CERMICS

QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

We present a new integral equation formulation of the polarizable continuum model (PCM) which allows one to treat in a single approach dielectrics of different nature: standard isotropic liquids, intrinsically anisotropic medialike liquid crystals and solid matrices, or ionic solutions. The present work shows that integral equation methods may be used with success also for the latter cases, which are usually studied with three-dimensional methods, by far less competitive in terms of computational effort. We present the theoretical bases which underlie the method and some numerical tests which show both a complete equivalence with standard PCM versions for isotropic solvents, and a good efficiency for calculations with anisotropic dielectrics.

We present the full implementation of the integral equation formalism (IEF) we have recently formulated to treat solvent effects. The method exploits a single common approach for dielectrics of very different nature: standard isotropic liquids, intrinsically anisotropic media like liquid crystals, and ionic solutions. We report here an analysis of its both formal and technical details as well as some numerical applications addressed to state the achieved generalization to all kinds of molecular solutes and to show the equally reliable performances in treating such different environmental systems. In particular, we report, for isotropic liquids, data of solvation free energies and static (hyper)polarizabilities of various molecular solutes in water, for anisotropic dielectrics, a study of an SN2 reaction, and finally, for ionic solution, a study of some structural aspects of ion pairing.

We present an efficient reduced-basis discretization procedure for partial differential equations with nonaffine parameter dependence. The method replaces nonaffine coefficient functions with a collateral reduced-basis expansion which then permits an (effectively affine) offline–online computational decomposition. The essential components of the approach are (i) a good collateral reduced-basis approximation space, (ii) a stable and inexpensive interpolation procedure, and (iii) an effective a posteriori estimator to quantify the newly introduced errors. Theoretical and numerical results respectively anticipate and confirm the good behavior of the technique.

Quantum ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). Quantum ESPRESSO stands for "opEn Source Package for Research in Electronic Structure, Simulation, and Optimization". It is freely available to researchers around the world under the terms of the GNU General Public License. Quantum ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively-parallel architectures, and a great effort being devoted to user friendliness. Quantum ESPRESSO is evolving towards a distribution of independent and inter-operable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

The solvation model proposed by Fattebert and Gygi [J. Comput. Chem. 23, 662 (2002)] and Scherlis et al. [J. Chem. Phys. 124, 074103 (2006)] is reformulated, overcoming some of the numerical limitations encountered and extending its range of applicability. We first recast the problem in terms of induced polarization charges that act as a direct mapping of the self-consistent continuum dielectric; this allows to define a functional form for the dielectric that is well behaved both in the high-density region of the nuclear charges and in the low-density region where the electronic wavefunctions decay into the solvent. Second, we outline an iterative procedure to solve the Poisson equation for the quantum fragment embedded in the solvent that does not require multigrid algorithms, is trivially parallel, and can be applied to any Bravais crystallographic system. Last, we capture some of the non-electrostatic or cavitation terms via a combined use of the quantum volume and quantum surface [M. Cococcioni, F. Mauri, G. Ceder, and N. Marzari, Phys. Rev. Lett. 94, 145501 (2005)] of the solute. The resulting self-consistent continuum solvation model provides a very effective and compact fit of computational and experimental data, whereby the static dielectric constant of the solvent and one parameter allow to fit the electrostatic energy provided by the polarizable continuum model with a mean absolute error of 0.3 kcal/mol on a set of 240 neutral solutes. Two parameters allow to fit experimental solvation energies on the same set with a mean absolute error of 1.3 kcal/mol. A detailed analysis of these results, broken down along different classes of chemical compounds, shows that several classes of organic compounds display very high accuracy, with solvation energies in error of 0.3-0.4 kcal/mol, whereby larger discrepancies are mostly limited to self-dissociating species and strong hydrogen-bond-forming compounds.

The Keller-Segel system describes the collective motion of cells which are attracted by a chemical substance and are able to emit it. In its simplest form it is a conservative drift-diffusion equation for the cell density coupled to an elliptic equation for the chemo-attractant concentration. It is known that, in two space dimensions, for small initial mass, there is global existence of solutions and for large initial mass blow-up occurs. In this paper we complete this picture and give a detailed proof of the existence of weak solutions below the critical mass, above which any solution blows-up in finite time in the whole Euclidean space. Using hypercontractivity methods, we establish regularity results which allow us to prove an inequality relating the free energy and its time derivative. For a solution with sub-critical mass, this allows us to give for large times an “intermediate asymptotics” description of the vanishing. In self-similar coordinates, we actually prove a convergence result to a limiting self-similar solution which is not a simple reflect of the diffusion.

We consider optimal execution strategies for block market orders placed in a\nlimit order book (LOB). We build on the resilience model proposed by Obizhaeva\nand Wang (2005) but allow for a general shape of the LOB defined via a given\ndensity function. Thus, we can allow for empirically observed LOB shapes and\nobtain a nonlinear price impact of market orders. We distinguish two\npossibilities for modeling the resilience of the LOB after a large market\norder: the exponential recovery of the number of limit orders, i.e., of the\nvolume of the LOB, or the exponential recovery of the bid-ask spread. We\nconsider both of these resilience modes and, in each case, derive explicit\noptimal execution strategies in discrete time. Applying our results to a\nblock-shaped LOB, we obtain a new closed-form representation for the optimal\nstrategy, which explicitly solves the recursive scheme given in Obizhaeva and\nWang (2005). We also provide some evidence for the robustness of optimal\nstrategies with respect to the choice of the shape function and the\nresilience-type.\n

Wireless communication in the TeraHertz band (0.1--10 THz) is envisioned as one of the key enabling technologies for the future sixth generation (6G) wireless communication systems scaled up beyond massive multiple input multiple output (Massive-MIMO) technology. However, very high propagation attenuations and molecular absorptions of THz frequencies often limit the signal transmission distance and coverage range. Benefited from the recent breakthrough on the reconfigurable intelligent surfaces (RIS) for realizing smart radio propagation environment, we propose a novel hybrid beamforming scheme for the multi-hop RIS-assisted communication networks to improve the coverage range at THz-band frequencies. Particularly, multiple passive and controllable RISs are deployed to assist the transmissions between the base station (BS) and multiple single-antenna users. We investigate the joint design of digital beamforming matrix at the BS and analog beamforming matrices at the RISs, by leveraging the recent advances in deep reinforcement learning (DRL) to combat the propagation loss. To improve the convergence of the proposed DRL-based algorithm, two algorithms are then designed to initialize the digital beamforming and the analog beamforming matrices utilizing the alternating optimization technique. Simulation results show that our proposed scheme is able to improve 50\% more coverage range of THz communications compared with the benchmarks. Furthermore, it is also shown that our proposed DRL-based method is a state-of-the-art method to solve the NP-hard beamforming problem, especially when the signals at RIS-assisted THz communication networks experience multiple hops.

Enhanced sampling algorithms have emerged as powerful methods to extend the utility of molecular dynamics simulations and allow the sampling of larger portions of the configuration space of complex systems in a given amount of simulation time. This review aims to present the unifying principles of and differences between many of the computational methods currently used for enhanced sampling in molecular simulations of biomolecules, soft matter and molecular crystals. In fact, despite the apparent abundance and divergence of such methods, the principles at their core can be boiled down to a relatively limited number of statistical and physical concepts. To enable comparisons, the various methods are introduced using similar terminology and notation. We then illustrate in which ways many different methods combine features of a relatively small number of the same enhanced sampling concepts. This review is intended for scientists with an understanding of the basics of molecular dynamics simulations and statistical physics who want a deeper understanding of the ideas that underlie various enhanced sampling methods and the relationships between them. This living review is intended to be updated to continue to reflect the wealth of sampling methods as they continue to emerge in the literature.

A direct inversion iterative subspace version of the relaxed constrained algorithm is found to be a very powerful convergence acceleration technique for the solution of the self-consistent field equations found in the Hartree–Fock method and Kohn–Sham-based density functional theory (KS-DFT). The present algorithm, abbreviated EDIIS, is benchmarked against the direct inversion iterative subspace method based on the commutator of the density and Fock matrices developed by Pulay (DIIS). Our findings indicate that while EDIIS is able to rapidly bring the density matrix from any initial guess to a solution region, the DIIS method is faster when the density matrix is close to convergence. Consequently, we propose a combination of EDIIS and DIIS methods, which is both very robust and highly efficient. We also show how EDIIS can detect the presence and determine the value of fractional occupations in KS-DFT.

In approximate Kohn-Sham density-functional theory, self-interaction manifests itself as the dependence of the energy of an orbital on its fractional occupation. This unphysical behavior translates into qualitative and quantitative errors that pervade many fundamental aspects of density-functional predictions. Here, we first examine self-interaction in terms of the discrepancy between total and partial electron removal energies, and then highlight the importance of imposing the generalized Koopmans' condition---that identifies orbital energies as opposite total electron removal energies---to resolve this discrepancy. In the process, we derive a correction to approximate functionals that, in the frozen-orbital approximation, eliminates the unphysical occupation dependence of orbital energies up to the third order in the single-particle densities. This non-Koopmans correction brings physical meaning to single-particle energies; when applied to common local or semilocal density functionals it provides results that are in excellent agreement with experimental data---with an accuracy comparable to that of GW many-body perturbation theory---while providing an explicit total energy functional that preserves or improves on the description of established structural properties.

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Abstract We develop an arbitrary-order primal method for diffusion problems on general polyhedral meshes. The degrees of freedom are scalar-valued polynomials of the same order at mesh elements and faces. The cornerstone of the method is a local (elementwise) discrete gradient reconstruction operator. The design of the method additionally hinges on a least-squares penalty term on faces weakly enforcing the matching between local element- and face-based degrees of freedom. The scheme is proved to optimally converge in the energy norm and in the L 2 -norm of the potential for smooth solutions. In the lowest-order case, equivalence with the Hybrid Finite Volume method is shown. The theoretical results are confirmed by numerical experiments up to order 4 on several polygonal meshes.

A Discontinuous Galerkin method is used for to the numerical solution of the time-domain Maxwell equations on unstructured meshes. The method relies on the choice of local basis functions, a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. The method is proved to be stable for cases with either metallic or absorbing boundary conditions, for a large class of basis functions. A discrete analog of the electromagnetic energy is conserved for metallic cavities. Convergence is proved for Discontinuous elements on tetrahedral meshes, as well as a discrete divergence preservation property. Promising numerical examples with low-order elements show the potential of the method.

We present a novel geometric approach for solving the stereo problem for an arbitrary number of images (greater than or equal to 2). It is based upon the definition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images. The Euler-Lagrange equations which are deduced from the variational principle provide a set of PDE's which are used to deform an initial set of surfaces which then move towards the objects to be detected. The level set implementation of these PDE's potentially provides an efficient and robust way of achieving the surface evolution and to deal automatically with changes in the surface topology during the deformation, i.e. to deal with multiple objects. Results of a two dimensional implementation of our theory are presented on synthetic and real images.

We propose and analyze a symmetric weighted interior penalty (SWIP) method to approximate in a Discontinuous\nGalerkin framework advection-diffusion equations with anisotropic and discontinuous diffusivity.\nThe originality of the method consists in the use of diffusivity-dependent weighted averages\nto better cope with locally small diffusivity (or equivalently with locally high P ́eclet numbers) on tted\nmeshes. The analysis yields convergence results for the natural energy norm that are optimal with respect\nto mesh-size and robust with respect to diffusivity. The convergence results for the advective derivative\nare optimal with respect to mesh-size and robust for isotropic diffusivity, as well as for anisotropic diffusivity\nif the cell P ́eclet numbers evaluated with the largest eigenvalue of the diffusivity tensor are large\nenough. Numerical results are presented to illustrate the performance of the proposed scheme.

Machine learning encompasses a set of tools and algorithms which are now\nbecoming popular in almost all scientific and technological fields. This is\ntrue for molecular dynamics as well, where machine learning offers promises of\nextracting valuable information from the enormous amounts of data generated by\nsimulation of complex systems. We provide here a review of our current\nunderstanding of goals, benefits, and limitations of machine learning\ntechniques for computational studies on atomistic systems, focusing on the\nconstruction of empirical force fields from ab-initio databases and the\ndetermination of reaction coordinates for free energy computation and enhanced\nsampling.\n

Machine learning (ML) is a promising enabler for the fifth generation (5G) communication systems and beyond.By imbuing intelligence into the network edge, edge nodes can proactively carry out decision-making, and thereby react to local environmental changes and disturbances while experiencing zero communication latency.To achieve this goal, it is essential to cater for high ML inference accuracy at scale under time-varying channel and network dynamics, by continuously exchanging fresh data and ML model updates in a distributed way.Taming this new kind of data traffic boils down to improving the communication efficiency of distributed learning by optimizing communication payload types, transmission techniques, and scheduling, as well as ML architectures, algorithms, and data processing methods.To this end, this article aims to provide a holistic overview of relevant communication and ML principles, and thereby present communication-efficient and distributed learning frameworks with selected use cases. SIGNIFICANCE AND MOTIVATIONThe pursuit of extremely stringent latency and reliability guarantees is essential in the fifth generation (5G) communication system and beyond [1], [2].In a wirelessly automated factory, the remote control of assembly robots should provision the same level of target latency and reliability offered by existing wired factory systems.To this end, for instance, control packets should be delivered within 1 ms with 99.99999% reliability [3]- [5].Things are becoming even more challenging in the emerging mission-critical applications beyond 5G.A prime example is the forthcoming nonterrestrial networks consisting of a massive constellation of low-altitude earth orbit (LEO) satellites [6]- [11].Given such

We build a bridge between the hybrid high-order (HHO) and the hybridizable discontinuous Galerkin (HDG) methods in the setting of a model diffusion problem. First, we briefly recall the construction of HHO methods and derive some new variants. Then, by casting the HHO method in mixed form, we identify the numerical flux so that the HHO method can be compared to HDG methods. In turn, the incorporation of the HHO method into the HDG framework brings up new, efficient choices of the local spaces and a new, subtle construction of the numerical flux ensuring optimal orders of convergence on meshes made of general shape-regular polyhedral elements. Numerical experiments comparing two of these methods are shown.