. It relies on stochastic estimates of prior volumes enclosed by likelihood contours, which limits the accuracy of the log-evidence calculation.…
Modern E(3)-Equivariant networks may be used to predict rotationally equivariant properties, including tensorial quantities. Three such quantities: the dielectric, piezoelectric, and elasticity tensors, are computationally expensive to…
Nested sampling provides an estimate of the evidence of a Bayesian inference problem via probing the likelihood as a function of the enclosed prior volume. However, the lack of precise values of the enclosed prior mass of the samples…
ACTest is an open-source toolkit developed in the Julia language. Its central goal is to automatically establish analytic continuation testing datasets, which include a large number of spectral functions and the corresponding Green's…
Based on the Jacobi polynomial expansion, an arbitrary high-order Discontinuous Galerkin solver for compressible flows on unstructured meshes is proposed in the present work. First, we construct orthogonal polynomials for 2D and 3D…
We explore the principles of many-body Hamiltonian complexity reduction via downfolding on an effective low-dimensional representation. We present a unique measure of fidelity between the effective (reduced-rank) description and the full…
In the domain of geometry and topology optimization, discovering geometries that optimally satisfy specific problem criteria is a complex challenge in both engineering and scientific research. In this work, we propose a new approach for the…
Mean-field modeling based on the Eshelby inclusion problem poses some difficulties when the non-linear Maxwell-type constitutive law is used for elasto-viscoplasticity. One difficulty is that this behavior involves different orders of time…
Soot is a component of atmospheric aerosols that affects climate by scattering and absorbing the sunlight. Soot particles are fractal aggregates composed of elemental carbon. In the atmosphere, the aggregates acquire coatings by…
Neural network force field models such as DeePMD have enabled highly efficient large-scale molecular dynamics simulations with ab initio accuracy. However, building such models heavily depends on the training data obtained by costly…
Recent advancements in Markov chain Monte Carlo (MCMC) sampling and surrogate modelling have significantly enhanced the feasibility of Bayesian analysis across engineering fields. However, the selection and integration of surrogate models…
A second-order-accurate finite volume method, hybridized by blending an extended double-flux algorithm and a traditionally conservative scheme, is developed. In this scheme, hybrid convective fluxes as well as hybrid interpolation…
The aim of this work is to develop a neural network for modelling incompressible hyperelastic behaviour with isotropic damage, the so-called Mullins effect. This is obtained through the use of feed-forward neural networks with special…
In this note, we establish some connections between standard (data-driven) neural network-based solvers for PDE and eigenvalue problems developed on one side in the applied mathematics and engineering communities (e.g. Deep-Ritz and Physics…
We study the accuracy of Kohn-Sham density functional theory (DFT) for warm- and hot-dense matter (WDM and HDM). Specifically, considering a wide range of systems, we perform accurate ab initio molecular dynamics simulations with…
This paper introduces the discrete-velocity-direction model (DVDM) in conjunction with the hyperbolic quadrature method of moments (HyQMOM) to develop a multidimensional spatial-temporal approximation of the BGK equation, termed DVD-HyQMOM.…
This paper presents a generalized flux-corrected transport (FCT) algorithm, which is shown to be total variation diminishing under some conditions. The new algorithm has improved properties from the standpoint of use and analysis. Results…