physics.comp-ph

arXiv:2404.10863v2 Announce Type: replace-cross Abstract: Hypo-elastoplasticity is a framework suitable for modeling the mechanics of many hard materials that have small elastic deformation and large plastic deformation. In most laboratory tests for these materials the Cauchy stress is in quasi-static equilibrium. Rycroft et al. discovered a mathematical correspondence between this physical system and the incompressible Navier-Stokes equations, and developed a projection method similar to Chorin's projection method (1968) for incompressible Newtonian fluids. Here, we improve the original projection method to simulate quasi-static hypo-elastoplasticity, by making three improvements. First, drawing inspiration from the second-order projection method for incompressible Newtonian fluids, we formulate a second-order in time numerical scheme for quasi-static hypo-elastoplasticity. Second, we implement a finite element method for solving the elliptic equations in the projection step, which provides both numerical benefits and flexibility. Third, we develop an adaptive global time-stepping scheme, which can compute accurate solutions in fewer timesteps. Our numerical tests use an example physical model of a bulk metallic glass based on the shear transformation zone theory, but the numerical methods can be applied to any elastoplastic material.

arXiv:2411.07422v3 Announce Type: replace Abstract: The numerical flux determines the performance of numerical methods for solving hyperbolic partial differential equations (PDEs). In this work, we compare a selection of 8 numerical fluxes in the framework of nonlinear semidiscrete finite volume (FV) schemes, based on Weighted Essentially Non-Oscillatory (WENO) spatial reconstruction and Deferred Correction (DeC) time discretization. The methodology is implemented and systematically assessed for order of accuracy in space and time up to seven. The numerical fluxes selected in the present study represent the two existing classes of fluxes, namely centred and upwind. Centred fluxes do not explicitly use wave propagation information, while, upwind fluxes do so from the solution of the Riemann problem via a wave model containing $A$ waves. Upwind fluxes include two subclasses: complete and incomplete fluxes. For complete upwind fluxes, $A=E$, where $E$ is the number of characteristic fields in the exact problem. For incomplete upwind ones, $A<E$. Our study is conducted for the one- and two-dimensional Euler equations, for which we consider the following numerical fluxes: Lax-Friedrichs (LxF), First-Order Centred (FORCE), Rusanov (Rus), Harten-Lax-van Leer (HLL), Central-Upwind (CU), Low-Dissipation Central-Upwind (LDCU), HLLC, and the flux computed through the exact Riemann solver (Ex.RS). We find that the numerical flux has an effect on the performance of the methods. The magnitude of the effect depends on the type of numerical flux and on the order of accuracy of the scheme. It also depends on the type of problem; that is, whether the solution is smooth or discontinuous, whether discontinuities are linear or nonlinear, whether linear discontinuities are fast- or slowly-moving, and whether the solution is evolved for short or long time.

arXiv:2406.00047v3 Announce Type: replace-cross Abstract: A central problem in quantum mechanics involves solving the Electronic Schrodinger Equation for a molecule or material. The Variational Monte Carlo approach to this problem approximates a particular variational objective via sampling, and then optimizes this approximated objective over a chosen parameterized family of wavefunctions, known as the ansatz. Recently neural networks have been used as the ansatz, with accompanying success. However, sampling from such wavefunctions has required the use of a Markov Chain Monte Carlo approach, which is inherently inefficient. In this work, we propose a solution to this problem via an ansatz which is cheap to sample from, yet satisfies the requisite quantum mechanical properties. We prove that a normalizing flow using the following two essential ingredients satisfies our requirements: (a) a base distribution which is constructed from Determinantal Point Processes; (b) flow layers which are equivariant to a particular subgroup of the permutation group. We then show how to construct both continuous and discrete normalizing flows which satisfy the requisite equivariance. We further demonstrate the manner in which the non-smooth nature ("cusps") of the wavefunction may be captured, and how the framework may be generalized to provide induction across multiple molecules. The resulting theoretical framework entails an efficient approach to solving the Electronic Schrodinger Equation.

arXiv:2501.12222v1 Announce Type: cross Abstract: We used our developed AI search engine~(InvDesFlow) to perform extensive investigations regarding ambient stable superconducting hydrides. A cubic structure Li$_2$AuH$_6$ with Au-H octahedral motifs is identified to be a candidate. After performing thermodynamical analysis, we provide a feasible route to experimentally synthesize this material via the known LiAu and LiH compounds under ambient pressure. The further first-principles calculations suggest that Li$_2$AuH$_6$ shows a high superconducting transition temperature ($T_c$) $\sim$ 140 K under ambient pressure. The H-1$s$ electrons strongly couple with phonon modes of vibrations of Au-H octahedrons as well as vibrations of Li atoms, where the latter is not taken seriously in other previously similar cases. Hence, different from previous claims of searching metallic covalent bonds to find high-$T_c$ superconductors, we emphasize here the importance of those phonon modes with strong electron-phonon coupling (EPC). And we suggest that one can intercalate atoms into binary or ternary hydrides to introduce more potential phonon modes with strong EPC, which is an effective approach to find high-$T_c$ superconductors within multicomponent compounds.

arXiv:2501.10594v1 Announce Type: cross Abstract: Accurate determination of the equation of state of dense hydrogen is essential for understanding gas giants. Currently, there is still no consensus on methods for calculating its entropy, which play a fundamental role and can result in qualitatively different predictions for Jupiter's interior. Here, we investigate various aspects of entropy calculation for dense hydrogen based on ab initio molecular dynamics simulations. Specifically, we employ the recently developed flow matching method to validate the accuracy of the traditional thermodynamic integration approach. We then clearly identify pitfalls in previous attempts and propose a reliable framework for constructing the hydrogen equation of state, which is accurate and thermodynamically consistent across a wide range of temperature and pressure conditions. This allows us to conclusively address the long-standing discrepancies in Jupiter's adiabat among earlier studies, demonstrating the potential of our approach for providing reliable equations of state of diverse materials.

arXiv:2312.09215v3 Announce Type: replace-cross Abstract: Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations. In this work, we adapt and generalize this framework in a quantum machine learning setting for a variety of problems, including the 2D Poisson's equation, second-order linear differential equation, system of differential equations, nonlinear Duffing and Riccati equation. In particular, we propose in the quantum setting a modified Self-Adaptive Physics-Informed Neural Network (SAPINN) approach, where self-adaptive weights are applied to problems with multi-objective loss functions. We further explore capturing correlations in our loss function using a quantum-correlated measurement, resulting in improved accuracy for initial value problems. We analyse also the use of entangling layers and their impact on the solution accuracy for second-order differential equations. The results indicate a promising approach to the near-term evaluation of differential equations on quantum devices.

arXiv:2501.12149v1 Announce Type: cross Abstract: Density functional theory (DFT) is probably the most promising approach for quantum chemistry calculations considering its good balance between calculations precision and speed. In recent years, several neural network-based functionals have been developed for exchange-correlation energy approximation in DFT, DM21 developed by Google Deepmind being the most notable between them. This study focuses on evaluating the efficiency of DM21 functional in predicting molecular geometries, with a focus on the influence of oscillatory behavior in neural network exchange-correlation functionals. We implemented geometry optimization in PySCF for the DM21 functional in geometry optimization problem, compared its performance with traditional functionals, and tested it on various benchmarks. Our findings reveal both the potential and the current challenges of using neural network functionals for geometry optimization in DFT. We propose a solution extending the practical applicability of such functionals and allowing to model new substances with their help.

arXiv:2408.02161v2 Announce Type: replace-cross Abstract: The added value of machine learning for weather and climate applications is measurable through performance metrics, but explaining it remains challenging, particularly for large deep learning models. Inspired by climate model hierarchies, we propose that a full hierarchy of Pareto-optimal models, defined within an appropriately determined error-complexity plane, can guide model development and help understand the models' added value. We demonstrate the use of Pareto fronts in atmospheric physics through three sample applications, with hierarchies ranging from semi-empirical models with minimal parameters to deep learning algorithms. First, in cloud cover parameterization, we find that neural networks identify nonlinear relationships between cloud cover and its thermodynamic environment, and assimilate previously neglected features such as vertical gradients in relative humidity that improve the representation of low cloud cover. This added value is condensed into a ten-parameter equation that rivals deep learning models. Second, we establish a machine learning model hierarchy for emulating shortwave radiative transfer, distilling the importance of bidirectional vertical connectivity for accurately representing absorption and scattering, especially for multiple cloud layers. Third, we emphasize the importance of convective organization information when modeling the relationship between tropical precipitation and its surrounding environment. We discuss the added value of temporal memory when high-resolution spatial information is unavailable, with implications for precipitation parameterization. Therefore, by comparing data-driven models directly with existing schemes using Pareto optimality, we promote process understanding by hierarchically unveiling system complexity, with the hope of improving the trustworthiness of machine learning models in atmospheric applications.

arXiv:2207.04443v3 Announce Type: replace Abstract: The finite element method offers attractive methods for the numerical solution of coupled field problems arising in sensors and actuator simulations of various physical domains, like electrodynamics, mechanics, and thermodynamics. With this application perspective and being open, accessible, and fast implementations are possible, openCFS was launched in 2020. It provides an open-source framework for implementing partial differential equations using the finite element method. In particular, the acoustic module is part of active development, including several key methods. These methods include the perfectly-matched layer technique, non-confirming interface formulations, Lagrangian basis function, Legendre basis functions, spectral element formulations, a nodal element type, edge-based element type (aeroacoustic post-processing), absorbing boundary conditions, frequency dependent-material for time-harmonic and time-dependent simulations. Time-dependent simulations, time-harmonic simulations, and eigenvalue simulations are supported. Several variants of acoustic equations are implemented, including the relevant source terms and wave operators for aeroacoustics. The package includes rotating domains and non-conforming interfaces for fan noise simulations. It also contains an API to the Python3 package pyCFS. This paper presents openCFS with a focus on the acoustic module.

arXiv:2501.06388v1 Announce Type: new Abstract: We present a realizability-preserving numerical method for solving a spectral two-moment model to simulate the transport of massless, neutral particles interacting with a steady background material moving with relativistic velocities. The model is obtained as the special relativistic limit of a four-momentum-conservative general relativistic two-moment model. Using a maximum-entropy closure, we solve for the Eulerian-frame energy and momentum. The proposed numerical method is designed to preserve moment realizability, which corresponds to moments defined by a nonnegative phase-space density. The realizability-preserving method is achieved with the following key components: (i) a discontinuous Galerkin (DG) phase-space discretization with specially constructed numerical fluxes in the spatial and energy dimensions; (ii) a strong stability-preserving implicit-explicit (IMEX) time-integration method; (iii) a realizability-preserving conserved to primitive moment solver; (iv) a realizability-preserving implicit collision solver; and (v) a realizability-enforcing limiter. Component (iii) is necessitated by the closure procedure, which closes higher order moments nonlinearly in terms of primitive moments. The nonlinear conserved to primitive and the implicit collision solves are formulated as fixed-point problems, which are solved with custom iterative solvers designed to preserve the realizability of each iterate. With a series of numerical tests, we demonstrate the accuracy and robustness of this DG-IMEX method.

arXiv:2402.10874v2 Announce Type: replace-cross Abstract: Despite extensive research on magnetic skyrmions and antiskyrmions, a significant challenge remains in crafting nontrivial high-order skyrmionic textures with varying, or even tailor-made, topologies. We address this challenge, by focusing on a construction pathway of skyrmionic metamaterials within a monolayer thin film and suggest several skyrmionic metamaterials that are surprisingly stable, i.e., long-lived, due to a self-stabilization mechanism. This makes these new textures promising for applications. Central to our approach is the concept of 'simulated controlled assembly', in short, a protocol inspired by 'click chemistry' that allows for positioning topological magnetic structures where one likes, and then allowing for energy minimization to elucidate the stability. Utilizing high-throughput atomistic-spin-dynamic simulations alongside state-of-the-art AI-driven tools, we have isolated skyrmions (topological charge Q=1), antiskyrmions (Q=-1), and skyrmionium (Q=0). These entities serve as foundational 'skyrmionic building blocks' to form the here reported intricate textures. In this work, two key contributions are introduced to the field of skyrmionic systems. First, we present a a novel combination of atomistic spin dynamics simulations and controlled assembly protocols for the stabilization and investigation of new topological magnets. Second, using the aforementioned methods we report on the discovery of skyrmionic metamaterials.

arXiv:2501.06933v1 Announce Type: new Abstract: We introduce Neural Discrete Equilibrium (NeurDE), a machine learning (ML) approach for long-term forecasting of flow phenomena that relies on a "lifting" of physical conservation laws into the framework of kinetic theory. The kinetic formulation provides an excellent structure for ML algorithms by separating nonlinear, non-local physics into a nonlinear but local relaxation to equilibrium and a linear non-local transport. This separation allows the ML to focus on the local nonlinear components while addressing the simpler linear transport with efficient classical numerical algorithms. To accomplish this, we design an operator network that maps macroscopic observables to equilibrium states in a manner that maximizes entropy, yielding expressive BGK-type collisions. By incorporating our surrogate equilibrium into the lattice Boltzmann (LB) algorithm, we achieve accurate flow forecasts for a wide range of challenging flows. We show that NeurDE enables accurate prediction of compressible flows, including supersonic flows, while tracking shocks over hundreds of time steps, using a small velocity lattice-a heretofore unattainable feat without expensive numerical root finding.

arXiv:2501.06300v1 Announce Type: new Abstract: We present a tensorization algorithm for constructing tensor train representations of functions, drawing on sketching and cross interpolation ideas. The method only requires black-box access to the target function and a small set of sample points defining the domain of interest. Thus, it is particularly well-suited for machine learning models, where the domain of interest is naturally defined by the training dataset. We show that this approach can be used to enhance the privacy and interpretability of neural network models. Specifically, we apply our decomposition to (i) obfuscate neural networks whose parameters encode patterns tied to the training data distribution, and (ii) estimate topological phases of matter that are easily accessible from the tensor train representation. Additionally, we show that this tensorization can serve as an efficient initialization method for optimizing tensor trains in general settings, and that, for model compression, our algorithm achieves a superior trade-off between memory and time complexity compared to conventional tensorization methods of neural networks.

arXiv:2501.07373v1 Announce Type: new Abstract: Accurate, interpretable, and real-time modeling of multi-body dynamical systems is essential for predicting behaviors and inferring physical properties in natural and engineered environments. Traditional physics-based models face scalability challenges and are computationally demanding, while data-driven approaches like Graph Neural Networks (GNNs) often lack physical consistency, interpretability, and generalization. In this paper, we propose Dynami-CAL GraphNet, a Physics-Informed Graph Neural Network that integrates the learning capabilities of GNNs with physics-based inductive biases to address these limitations. Dynami-CAL GraphNet enforces pairwise conservation of linear and angular momentum for interacting nodes using edge-local reference frames that are equivariant to rotational symmetries, invariant to translations, and equivariant to node permutations. This design ensures physically consistent predictions of node dynamics while offering interpretable, edge-wise linear and angular impulses resulting from pairwise interactions. Evaluated on a 3D granular system with inelastic collisions, Dynami-CAL GraphNet demonstrates stable error accumulation over extended rollouts, effective extrapolations to unseen configurations, and robust handling of heterogeneous interactions and external forces. Dynami-CAL GraphNet offers significant advantages in fields requiring accurate, interpretable, and real-time modeling of complex multi-body dynamical systems, such as robotics, aerospace engineering, and materials science. By providing physically consistent and scalable predictions that adhere to fundamental conservation laws, it enables the inference of forces and moments while efficiently handling heterogeneous interactions and external forces.

arXiv:2405.18874v2 Announce Type: replace-cross Abstract: The dot product attention mechanism, originally designed for natural language processing tasks, is a cornerstone of modern Transformers. It adeptly captures semantic relationships between word pairs in sentences by computing a similarity overlap between queries and keys. In this work, we explore the suitability of Transformers, focusing on their attention mechanisms, in the specific domain of the parametrization of variational wave functions to approximate ground states of quantum many-body spin Hamiltonians. Specifically, we perform numerical simulations on the two-dimensional $J_1$-$J_2$ Heisenberg model, a common benchmark in the field of quantum many-body systems on lattice. By comparing the performance of standard attention mechanisms with a simplified version that excludes queries and keys, relying solely on positions, we achieve competitive results while reducing computational cost and parameter usage. Furthermore, through the analysis of the attention maps generated by standard attention mechanisms, we show that the attention weights become effectively input-independent at the end of the optimization. We support the numerical results with analytical calculations, providing physical insights of why queries and keys should be, in principle, omitted from the attention mechanism when studying large systems.

arXiv:2409.12483v2 Announce Type: replace-cross Abstract: Numerical methods of the ADER family, in particular finite-element ADER-DG and finite-volume ADER-WENO methods, are among the most accurate numerical methods for solving quasilinear PDE systems. The internal structure of ADER-DG and ADER-WENO numerical methods contains a large number of basic linear algebra operations related to matrix multiplications. The main interface of software libraries for matrix multiplications for high-performance computing is BLAS. This paper presents an effective method for integration the standard functions of the BLAS interface into the implementation of these numerical methods. The calculated matrices are small matrices; at the same time, the proposed implementation makes it possible to effectively use existing JIT technologies. The proposed approach immediately operates on AoS, which makes it possible to efficiently calculate flux, source and non-conservative terms without need to carry out transposition. The obtained computational costs demonstrated that the effective implementation, based on the use of the JIT functions of the BLAS, outperformed both the implementation based on the general BLAS functions and the vanilla implementations by several orders of magnitude. At the same time, the complexity of developing an implementation based on the approach proposed in this work does not exceed the complexity of developing a vanilla implementation.

arXiv:2501.07547v1 Announce Type: new Abstract: We propose a high-order spacetime wavelet method for the solution of nonlinear partial differential equations with a user-prescribed accuracy. The technique utilizes wavelet theory with a priori error estimates to discretize the problem in both the spatial and temporal dimensions simultaneously. We also propose a novel wavelet-based recursive algorithm to reduce the system sensitivity stemming from steep initial and/or boundary conditions. The resulting nonlinear equations are solved using the Newton-Raphson method. We parallelize the construction of the tangent operator along with the solution of the system of algebraic equations. We perform rigorous verification studies using the nonlinear Burgers' equation. The application of the method is demonstrated solving Sod shock tube problem using the Navier-Stokes equations. The numerical results of the method reveal high-order convergence rates for the function as well as its spatial and temporal derivatives. We solve problems with steep gradients in both the spatial and temporal directions with a priori error estimates.

arXiv:2404.19602v2 Announce Type: replace-cross Abstract: In this article, we investigate some issues related to the quantification of uncertainties associated with the electrical properties of graphene nanoribbons. The approach is suited to understand the effects of missing information linked to the difficulty of fixing some material parameters, such as the band gap, and the strength of the applied electric field. In particular, we focus on the extension of particle Galerkin methods for kinetic equations in the case of the semiclassical Boltzmann equation for charge transport in graphene nanoribbons with uncertainties. To this end, we develop an efficient particle scheme which allows us to parallelize the computation and then, after a suitable generalization of the scheme to the case of random inputs, we present a Galerkin reformulation of the particle dynamics, obtained by means of a generalized Polynomial Chaos approach, which allows the reconstruction of the kinetic distribution. As a consequence, the proposed particle-based scheme preserves the physical properties and the positivity of the distribution function also in the presence of a complex scattering in the transport equation of electrons. The impact of the uncertainty of the band gap and applied field on the electrical current is analysed.

arXiv:2311.10872v3 Announce Type: replace-cross Abstract: Since viscoelastic two-phase flows arise in various industrial and natural processes, developing accurate and efficient software for their detailed numerical simulation is a highly relevant and challenging research task. We present a geometrical unstructured Volume-of-Fluid (VOF) method for handling two-phase flows with viscoelastic liquid phase, where the latter is modeled via generic rate-type constitutive equations and a one-field description is derived by conditional volume averaging of the local instantaneous bulk equations and interface jump conditions. The method builds on the plicRDF-isoAdvector geometrical VOF solver that is extended and combined with the modular framework DeboRheo for viscoelastic computational fluid dynamics (CFD). A piecewise-linear geometrical interface reconstruction technique on general unstructured meshes is employed for discretizing the viscoelastic stresses across the fluid interface. DeboRheo facilitates a flexible combination of different rheological models with appropriate stabilization methods to address the high Weissenberg number problem.

arXiv:2501.03383v1 Announce Type: cross Abstract: Increasing HPC cluster sizes and large-scale simulations that produce petabytes of data per run, create massive IO and storage challenges for analysis. Deep learning-based techniques, in particular, make use of these amounts of domain data to extract patterns that help build scientific understanding. Here, we demonstrate a streaming workflow in which simulation data is streamed directly to a machine-learning (ML) framework, circumventing the file system bottleneck. Data is transformed in transit, asynchronously to the simulation and the training of the model. With the presented workflow, data operations can be performed in common and easy-to-use programming languages, freeing the application user from adapting the application output routines. As a proof-of-concept we consider a GPU accelerated particle-in-cell (PIConGPU) simulation of the Kelvin- Helmholtz instability (KHI). We employ experience replay to avoid catastrophic forgetting in learning from this non-steady process in a continual manner. We detail challenges addressed while porting and scaling to Frontier exascale system.