Brute-force Computation Research Articles

Finding high-performance MOFs for effective SF6/N2 separation through high-throughput computational screening and machine learning

Abstract Given the rapidly expanding pool of synthesized and hypothetical metal–organic frameworks (MOFs), testing every single material for SF6/N2 separation by iterative experimental methods or computationally demanding molecular simulations is not practical. In this study, we integrated high-throughput computational screening and machine learning (ML) approaches to evaluate SF6/N2 mixture adsorption and separation performances of over 25 000 different types of synthesized and hypothetical MOFs (hypoMOFs), representing the largest set of structures studied for SF6/N2 separation to date. SF6/N2 mixture adsorption data that we produced for synthesized MOFs using molecular simulations were utilized to develop ML models to accurately and quickly predict SF6 and N2 uptakes, SF6/N2 selectivities, SF6 working capacities, adsorbent performance scores, and regenerabilities of both synthesized and hypoMOFs. Results showed the MOF space that we studied exhibits very high SF6/N2 selectivities in the range of 1.8–4204 at 1 bar in addition to high SF6 working capacities between 0.04–5.68 mol kg−1 at an adsorption pressure of 1 bar and desorption pressure of 0.1 bar at room temperature. The top-performing MOF adsorbents for SF6/N2 mixture separation were identified to have Zn, Cu, Ni metals; terphenyl, pyridine, naphthalene linkers; and medium pore sizes. Our comprehensive computational approach offers a highly efficient alternative to brute-force computer simulations by enabling the rapid assessment of the MOF adsorbents for SF6/N2 separation and provides molecular insights into the key structural features of the most promising adsorbents.

Machine learning accelerated discovery of corrosion-resistant high-entropy alloys

Corrosion has a wide impact on society, causing catastrophic damage to structurally engineered components. An emerging class of corrosion-resistant materials are high-entropy alloys. However, high-entropy alloys live in high-dimensional composition and configuration space, making materials designs via experimental trial-and-error or brute-force ab initio calculations almost impossible. Here we develop a physics-informed machine-learning framework to identify corrosion-resistant high-entropy alloys. Three metrics are used to evaluate the corrosion resistance, including single-phase formability, surface energy and the compactness of oxide films formed on an alloy surface evaluated by Pilling–Bedworth ratios. We used random forest models to predict the single-phase formability, trained on an experimental dataset. Machine learning inter-atomic potentials were employed to calculate surface energies and Pilling–Bedworth ratios, which are trained on first-principles data fast sampled using embedded atom models. A combination of random forest models and high-fidelity machine learning potentials represents the first of its kind to relate chemical compositions to corrosion resistance of high-entropy alloys, paving the way for automatic design of materials with superior corrosion protection. This framework was demonstrated on AlCrFeCoNi high-entropy alloys and we identified composition regions with high corrosion resistance from a wide range of compositions. Machine learning predicted lattice constants and surface energies are consistent with values by first-principles calculations. The predicted single-phase formability and corrosion-resistant compositions of AlCrFeCoNi agree well with experiments. This framework provides a computationally efficient approach to navigate high-dimensional composition space of high-entropy alloys. It is general in its application and applicable to other complex materials, enabling high-throughput screening of material candidates and potentially accelerating the iteration of integrated computational materials engineering.

Accelerated Discovery of Metal–Organic Frameworks for CO2 Capture by Artificial Intelligence

Accelerated Discovery of Metal–Organic Frameworks for CO₂ Capture by Artificial Intelligence

Evidence for the utility of quantum computing before fault tolerance

Quantum computing promises to offer substantial speed-ups over its classical counterpart for certain problems. However, the greatest impediment to realizing its full potential is noise that is inherent to these systems. The widely accepted solution to this challenge is the implementation of fault-tolerant quantum circuits, which is out of reach for current processors. Here we report experiments on a noisy 127-qubit processor and demonstrate the measurement of accurate expectation values for circuit volumes at a scale beyond brute-force classical computation. We argue that this represents evidence for the utility of quantum computing in a pre-fault-tolerant era. These experimental results are enabled by advances in the coherence and calibration of a superconducting processor at this scale and the ability to characterize1 and controllably manipulate noise across such a large device. We establish the accuracy of the measured expectation values by comparing them with the output of exactly verifiable circuits. In the regime of strong entanglement, the quantum computer provides correct results for which leading classical approximations such as pure-state-based 1D (matrix product states, MPS) and 2D (isometric tensor network states, isoTNS) tensor network methods2,3 break down. These experiments demonstrate a foundational tool for the realization of near-term quantum applications4,5.

Rényi entanglement entropy after a quantum quench starting from insulating states in a free boson system

We investigate the time-dependent R\'{e}nyi entanglement entropy after a quantum quench starting from the Mott-insulating and charge-density-wave states in a one-dimensional free boson system. The second R\'{e}nyi entanglement entropy is found to be the negative of the logarithm of the permanent of a matrix consisting of time-dependent single-particle correlation functions. From this relation and a permanent inequality, we obtain rigorous conditions for satisfying the volume-law entanglement growth. We also succeed in calculating the time evolution of the R\'{e}nyi entanglement entropy in unprecedentedly large systems by brute-force computations of the permanent. We discuss possible applications of our findings to the real-time dynamics of noninteracting bosonic systems.

Bifurcations in a forced Wilson-Cowan neuron pair

We investigate bifurcations of periodic solutions observed in the forced Wilson-Cowan neuron pair by both the brute-force computation and the shooting method. By superimposing the results given by both methods, a detailed topological classification of periodic solutions is achieved that includes tori and chaos attractors in the parameter space is achieved. We thoroughly explore the parameter space composed of threshold values, amplitude, and angular velocity of an external forcing term. Many bifurcation curves that are invisible when using brute-force method are solved by the shooting method. We find out a typical bifurcation structure including Arnold tongue in the angular velocity and the amplitude of the external force parameter plane, and confirm its fractal structure. In addition, the emergence of periodic bursting responses depending on these patterns is explained.

Rapid Numerical Analysis of Electrically Large PEC Platforms With Local Variations via a Platform Green’s Function Method

The aim of this article is to perform a rapid electromagnetic (EM) analysis of large perfectly electric conducting (PEC) platforms with local variations. Such problems often require many-query simulations to navigate complex parameter spaces and thus quickly become computationally expensive. The proposed work starts with a stationary-variable domain decomposition, where the computational domain is decomposed into large fixed parts and small portions with local variations. Subsequently, we introduce a separable and compressible platform Green’s function at the outer surface of those variable subdomains in an upfront offline calculation. Once obtained, the online computational complexity does not depend on the size of the in situ platform. With the validation of numerical results, we conclude that the proposed work has the potential to greatly speed up the online evaluation of local designs and optimizations compared to the brute-force computation.

Semi-experimental equilibrium (re SE) and theoretical structures of hydrazoic acid (HN3).

Hydrazoic acid (HN3) is used as a case study for investigating the accuracy and precision by which a molecular structure-specifically, a semi-experimental equilibrium structure (re SE)-may be determined using current state-of-the-art methodology. The influence of the theoretical corrections for effects of vibration-rotation coupling and electron-mass distribution that are employed in the analysis is explored in detail. The small size of HN3 allowed us to deploy considerable computational resources to probe the basis-set dependence of these corrections using a series of coupled-cluster single, double, perturbative triple [CCSD(T)] calculations with cc-pCVXZ (X = D, T, Q, 5) basis sets. We extrapolated the resulting corrections to the complete basis set (CBS) limit to obtain CCSD(T)/CBS corrections, which were used in a subsequent re SE structure determination. The re SE parameters obtained using the CCSD(T)/cc-pCV5Z corrections are nearly identical to those obtained using the CCSD(T)/CBS corrections, with uncertainties in the bond distances and angles of less than 0.0006 Å and 0.08°, respectively. The previously obtained re SE structure using CCSD(T)/ANO2 agrees with that using CCSD(T)/cc-pCV5Z to within 0.000 08 Å and 0.016° for bond distances and angles, respectively, and with only 25% larger uncertainties, validating the idea that re SE structure determinations can be carried out with significantly smaller basis sets than those needed for similarly accurate, strictly ab initio determinations. Although the purely computational re structural parameters [CCSD(T)/cc-pCV6Z] fall outside of the statistical uncertainties (2σ) of the corresponding re SE structural parameters, the discrepancy is rectified by applying corrections to address the theoretical limitations of the CCSD(T)/cc-pCV6Z geometry with respect to basis set, electron correlation, relativity, and the Born-Oppenheimer approximation, thereby supporting the contention that the semi-experimental approach is both an accurate and vastly more efficient method for structure determinations than is brute-force computation.

Development of Uncertainty Analysis Techniques for the Fission Matrix–Based Neutron Transport Code RAPID

The combined fission matrix (CFM) method is a newly developed neutron transport theory. This method estimates the fission matrix of the reactor core or spent fuel pool by combining a set of database fission matrices. The RAPID neutron transport code based on the CFM routine was developed originally for the spent fuel storage system and has been applied to the reactor core calculation in recent years. It can perform high-fidelity whole-core transport calculations within minutes. However, since the fission matrix database is obtained from Monte Carlo calculations, the uncertainty in the fission matrix will inevitably pass to its eigenvalue and eigenvector. The RAPID code also uses the fission matrix homogenization and interpolation techniques to further improve the calculation efficiency. Therefore, it is difficult to establish a relationship between the fission matrix elements’ uncertainty and the resulting eigenvalue and eigenvector uncertainties. This paper proposes two uncertainty analysis methods to obtain the eigenvalue and eigenvector uncertainties. The fission matrix resampling method resamples the database fission matrix elements according to each individual uncertainty. This method could generate many fission matrix databases at little additional costs and analyze the eigenvalue and eigenvector uncertainties from these resampled fission matrix coefficients. The analog uncertainty analysis method predicts the eigenvalue uncertainty from the uncertainty of the total fission rate in a fixed-source calculation, which yields a fission matrix column. Both uncertainty analysis methods have been validated against the reference brute-force calculations on a single-pin model and the BEAVRS whole-core model. It shows that the fission matrix resampling method could well estimate the uncertainties in the fission matrix eigenvalue and eigenvector. The analog uncertainty analysis method can accurately predict the eigenvalue uncertainty, which provides a guideline for the number of neutron histories simulated per fixed-source calculation.

Machine learning potential for interacting dislocations in the presence of free surfaces

Computing the total energy of a system of N interacting dislocations in the presence of arbitrary free surfaces is a difficult task, requiring Finite Element (FE) numerical calculations. Worst, high accuracy requires very fine meshes in the proximity of each dislocation core. Here we show that FE calculations can be conveniently replaced by a Machine Learning (ML) approach. After formulating the elastic problem in terms of one and two-body terms only, we use Sobolev training to obtain consistent information on both energy and forces, fitted using a feed-forward neural network (NN) architecture. As an example, we apply the proposed methodology to corrugated, heteroepitaxial semiconductor films, searching for the minimum-energy dislocation distributions by using Monte Carlo. Importantly, the presence of an interaction cutoff allows for the application of the method to systems of different sizes without the need to repeat training. Millions of energy evaluations are performed, a task which would have been impossible by brute-force FE calculations. Finally, we show how forces can be exploited in running 2D ML-based dislocation dynamics simulations.

An iterative prediction method for designing the moderator used for the boron neutron capture therapy.

To conduct research related to slow neutrons, fast neutrons must be mode-rated and shifted to the desired energy region. In this research, an iterated prediction method, in which the neutron transportation properties of all materials were characterized by a reflection matrix, , and a transmission matrix, , was proposed to bypass a time-consuming Monte Carlo simulation and predict the performance of the moderator, including the epithermal neutron flux and the dose of fast neutrons and gamma rays, used for boron neutron capture therapy (BNCT). To find the optimal solution in the huge parameter space, a genetic algorithm combined with transmission and reflection matrices was utilized. The results showed that a 70-loop iteration was able to find a design for the moderator of BNCT with almost 80 higher epithermal neutron flux per kilowatt than that of the empirically optimized moderator that was previously reported in the literature. Compared with the Monte Carlo method, this method had the advantage of reducing the calculation time and statistical errors. The genetic algorithm with matrices (GAM) method can be used to find an optimal solution in a huge parameter space without brute-force calculations. It could be a promising method for designing the moderator for thermal or epithermal neutronusages.

Third-order perturbation expansion of the two-point correlation function of the dissipative quantum φ4 theory

We analytically calculate the perturbation expansion of the two-point correlation function (propagator) of the scalar, dissipative quantum ${\ensuremath{\varphi}}^{4}$ theory up to third order in the interaction parameter $\ensuremath{\lambda}$. The calculations are carried out with two different methods. The first is based on a brute force computation of all interactions appearing in the perturbation expansion term by term at the given order of the perturbation, supported by the use of a symbolic mathematical code. The second uses an efficient perturbation scheme which allows one to hierarchically organize terms within a given order in the perturbation expansion based on the number of occurrences of the free evolution operator ${\mathcal{R}}_{s}^{\mathrm{free}}$; in addition, it allows one to utilize information from already computed lower-order terms in the calculation of higher-order terms. The two methods yield the same result. In the limit of zero dissipation (zero friction coefficient $\ensuremath{\gamma}$), our result coincides with that obtained from the Lagrangian approach in $D=d+1$ dimensions ($d$ denotes the number of space dimensions, while $D$ includes the time dimension) with the use of $D$-dimensional vectors, re-expressed in terms of only $d$-dimensional space integrals by integrating out the zero component. We have also verified that the value of the critical coupling constant ${\ensuremath{\lambda}}^{*}$ as a function of space dimensionality $d$, which can be used to evaluate perturbation expansions at the physical length scale ${\ensuremath{\ell}}_{m}$, comes out correctly from our third-order calculation.

Linear and brute force stability of orthogonal moment multiple-relaxation-time lattice Boltzmann methods applied to homogeneous isotropic turbulence.

Multiple-relaxation-time (MRT) lattice Boltzmann methods (LBM) based on orthogonal moments exhibit lattice Mach number dependent instabilities in diffusive scaling. The present work renders an explicit formulation of stability sets for orthogonal moment MRT LBM. The stability sets are defined via the spectral radius of linearized amplification matrices of the MRT collision operator with variable relaxation frequencies. Numerical investigations are carried out for the three-dimensional Taylor-Green vortex benchmark at Reynolds number 1600. Extensive brute force computations of specific relaxation frequency ranges for the full test case are opposed to the von Neumann stability set prediction. Based on that, we prove numerically that a scan over the full wave space, including scaled mean flow variations, is required to draw conclusions on the overall stability of LBM in turbulent flow simulations. Furthermore, the von Neumann results show that a grid dependence is hardly possible to include in the notion of linear stability for LBM. Lastly, via brute force stability investigations based on empirical data from a total number of 22 696 simulations, the existence of a deterministic influence of the grid resolution is deduced. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

The Nonlinear Radiative Feedback Effects in the Arctic Warming

The analysis of radiative feedbacks requires the separation and quantification of the radiative contributions of different feedback variables, such as atmospheric temperature, water vapor, surface albedo, cloud, etc. It has been a challenge to include the nonlinear radiative effects of these variables in the feedback analysis. For instance, the kernel method that is widely used in the literature assumes linearity and completely neglects the nonlinear effects. Nonlinear effects may arise from the nonlinear dependency of radiation on each of the feedback variables, especially when the change in them is of large magnitude such as in the case of the Arctic climate change. Nonlinear effects may also arise from the coupling between different feedback variables, which often occurs as feedback variables including temperature, humidity and cloud tend to vary in a coherent manner. In this paper, we use brute-force radiation model calculations to quantify both univariate and multivariate nonlinear feedback effects and provide a qualitative explanation of their causes based on simple analytical models. We identify these prominent nonlinear effects in the CO2-driven Arctic climate change: 1) the univariate nonlinear effect in the surface albedo feedback, which results from a nonlinear dependency of planetary albedo on the surface albedo, which causes the linear kernel method to overestimate the univariate surface albedo feedback; 2) the coupling effect between surface albedo and cloud, which offsets the univariate surface albedo feedback; 3) the coupling effect between atmospheric temperature and cloud, which offsets the very strong univariate temperature feedback. These results illustrate the hidden biases in the linear feedback analysis methods and highlight the need for nonlinear methods in feedback quantification.

Prism – A novel approach to dead body cooling and its parameters

In temperature based death time estimation, the mathematical description by Marshall and Hoare is combined with the parameters defined and additional correction factors introduced by Henssge in the Nomogram method (summarized as MHH). Parameters and correction factors however leave room for subjectivity and disagreement. Elevation of rectal temperature at the time of death has been acknowledged as problematic for death time estimation in several studies, but has neither been solved nor systematically integrated into death time estimation methodology. Ambient temperature, when non-constant and/or unknown, may introduce additional errors. Further problems may arise if the fundamental relationship between torso dimensions and total body weight is not comparable to Henssge’s dummy cooling model. In this study we present a novel methodological approach to temperature based death time estimation, in which relevant parameters for calculations may be evaluated, corrected and generated using brute-force calculations. Consistency of death time over the course of cooling is used as brute-force target. The calculations produce momentary cooling weights, which are graphed over time. Cooling weight graphs can be analyzed to draw conclusions related to different parameters. The method was used on artificial ideal cooling data which was generated according to MHH for known parameters. Correctness of assumed parameters was confirmed by a linear horizontal path of the cooling weight graph. However, controlled false value input resulted in characteristic graph variations. Elevated rectal temperature at the time of death was detectable from the curve shape until hours after cooling below regular temperature at death. False high and false low ambient temperature produced positive and negative curve slopes. Overall, the method acts much like a prism which breaks up light into its elemental colors. It holds potential for application both in scientific settings and practical case work.

A stochastic analysis method of transient responses using harmonic wavelets, part 2: Time-dependent vehicle-bridge systems

Conventional stochastic response analysis methods of vehicle-bridge (VB) systems involve a brute-force calculation based on a large number of simulations, which imposes huge computational burdens because the dynamic analysis of a time-dependent VB system requires repeated assembles of system matrices. This paper proposes a novel stochastic analysis method of transient responses for time-dependent VB systems based on periodic generalized harmonic wavelets (GHW). We establish the equations of motion of the VB system and reveal the orthogonal characteristic relationships between the time-dependent system matrices and the wavelet functions. Then, two sets of linear algebraic equations of wavelet coefficients are established for describing the time-dependent VB system, and the time-varying power spectral density functions of system responses are obtained in a semi-analytical form. The stochastic response analysis of the time-dependent VB system is therefore converted into solving a set of linear algebraic equations, which significantly simplifies the stochastic response analysis. The accuracy and efficiency of the proposed method are validated via comparison against the Monte Carlo simulations of nonstationary stochastic analyses of a highway bridge and a railway bridge, respectively. The proposed method provides a high-efficient way to estimate the time-varying power spectral density functions of stochastic responses of time-dependent VB systems.

Equal Sums of Quartics (In Context with the Richmond Equation) (ax<sup>4</sup>+by<sup>4</sup>+cz<sup>4</sup>+dw<sup>4</sup>=0)

Consider the below mentioned Equation: ax4+by4+cz4+dw4=0---[1]. In section (1) we consider solution's with the condition on the coefficient's of equation[1]. Namely the product (abcd)=square. In section [2] we consider the coefficients of Equation [1], with the product of coefficient's (abcd) not equal to a square. Historically Equation [1] has been studied by Ajai Choudhry, A. Bremner, M.Ulas [ref. 5] in 2014. Also Richmond [ref. 1 & 2] has done some ground work in 1944 & 1948. This paper has gone a step further, by finding many parametric solutions & new small numerical solutions by the use of unique Identities. The identities are unique, because they are of mixed powers (combination of quartic & quadratic variables) which are then converted to only degree four identities. As an added bonus in section [B], we came up with a few quartic (4-1-n ) numerical solutions for (n < 50) by elliptical mean's. A table of numerical solutions for the (4-1-n) Equation arrived at by brute force computer search is also given [ref # 7].

A Hybrid-CPU-FPGA-based Solution to the Recovery of Sha256crypt-hashed Passwords

This paper presents an accelerator design for the password recovery of sha256crypt based on hybrid CPU-FPGA devices. By applying the brute-force attack computation model proposed in this paper, we decompose the sha256crypt function into two types of operations, namely the data dispatching and the block transforming. The data dispatching operation generates message blocks and the block transforming operation transforms message blocks into digests. These two operations are efficiently accelerated by the customized data dispatch unit and the pipelined block transform unit, respectively. Difficulties of adopting the pipeline technique are addressed also with the following techniques. The group scheduling is used to solve the data dependency that stalls the pipeline. The look-ahead execution eliminates the uncertainty of the execution path. The data path pruning and spatial-temporal multiplexing reduce the resource overhead of non-computing units.The proposed accelerator design is implemented and evaluated on the Xilinx Zynq-7000 XC7Z030-3 SoC. Our experimental results show that the proposed accelerator can improve energy efficiency by 2.54x over the state-of-the-art password recovery tool Hashcat running on an NVIDIA GTX1080Ti GPU. Compared with the pure FPGA-based implementation in John-the-Ripper, the proposed accelerator improves energy efficiency by 1.64x and improves resource efficiency by 1.69x.

Weighted ensemble milestoning (WEM): A combined approach for rare event simulations.

To directly simulate rare events using atomistic molecular dynamics is a significant challenge in computational biophysics. Well-established enhanced-sampling techniques do exist to obtain the thermodynamic functions for such systems. However, developing methods for obtaining the kinetics of long timescale processes from simulation at atomic detail is comparatively less developed an area. Milestoning and the weighted ensemble (WE) method are two different stratification strategies; both have shown promise for computing long timescales of complex biomolecular processes. Nevertheless, both require a significant investment of computational resources. We have combined WE and milestoning to calculate observables in orders-of-magnitude less central processing unit and wall-clock time. Our weighted ensemble milestoning method (WEM) uses WE simulation to converge the transition probability and first passage times between milestones, followed by the utilization of the theoretical framework of milestoning to extract thermodynamic and kinetic properties of the entire process. We tested our method for a simple one-dimensional double-well potential, for an eleven-dimensional potential energy surface with energy barrier, and on the biomolecular model system alanine dipeptide. We were able to recover the free energy profiles, time correlation functions, and mean first passage times for barrier crossing events at a significantly small computational cost. WEM promises to extend the applicability of molecular dynamics simulation to slow dynamics of large systems that are well beyond the scope of present day brute-force computations.

Extraction of mechanical properties of materials through deep learning from instrumented indentation

Instrumented indentation has been developed and widely utilized as one of the most versatile and practical means of extracting mechanical properties of materials. This method is particularly desirable for those applications where it is difficult to experimentally determine the mechanical properties using stress-strain data obtained from coupon specimens. Such applications include material processing and manufacturing of small and large engineering components and structures involving the following: three-dimensional (3D) printing, thin-film and multilayered structures, and integrated manufacturing of materials for coupled mechanical and functional properties. Here, we utilize the latest developments in neural networks, including a multifidelity approach whereby deep-learning algorithms are trained to extract elastoplastic properties of metals and alloys from instrumented indentation results using multiple datasets for desired levels of improved accuracy. We have established algorithms for solving inverse problems by recourse to single, dual, and multiple indentation and demonstrate that these algorithms significantly outperform traditional brute force computations and function-fitting methods. Moreover, we present several multifidelity approaches specifically for solving the inverse indentation problem which 1) significantly reduce the number of high-fidelity datasets required to achieve a given level of accuracy, 2) utilize known physical and scaling laws to improve training efficiency and accuracy, and 3) integrate simulation and experimental data for training disparate datasets to learn and minimize systematic errors. The predictive capabilities and advantages of these multifidelity methods have been assessed by direct comparisons with experimental results for indentation for different commercial alloys, including two wrought aluminum alloys and several 3D printed titanium alloys.