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In this paper we present the Markovian Multiagent Monte-Carlo Second Order Self-Consistent Field Algorithm (M3-SOSCF). This algorithm provides a highly reliable methodology for converging SCF calculations in single-reference methods using a modified differential evolution approach. Additionally, M3 is embarrassingly parallel and modular in regards to Newton–Raphson subroutines. We show that M3 is able to surpass contemporary SOSCFs in reliability, which is illustrated by a benchmark employing poor initial guesses and a second benchmark with SCF calculations which face difficulties using standard SCF algorithms. Furthermore, we analyse inherent properties of M3 and show that in addition to its robustness and efficiency, it is more user-friendly than current SOSCFs. [ABSTRACT FROM AUTHOR]

Traditional x-ray sources used today for multiple applications, such as medical imaging (computed tomography, radiography, mammography, and interventional radiology) or industrial inspection, are vacuum based electron beam devices that include several key components, such as electron emitters, electron guns/cathodes, and anodes/targets. The associated electronics for electron beam generation, focusing and control, and beam acceleration are located outside the vacuum chamber. The general topology of these tubes has been directionally unchanged for more than 100 years; however, tube design remains a long, inefficient, tedious, and complex process; blind design of experiments do not necessarily make the process more efficient. As a case study, in this paper, we introduce the differential evolution (DE), an artificial intelligence-based optimization algorithm, for the design optimization of x-ray source beam optics. Using a small-scale design problem, we demonstrate that DE can be an effective optimization method for x-ray source beam optics design. [ABSTRACT FROM AUTHOR]

The time dependent density matrix renormalization group (TD-DMRG) has become one of the cutting edge methods of quantum dynamics for complex systems. In this paper, we comparatively study the accuracy of three time evolution schemes in the TD-DMRG, the global propagation and compression method with the Runge-Kutta algorithm (P&C-RK), the time dependent variational principle based methods with the matrix unfolding algorithm (TDVP-MU), and with the projector-splitting algorithm (TDVP-PS), by performing benchmarks on the exciton dynamics of the Fenna-Matthews-Olson complex. We show that TDVP-MU and TDVP-PS yield the same result when the time step size is converged and they are more accurate than P&C-RK4, while TDVP-PS tolerates a larger time step size than TDVP-MU. We further adopt the graphical processing units to accelerate the heavy tensor contractions in the TD-DMRG, and it is able to speed up the TDVP-MU and TDVP-PS schemes by up to 73 times. [ABSTRACT FROM AUTHOR]

This paper describes the design process of a low-frequency sound absorptive panel composed of differently tuned Helmholtz resonators (HRs), considering size and fabrication constraints relevant for applications in the building sector. The paper focuses on cylindrical and spiral resonators with embedded necks that are thin and can achieve high absorption. the mutual interaction between the resonators was modeled based on the radiation impedance method and it plays a key component in enhancing the absorption performance of the array. The differential evolution search algorithm was used to design the resonators and modify their mutual interaction to derive the absorption performance of multiple HR arrays for comparison. Optimizations to the resonator configuration and the neck resistance were implemented to produce a unit panel that has a broadband absorption performance with emphasis on the low to mid frequencies and is thin and light in weight. Unit panels with dimensions of 20 cm × 20 cm , consisting of 29 cylindrical HRs designed to absorb in the 25–900 Hz frequency range, were constructed and tested in a custom-built impedance tube. The measured absorption performance of these panels is consistent with the theoretical predictions. [ABSTRACT FROM AUTHOR]

This paper studies the existence, regularity, and asymptotic properties of solutions for a class of neutral differential evolution equations with nonlocal initial conditions on an infinite interval. The existence and regularity of solutions of the considered equation are, respectively, investigated by the theory of fractional power operators and fixed point theorems under some assumptions for nonlinear functions. Then, under suitable conditions, asymptotic properties, including stability and existence of global attracting sets and quasi-invariant sets of mild solutions, are also discussed in the context. Finally, an example is presented to illustrate the applications of the obtained abstract results. [ABSTRACT FROM AUTHOR]

For ultrashort-term wind power prediction, an optimized extreme learning machine method based on biogeography-based optimization (BBO-KELM) is proposed. The kernel extreme learning machine (KELM) method only uses the kernel function to represent the unknown nonlinear feature map of the hidden layer and does not need to select the number of nodes of the hidden layer. Meanwhile, the output weight of the network is calculated by the regularized least squares algorithm. The BBO algorithm, which is a new evolutionary algorithm (EA) motivated by biogeography, which is the study of the distribution of biological species through time and space, is efficient in solving high dimensional, multiobjective optimization problems. In this paper, the KELM method is optimized using the BBO algorithm to optimize the selection of input variable sets, the parameters of the kernel function, and the Tikhonov regularization coefficient, so as to further improve the learning performance of the KELM method. To verify the effectiveness of the BBO-KELM method proposed in this paper, the BBO-KELM method is applied to ultrashort-term wind power prediction research in different regions and is compared with benchmark methods such as persistence, neural networks, support vector machine, extreme learning machine (ELM), and other optimized ELM (O-ELM) or KELM (O-KELM) methods such as BBO-ELM, particle swarm optimization (PSO)-ELM, differential evolution-KELM, simulated annealing-KELM, and PSO-KELM, under the same conditions. Experimental results show that the BBO-KELM methods with cosine migration can give better prediction accuracy; in addition, in the proposed method, the parameters of the kernel function do not need to be selected by trial-and-error and the relevant input variables can be automatically selected, improving the generalization capability. [ABSTRACT FROM AUTHOR]

A coil system to generate a uniform field is urgently needed in quantum experiments. However, general coil configurations based on the analytical method have not considered practical restrictions, such as the region for coil placement due to holes in the center of the magnetic shield, which could not be directly applied in most of the quantum experiments. In this paper, we develop a coil design method for quantum experiments using hybrid machine learning. The algorithm part consists of a machine learner based on an artificial neural network and a differential evolution (DE) learner. The cooperation of both learners demonstrates its higher efficiency than a single DE learner and robustness in the coil optimization problem compared with analytical proposals. With the help of a DE learner, in numerical simulation, a machine learner can successfully design coaxial coil systems that generate fields whose relative inhomogeneity in a 25 mm-long central region is ∼10−6 under constraints. In addition, for experiments, a coil system with 0.069% inhomogeneity of the field, designed by a machine learner, is constructed, which is mainly limited by machining the precision of the circuit board. Benefitting from machine learning's high-dimension optimization capabilities, our coil design method is convenient and has potential for various quantum experiments. [ABSTRACT FROM AUTHOR]

Although the theory of density evolution in maps and ordinary differential equations is well developed, the situation is far from satisfactory in continuous time systems with delay. This paper reviews some of the work that has been done numerically, the interesting dynamics that have emerged, and the largely unsuccessful attempts that have been made to analytically treat the evolution of densities in differential delay equations. We also present a new approach to the problem and illustrate it with a simple example. [ABSTRACT FROM AUTHOR]

An error criterion is essential in the process of parameter extraction of photovoltaic (PV) modules by fitting I–V curves, which exerts a huge influence on the accuracy of the extracted parameters. This paper proposes a new integrated current–voltage error criterion, named EC-I&V(x), which takes into account the intrinsic I–V properties of the PV module. The deviation in both current and voltage is considered by combining the mean squared error of the current and voltage in different data regions. Four optimization methods are used to validate the proposed error criterion, including guaranteed convergence particle swarm optimization, differential evolution, shuffled complex evolution, and an artificial bee colony algorithm. Different methods with the proposed error criterion are applied to synthetic I–V curves with variable error levels and measured I–V data under different operating conditions. Comparing with the traditional current based error criterion, more accurate results are obtained by using the proposed EC-I&V(x) at different error levels for different optimization methods. The proposed EC-I&V(x) not only improves the accuracy of each extracted parameter but also improves the accuracy of the estimated I–V property near maximum power points. [ABSTRACT FROM AUTHOR]

A differential evolution (DE) global optimization method for all-electron orbital-free density functional theory (OF-DFT) is presented. This optimization method does not need information about function derivatives to find extreme solutions. Results for a series of known orbital-free energy functionals are presented. Ground state energies of atoms (H to Ar) are obtained by direct minimization of the energy functional without using either Lagrange multipliers or damping procedures for reaching convergence. Our results are in agreement with previous OF-DFT calculations obtained using the standard Newton–Raphson and trust region methods. Being a zero-order method, the DE method can be applied to optimization problems dealing with non-differentiable functionals or functionals with non-closed forms. [ABSTRACT FROM AUTHOR]

Obtaining the temporal shape of an ultrashort laser pulse using the method of dispersion scan entails solving a nonlinear inverse problem, a challenging prospect on its own, yet still aggravated when the pulse shape being measured is temporally varying from pulse to pulse. For this purpose, we use a Differential Evolution (DE) algorithm enhanced by three different regularization methods. The DE algorithm in its standard form is insufficient for reconstructing the pulse in the case of unstable pulse trains. By modifying it to retrieve two independent functions and with the help of regularization, we were able to show that it is possible to simultaneously infer the average length and the coherence length of the pulses. The latter is the shortest pulse the laser source can produce. We also discuss the three different approaches for regularization used in this paper, and from the numerical results we present, we can conclude that a spline-based regularization method is far superior compared to the two other methods under investigation. [ABSTRACT FROM AUTHOR]

To improve the accuracy of short-term load forecasting, a differential evolution algorithm (DE) based least squares support vector regression (LSSVR) method is proposed in this paper. Through optimizing the regularization parameter and kernel parameter of the LSSVR by DE, a short-term load forecasting model which can take load affected factors such as meteorology, weather, and date types into account is built. The proposed LSSVR method is proved by implementing short-term load forecasting on the real historical data of Yangquan power system in China. The average forecasting error is less than 1.6%, which shows better accuracy and stability than the traditional LSSVR and Support vector regression. The result of implementation of short-term load forecasting demonstrates that the hybrid model can be used in the short-term forecasting of the power system more efficiently [ABSTRACT FROM AUTHOR]

For wideband receiver systems, it is challenging to compensate the in-phase/quadrature (I/Q) phase mismatch by traditional methods, especially with a time delay deviation (TDD) between the I/Q channels. Considering the above situation, this paper proposes a full-scale I/Q phase imbalance model concerning TDD. The model divides phase mismatch into two parts, i.e., the linear phase (LP) part and the nonlinear phase part, and compensates each part with the corresponding compensation module separately. The design strategy of the compensation module is innovatively transformed into a constrained nonlinear optimization problem, and a metaheuristic algorithm, the flower pollination algorithm (FPA), is utilized to be the optimizer. The results of the contrast simulation with the LP elimination method show the efficiency of the proposed method. In addition, the superiority of the FPA-based structure is verified by comparing with other metaheuristic algorithms, the artificial bee colony technique, the bat algorithm, and the differential evolution algorithm, in terms of the compensation accuracy, algorithm stability, runtime consumption, and convergence performance. Ultimately, the image rejection ratio improvement on the actual platform after compensation is measured, which validates the proposed compensation structure and the corresponding optimization method practically, and the FPA is still the best choice among the competent optimizers. [ABSTRACT FROM AUTHOR]

Ramp-wave dynamic-compression experiments are used to examine quasi-isentropic loading paths in materials. The gradual and continuous increase in pressure created by ramp waves make these types of experiments ideal for studying nonequilibrium material behavior, such as solidification kinetics. In ramp-wave compression experiments, the input drive pressure to the experimental setup may be exerted through one of a number of different mechanisms (e.g., magnetic fields, gas-gun-driven impactors, or high-energy lasers) and is generally required for simulating such experiments. Yet, regardless of the specific mechanism, this drive pressure cannot be measured directly (measurements are generally taken at a location near the back of the experimental setup through a transparent window), leading to an inverse problem where one must determine the drive pressure at the front of the experimental setup (i.e., the input) that corresponds to the particle velocity (the output) measured near the back of the experimental setup. We solve this inverse problem using a heuristic optimization algorithm, known as differential evolution, coupled with a multiphysics, hydrodynamics code that simulates the compression of the experimental setup. By running many rounds of forward simulations of the experimental setup, our optimization process iteratively searches for a drive pressure that is optimized to closely reproduce the experimentally measured particle velocity near the back of the experimental setup. While our optimization methodology requires a significant number of hydrodynamics simulations to be conducted, many of these can be performed in parallel, which greatly reduces the time cost of our methodology. One novel aspect of our method for determining the drive pressure is that it does not require physical modeling of the drive mechanism and can thus be broadly applied to many types of ramp-compression experiments, regardless of the drive mechanism. [ABSTRACT FROM AUTHOR]

Machine learning is becoming a more and more versatile tool describing condensed matter systems. Here, we employ the feed-forward and the convolutional neural networks to describe the frequency shifts of the amide I mode vibration of N-methylacetamide (NMA) in water. For a given dataset of configurations of an NMA molecule solvated by water, we obtained comparable or improved results for describing vibrational solvatochromic frequency shift with the neural network approach, compared to the previously developed differential evolution algorithm approach. We compared the performance of the atom centered symmetry functions (ACSFs) and simple polynomial functions as descriptors for the solvated system and found that the polynomial function performs better than the ACSFs employed in the description of the amide I vibrational solvatochromism. [ABSTRACT FROM AUTHOR]

We model the solvation-induced vibrational frequency shifts of the amide I and amide II modes of N-methylacetamide in water and the nitrile stretch mode of acetonitrile in water by expressing the frequency shift as a polynomial function expanded by the inverse power of interatomic distances. The coefficients of the polynomial are optimized to minimize the deviation between the predicted frequency shifts and those calculated with quantum chemistry methods. Here, we show that a differential evolution algorithm combined with singular value decomposition is useful to find the optimum set of coefficients of polynomial terms. The differential evolution optimization shows that only a few terms in the polynomial are dominant in the contribution to the vibrational frequency shifts. We anticipate that the present work paves the way for further developing different genetic algorithms and machine learning schemes for their applications to vibrational spectroscopic studies. [ABSTRACT FROM AUTHOR]

The assembly error of flexible joints and the change in joint stiffness during movement make the actual value of joint parameters inconsistent with the given value, which affects the joint control accuracy. In order to suppress the influence of parameters error, a parameters identification method for flexible joint combined offline identification and online compensation is proposed. First, the offline identification model of inertia, mass, and damping and the online identification model of joint stiffness are established, respectively. Then, a hybrid tracking differentiator based on an improved Sigmoid function is designed to track the differential signals of joint motion parameters, and the Lyapunov function is designed to prove its convergence. The adaptive differential evolution is used as the identification algorithm, and the improved adaptive crossover, mutation factor, and Metropolis acceptance criterion are designed to improve the convergence speed. Finally, a feedforward control structure based on identification is designed to compensate for the model deviation. Simulation and experimental results show that the improved differentiator can effectively improve the tracking speed and derivation accuracy of the signals. Compared with other algorithms, the proposed identification method has a faster convergence speed and higher identification accuracy, and feedforward compensation control can effectively correct model parameters and improve control accuracy. [ABSTRACT FROM AUTHOR]

When designing sound packages, often fully filling the available space with acoustic materials is not the most absorbing solution. Better solutions can be obtained by creating cavities of air pockets, but determining the most optimal shape and topology that maximises sound absorption is a computationally challenging task. Many recent topology optimisation applications in acoustics use heuristic methods such as solid-isotropic-material-with-penalisation (SIMP) to quickly find near-optimal solutions. This study investigates seven heuristic and metaheuristic optimisation approaches including SIMP applied to topology optimisation of acoustic porous materials for absorption maximisation. The approaches tested are hill climbing, constructive heuristics, SIMP, genetic algorithm, tabu search, covariance-matrix-adaptation evolution strategy (CMA-ES), and differential evolution. All the algorithms are tested on seven benchmark problems varying in material properties, target frequencies, and dimensions. The empirical results show that hill climbing, constructive heuristics, and a discrete variant of CMA-ES outperform the other algorithms in terms of the average quality of solutions over the different problem instances. Though gradient-based SIMP algorithms converge to local optima in some problem instances, they are computationally more efficient. One of the general lessons is that different strategies explore different regions of the search space producing unique sets of solutions. [ABSTRACT FROM AUTHOR]

Proton imaging is a powerful technique for imaging electromagnetic fields within an experimental volume, in which spatial variations in proton fluence are a result of deflections to proton trajectories due to interaction with the fields. When deflections are large, proton trajectories can overlap, and this nonlinearity creates regions of greatly increased proton fluence on the image, known as caustics. The formation of caustics has been a persistent barrier to reconstructing the underlying fields from proton images. We have developed a new method for reconstructing the path-integrated magnetic fields, which begins to address the problem posed by caustics. Our method uses multiple proton images of the same object, each image at a different energy, to fill in the information gaps and provide some uniqueness when reconstructing caustic features. We use a differential evolution algorithm to iteratively estimate the underlying deflection function, which accurately reproduces the observed proton fluence at multiple proton energies simultaneously. We test this reconstruction method using synthetic proton images generated for three different, cylindrically symmetric field geometries at various field amplitudes and levels of proton statistics and present reconstruction results from a set of experimental images. The method we propose requires no assumption of deflection linearity and can reliably solve for fields underlying linear, nonlinear, and caustic proton image features for the selected geometries and is shown to be fairly robust to noise in the input proton intensity. [ABSTRACT FROM AUTHOR]

Weakly coupled limit cycle oscillators can be reduced into a system of weakly coupled phase models. These phase models are helpful to analyze the synchronization phenomena. For example, a phase model of two oscillators has a one-dimensional differential equation for the evolution of the phase difference. The existence of fixed points determines frequency-locking solutions. By treating each oscillator as a black-box possessing a single input and a single output, one can investigate various control algorithms to change the synchronization of the oscillators. In particular, we are interested in a delayed feedback control algorithm. Application of this algorithm to the oscillators after a subsequent phase reduction should give the same phase model as in the control-free case, but with a rescaled coupling strength. The conventional delayed feedback control is limited to the change of magnitude but does not allow the change of sign of the coupling strength. In this work, we present a modification of the delayed feedback algorithm supplemented by an additional unstable degree of freedom, which is able to change the sign of the coupling strength. Various numerical calculations performed with Landau–Stuart and FitzHugh–Nagumo oscillators show successful switching between an in-phase and anti-phase synchronization using the provided control algorithm. Additionally, we show that the control force becomes non-invasive if our objective is stabilization of an unstable phase difference for two coupled oscillators. [ABSTRACT FROM AUTHOR]

A novel algorithm for the ultrashort laser pulse characterization method of interferometric frequencyresolved optical gating (iFROG) is presented. Based on a genetic method, namely, differential evolution, the algorithm can exploit all available information of an iFROG measurement to retrieve the complex electric field of a pulse. The retrieval is subjected to a series of numerical tests to prove the robustness of the algorithm against experimental artifacts and noise. These tests show that the integrated error-correction mechanisms of the iFROG method can be successfully used to remove the effect from timing errors and spectrally varying efficiency in the detection. Moreover, the accuracy and noise resilience of the new algorithm are shown to outperform retrieval based on the generalized projections algorithm, which is widely used as the standard method in FROG retrieval. The differential evolution algorithm is further validated with experimental data, measured with unamplified three-cycle pulses from a mode-locked Ti:sapphire laser. Additionally introducing group delay dispersion in the beam path, the retrieval results show excellent agreement with independent measurements with a commercial pulse measurement device based on spectral phase interferometry for direct electric-field retrieval. Further experimental tests with strongly attenuated pulses indicate resilience of differential-evolution-based retrieval against massive measurement noise. [ABSTRACT FROM AUTHOR]

Conventional beamforming with a microphone array is a well-established method for localizing and quantifying sound sources. It provides estimates for the source strengths on a predefined grid by determining the agreement between the pressures measured and those modeled for a source located at the grid point under consideration. As such, conventional beamforming can be seen as an exhaustive search for those locations that provide a maximum match between measured and modeled pressures. In this contribution, the authors propose to, instead of the exhaustive search, use an efficient global optimization method to search for the source locations that maximize the agreement between model and measurement. Advantages are two-fold. First, the efficient optimization allows for inclusion of more unknowns, such as the source position in three-dimensional or environmental parameters such as the speed of sound. Second, the model for the received pressure field can be readily adapted to reflect, for example, the presence of more sound sources or environmental parameters that affect the received signals. For the work considered, the global optimization method, Differential Evolution, is selected. Results with simulated and experimental data show that sources can be accurately identified, including the distance from the source to the array. [ABSTRACT FROM AUTHOR]