Initial Guess Research Articles

Rapid cooperative optimization of continuous trajectory for electric sails in multiple formation reconstruction scenarios

In satellite formation missions, conventional low-thrust spacecraft need to continuously consume fuel to maintain a stable formation configuration, which limits the mission period. The electric sail is more conducive to long-term scenarios and multiple formation reconstruction due to its propellant-free characteristic. However, electric sails rely on the solar wind to adjust attitude, which results in a slower control. Therefore, the propulsive acceleration of the electric sail is required to be continuous. Besides, a fast and reasonable initial guess is necessary for accurate design methods such as direct and indirect methods in complex formation missions. Accordingly, the rapid optimization of continuous cooperative trajectory of electric sails in multiple formation reconstruction scenarios with the integrative Bezier shaping approach (IBSA) was implemented in this study. Multiple deputy electric sails arrived at multiple determined positions relative to the chief electric sail at the same time and avoided collisions through distance constraints during multiple formation reconstructions. During multiple reconstructions of the formation, the velocity and acceleration of deputy electric sails are constrained to be continuous. In the proposed method, the relative motion is described without simplified steps, which is more suitable for general elliptic orbits. For electric sail formation, the analytical state and analytical acceleration based on the IBSA are derived. Additionally, in the IBSA, the relationship between Bezier coefficients and relative states replaces the boundary constraints and intermediate constraints of the proposed NLP problem, which can greatly improve the solution efficiency. However, in this paper, IBSA not only represents the multi-segment trajectory optimization problem as an overall optimization problem, but also considers multiple electric sails at the same time. To verify the rapidity and accuracy of the proposed method, numerous numerical simulations were carried out on the electric sail formation. Compared with traditional BSA, the IBSA can get better overall index in a shorter computing time. Taking the result of IBSA as the initial value, the Gauss pseudospectral method (GPM) can further optimize the cooperative trajectories and converge to a better result. Through the comparison of the results, it is found that the overall index of the IBSA is only 16.81% different from the GPM but the calculation time is only 0.28% of the GPM, which is of great significance for the design of multiple formation reconstruction missions with long period.

A stable and effective calibration method for defocused cameras using synthetic speckle patterns

Well-focused and sharp target images are essential in traditional calibration, but they generally cause difficulty and inconvenience in image acquisition in practical applications. To address this problem, a stable and effective calibration method for defocused cameras is proposed in this study. Firstly, two speckle patterns are created, one of which has control points to estimate the initial value while the other, used for point pair match registration, is without control points. They are subsequently displayed on a fixed monitor and captured at each camera pose. Secondly, the initial guess for the control points is estimated using the proposed method. The retrieval of query points can then be done with high accuracy using the digital image correlation algorithm. Finally, all the calibration parameters, including lens distortion, are calculated using the plane calibration algorithm. The experiment in this study demonstrates the practicality and effectiveness of the proposed method. The accuracy and precision were quantitatively evaluated by the mean reprojection error, which was 0.057 pixels.

Low-thrust station-keeping towards exploiting the inclined geosynchronous dynamics

Small satellite constellations in Inclined Geosynchronous Orbits (IGSO) provide an alternative to the increasingly crowded Geostationary Orbit belt. Satellite platforms equipped with full-electric propulsion systems are of great capacity for the advantages of significant propellant saving. This work focuses on the IGSO constellation design and its low-thrust station-keeping strategies. An analytical dynamical model based on a triple-averaged Hamiltonian formulation with respect to the ecliptic plane is first applied for a preliminary selection of the frozen orbits, which can serve as the baseline orbit for the whole constellation. Afterwards, the impact of the inclination on the manifolds in the eccentricity vector space is analyzed and the station-keeping slot for IGSO satellites is defined. Then, the low-thrust arc is designed to make the drifting arc closed, which maximize the long-term behaviors due to the resonances. Moreover, by feeding a three-impulse solution to the initial costate guess, an efficient solver to guarantee the convergence of the indirect optimization is proposed. Finally, the efficiency of the constellation design approach and the low-thrust SK strategy are validated via numerical simulations.

Minimum-fuel low-thrust trajectories to the Moon

An approach to solve the problem of optimizing multi-revolution thrust limited trajectories with constant exhaust velocity between the Earth orbit and the orbit around the Moon is considered. An indirect approach is used to solve the lunar trajectory optimization problem, based on the application of the Pontryagin's maximum principle and continuation method. At all segments of the trajectory, the gravities of the Earth, the Moon and the Sun are taken into account. The trajectory to the Moon is divided into geocentric and selenocentric segments, which are connected at the libration point EML1 of the Earth-Moon system. To ensure the choice of the optimal relation between the angular distance and the transfer duration of each segment, the problem of optimizing the trajectory with a fixed angular distance and free time of flight is considered. Solving a sequence of optimization problems for the limited power trajectory, the minimum-thrust trajectory and the minimum-fuel trajectory avoids the need to choose an initial guess for unknown initial costate variables. The numerical examples of optimizing the multi-revolution low-thrust transfers from the highly elliptical orbit around the Earth to the circular orbit around the Moon are given.

Designing Globally Time-Optimal Entangling Gates Using Geometric Space Curves

High-fidelity entangling gates are essential for quantum computation. Currently, most approaches to designing such gates are based either on simple, analytical pulse waveforms or on ones obtained from numerical optimization techniques. In both cases, it is typically not possible to obtain a global understanding of the space of waveforms that generate a target gate operation, which can make it challenging to identify globally time-optimal waveforms that respect amplitude and bandwidth constraints. Here, we show that in the case of weakly coupled qubits, it is possible to find all pulses that implement a target entangling gate in near-minimal time. We do this by mapping quantum evolution onto geometric space curves. We derive the minimal conditions these curves must satisfy in order to guarantee a gate with a desired entangling power is implemented. Pulse waveforms are extracted from the curvatures of these curves. We illustrate our method by designing fast, cnot-equivalent entangling gates for silicon quantum dot spin qubits with fidelities exceeding 99 %. We show that fidelities can be further improved while maintaining low bandwidth requirements by using geometrically derived pulses as initial guesses in numerical optimization routines.

Meta-GGA Density Functional Calculations on Atoms with Spherically Symmetric Densities in the Finite Element Formalism.

Density functional calculations on atoms are often used for determining accurate initial guesses as well as generating various types of pseudopotential approximations and efficient atomic-orbital basis sets for polyatomic calculations. To reach the best accuracy for these purposes, the atomic calculations should employ the same density functional as the polyatomic calculation. Atomic density functional calculations are typically carried out employing spherically symmetric densities, corresponding to the use of fractional orbital occupations. We have described their implementation for density functional approximations (DFAs) belonging to the local density approximation (LDA) and generalized gradient approximation (GGA) levels of theory as well as Hartree-Fock (HF) and range-separated exact exchange [Lehtola, S. Phys. Rev. A 2020, 101, 012516]. In this work, we describe the extension to meta-GGA functionals using the generalized Kohn-Sham scheme, in which the energy is minimized with respect to the orbitals, which in turn are expanded in the finite element formalism with high-order numerical basis functions. Furnished with the new implementation, we continue our recent work on the numerical well-behavedness of recent meta-GGA functionals [Lehtola, S.; Marques, M. A. L. J. Chem. Phys. 2022, 157, 174114]. We pursue complete basis set (CBS) limit energies for recent density functionals and find many to be ill-behaved for the Li and Na atoms. We report basis set truncation errors (BSTEs) of some commonly used Gaussian basis sets for these density functionals and find the BSTEs to be strongly functional dependent. We also discuss the importance of density thresholding in DFAs and find that all of the functionals studied in this work yield total energies converged to 0.1 μEh when densities smaller than 10-11a0-3 are screened out.

A high-order deferred correction method for the solution of free boundary problems using penalty iteration, with an application to American option pricing

This paper presents a high-order deferred correction algorithm combined with penalty iteration for solving free and moving boundary problems, using a fourth-order finite difference method. Typically, when free boundary problems are solved on a fixed computational grid, the order of the solution is low due to the discontinuity in the solution at the free boundary, even if a high-order method is used. Using a detailed error analysis, we observe that the order of convergence of the solution can be increased to fourth-order by solving successively corrected finite difference systems, where the corrections are derived from the previously computed lower order solutions. The corrections are applied solely to the right-hand side, and leave the finite difference matrix unchanged. The penalty iterations converge quickly given a good initial guess. We demonstrate the accuracy and efficiency of our algorithm using several examples. Numerical results show that our algorithm gives fourth-order convergence for both the solution and the free boundary location. We also test our algorithm on the challenging American put option pricing problem. Our algorithm gives the expected high-order convergence.

Identification and validation of constitutive parameters of a Hencky-type discrete model via experiments on millimetric pantographic unit cells

Pantographic metamaterial design benefits from model identification procedures starting from what can be considered as the elementary unit cell of larger pantographic structures. Results from a tensile experiment and digital image correlation are utilized to identify the constitutive parameters of a discrete Hencky-type model for a millimetric pantographic cell. In the performed calibration, two different cost functions are formulated. First, the cost function is based upon measured resultant forces on the specimen boundaries. Then, the second cost function is based upon the measured pivot displacements in addition to reaction forces. The second cost functions thus exploits the pivot kinematics, which is a key feature of the deformation of pantographic structures. The identified model is further validated by predicting the reaction forces and pivot displacements of the same specimen subjected to compression. It is shown that the identification with the cost function incorporating pivot displacements is superior. It is also noted that the calibrated parameters deviate considerably from their initial guess derived from the linear Saint Venant problem, thereby indicating microscale nonlinear affects in otherwise linear reaction force-prescribed displacement responses at the macroscale.

Theoretical investigation of Aryl/Alkyl halide reduction with hydrated electrons from energy and AIMD aspects.

In this study, the reactions of hydrated electron (e-(aq)) with alkyl and aryl halides were simulated with an ab initial molecular dynamics (AIMD) method to reveal the underlying mechanism. An original protocol was developed for preparing the proper initial wavefunction guess of AIMD, in which a single electron was curled in a tetrahedral cavity of four water molecules. Our results show that the stability of e-(aq) increases with the hydrogen bond grid integrity. The organic halides prefer to react with e-(aq) in neutral or alkaline environment, while they are more likely to react with hydrogen radical (the product of e-(aq) and proton) under acidic conditions. The reaction between fluorobenzene/fluoromethane and hydrogen radical is considered as the least favorable reaction due to the highest reaction barriers. The bond dissociation energy (BDE) suggested that the cleavage of the carbon-halogen bond of their anion radical might be a thermodynamically favorable reaction. AIMD results indicated that the LUMO or higher orbitals were the e-(aq) migration destination. The transplanted electron enhanced carbon-halogen bond vibration intensively, leading to bond cleavage. The solvation process of the departing halogen anions was observed in both fluorobenzene and fluoromethane AIMD simulation, indicating that it might have a significant effect on enthalpy. Side reactions and byproducts obtained during the AIMD simulation suggested the complexity of the e-(aq) reactions and further investigation was needed to fully understand the reaction mechanisms. This study provided theoretical insight into the pollutant environmental fate and constructed a methodological foundation for AIMD simulation of analogous free radical reactions. The theoretical calculation was conducted on the combination of Gaussian16 and ORCA5.0.3 software packages. The initial geometries, as well as the wavefunction initial guesses, were obtained at PBE0/ma-def2-TZVP/IEFPCM-water level in Gaussian16 unless otherwise stated. AIMD simulations were performed at the same level in ORCA. Wavefunction analysis was carried out with Multiwfn. The details methods were described in the section "Computational details" section.

Acoustic full waveform inversion for 2-D ambient noise source imaging

SUMMARYWe present a method for estimating seismic ambient noise sources by acoustic full waveform inversion (FWI) of interstation cross-correlations. The method is valid at local scales for laterally heterogeneous media, and ambient noise sources confined to the Earth’s surface. Synthetic tests performed using an actual field array geometry, are used to illustrate three unique aspects of our work. First: the method is able to recover noise sources of arbitrary spatial distribution, both within and outside the receiver array, with high fidelity. This holds true for complex velocity models and does not require a good initial guess for inversion, thereby addressing an outstanding issue in the existing research literature. Second: we analyse the extent of biases in source inversion that arise due to inaccurate velocity models. Our findings indicate that source inversion using simplified (e.g. homogeneous) velocity models may work reliably when lateral variations in velocity structure are limited to 5 or 10 per cent in magnitude, but is vitiated by strong variations of 20 per cent or higher, wherein the effect of strong scattering and/or phase distortions become significant. Finally, our technique is implemented without the adjoint method, which is usually inextricably linked to FWI. Inversions are performed using source kernels computed for each receiver pair, and this approach is computationally tractable for real-world problems with small aperture seismic arrays.

Інтервальна оцінка показників надійності за результатами випробувань компонентів складної системи

The goal of this work is to find the lower estimate of the no-failure probability (NFP) of a complex monotonic nonrecoverable system from the results of independent binomial tests of its components. Using the general-and-probabilistic method, the NFP is considered as a probability function polynomial, which is a linear homogeneous polynomial in each of the S variables where S is the number of system component types. Based on the method of confidence sets, the NFP lower estimate is found as the minimum of a function of an unknown multidimensional parameter at a probability of the aggregate test results (failure-free operation) of the system components equal to one minus the guaranteed confidence coefficient. The paper reports a system of equations, each of which for two component types relates the component reliability derivatives of the NFP (and one more equation relates the component reliability and the confidence coefficient). Conditions are found for the initial guess in a numerical solution of the above system of nonlinear equations (the number of the conditions is equal to the number of the component types minus one; each condition is a like sign for two functions each of which depends on the probability of the test results of a particular component type and the component reliability of this probability). In some specific cases, the program dimension can be reduced due to the simple structure of the probability function polynomial. The presented method gives a confidence reliability estimate with a guaranteed confidence coefficient for complex system that cannot be reduced to a serial-parallel or a parallel-serial structure and consist of components with an arbitrary type of failure time distribution. The method allows one to get an estimate at a small number of tests and a small number of failures or in their absence, which is of especial importance for high-reliability systems.

A GOOD INITIAL GUESS FOR APPROXIMATING NONLINEAR OSCILLATORS BY THE HOMOTOPY PERTURBATION METHOD

A good initial guess and an appropriate homotopy equation are two main factors in applications of the homotopy perturbation method. For a nonlinear oscillator, a cosine function is used in an initial guess. This article recommends a general approach to construction of the initial guess and the homotopy equation. Duffing oscillator is adopted as an example to elucidate the effectiveness of the method.

Geometric Analysis of Sun-Assisted Lunar Transfer Trajectories in the Planar Bicircular Four-Body Model

This research presents a geometric analysis of Sun-assisted low-energy lunar transfers and several convenient tools that enable the systematic trajectory design in the framework of the planar bicircular restricted four-body problem. By analogy with the patched conic approximation approach for high-energy transfers, a Sun-assisted low-energy trajectory is divided into three legs. Two interior legs, departing and arriving, are located inside the Earth–Moon region of prevalence and designed in the Earth–Moon circular restricted three-body problem, whereas the exterior leg lies outside the region of prevalence and is calculated in the Earth–Moon–Sun bicircular restricted four-body model. The whole trajectory is obtained by smoothly patching the three legs on the boundary of the region of prevalence. The arrival conditions are met by targeting a specific point in the L2 lunar gateway. The interior legs are easily adjustable to the four-body dynamics. The database of planar lunar transfer trajectories can be used to select an initial guess for the multiple-shooting procedure of designing a three-dimensional Sun-assisted lunar transfer in high-fidelity dynamical models.

A gradient based numerical algorithm to solve inverse dynamic viscoelastic problems of multi-variable identification

A gradient based numerical method is put forward to solve the inverse dynamic viscoelastic problem with multi-variable identification for the constitutive and TKBC (third kind boundary conditions) related parameters. A three parameter model is employed to describe the time dependent TKBC concerned with structural interaction, and is formulated in the forward and inverse dynamic viscoelastic analysis. In addition to the reliable platform provided by TPAA-SBFEM to gain the solution of forward problems, a piecewise recursive adaptive algorithm is developed to obtain the derivatives required in the sensitivity analysis, which is able to provide a stable temporal solution accuracy for different step sizes. SBFEM (Scaled Boundary Finite Element Method) is stressed in the structural analysis with its own advantages, such as the efficient and convenient treatment of stress singularity problem and flexibility of mesh generation with polygonal elements and image based quadtree gridding. The inverse problem of identification is solved by the Levenberg-Marquardt method, and the regional inhomogeneity, crack, initial guess, location/number of measurement points, material contrast ratios, and noisy data are taken into account. Numerical examples are provided to verify the proposed approach, and the satisfactory results are achieved.

Computer‐assisted synthetic planning considering reaction kinetics based on transition state automated generation method

AbstractOrganic synthesis facilitates the conversion of raw materials into high‐value chemicals. Computer‐assisted synthetic planning plays a vital role in designing synthetic pathways, which are usually evaluated by the reaction probability using deep learning models. However, this criterion is generally hard to describe real reaction behaviors such as reaction kinetics. Therefore, this article aims to establish a reaction kinetics‐based retrosynthesis planning framework to design synthetic pathways with well‐performed reaction kinetics. The key contribution of this work is developing a method for the GENeration of initial guesses of Transition States based on Reactive Sites (GENiniTS‐RS) to automatically and fast generate the initial guesses of transition states for the transition state theory‐based reaction kinetic model without sampling the minimum energy path from reactants to products. Finally, two case studies involving the design of synthetic pathways for aspirin and ibuprofen are presented to demonstrate the feasibility and effectiveness of the proposed framework.

Prediction of pore-scale flow in heterogeneous porous media from periodic structures using deep learning

Data-driven deep learning models are emerging as a promising method for characterizing pore-scale flow through complex porous media while requiring minimal computational power. However, previous models often require extensive computation to simulate flow through synthetic porous media for use as training data. We propose a convolutional neural network trained solely on periodic unit cells to predict pore-scale velocity fields of complex heterogeneous porous media from binary images without the need for further image processing. Our model is trained using a range of simple and complex unit cells that can be obtained analytically or numerically at a low computational cost. Our results show that the model accurately predicts the permeability and pore-scale flow characteristics of synthetic porous media and real reticulated foams. We significantly improve the convergence of numerical simulations by using the predictions from our model as initial guesses. Our approach addresses the limitations of previous models and improves computational efficiency, enabling the rigorous characterization of large batches of complex heterogeneous porous media for a variety of engineering applications.

Kinetostatic Modeling of Tendon-Driven Parallel Continuum Robots

Tendon-driven parallel continuum robots (PCR) consist of multiple individual continuous kinematic chains, that are actuated in bending utilizing tendons routed along their backbones. This work derives and proposes a Cosserat rod based kinetostatic modeling framework for such parallel structures that allows for efficiently solving the forward, inverse and velocity kinetostatic problems. Using this model, the kinematic properties such as reachable workspace, singularities, manipulability, and compliance of tendon-driven PCR are studied in detail. Experiments are conducted using a real robotic prototype to validate the derived modeling approach. Overall, a median pose accuracy of 4.9 mm, corresponding to 3.4% of the continuum robots' lengths, and 6.2 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\circ$</tex-math></inline-formula> is achieved. The median of the model's computation time results in 0.51 s on standard computing hardware. Fast computations of below 100 ms can be achieved, if an appropriate initial guess for solving the kinetostatic model is available, making the model suitable for a range of different applications including optimization or control.

Boundary-value-problem examination of the stability of a symmetrical rotor partially filled with a viscous incompressible fluid

Instabilities in a rotor system partially filled with a fluid can have an exponentially increasing amplitude, and this can cause catastrophic damage. Numerous theoretical models have been proposed, and numerous experiments have been conducted to investigate the mechanisms of this phenomenon. However, the explanation of the existence of the first unstable region induced by a viscous incompressible fluid is unclear, and only one solving method, a standard finite difference procedure, was proposed in 1991 for solving the instabilities in a system containing a symmetric rotor partially filled with a viscous incompressible fluid. To better understand the mechanisms of the instability induced by the viscous fluid, based on the linearized two-dimensional Navier–Stokes equations, this system's differential equations are transferred to solve the characteristic equations with boundary conditions. A Matlab boundary value problem (BVP) solver bvp5c proposed in 2008 is an efficient tool to solve this problem by uncoupling the boundary conditions with unknown initial guess. Applying this approach to a rotor system allows the instability regions to be obtained. In this study, first, the radial and tangential velocities and pressure fluctuations along the radial direction of a disk filled with fluid were examined. Then, parametric analysis of the effect of the Reynolds number R e c r, filling ratio H, damping ratio C, and mass ratio m on the system's stability was conducted. Using this calculation method allowed the first exploration of some new laws regarding the instabilities. These results will benefit the further understanding of the existence of the first unstable region of a rotor partially filled with a viscous incompressible fluid.

Parsimonious physics-informed random projection neural networks for initial value problems of ODEs and index-1 DAEs.

We present a numerical method based on random projections with Gaussian kernels and physics-informed neural networks for the numerical solution of initial value problems (IVPs) of nonlinear stiff ordinary differential equations (ODEs) and index-1 differential algebraic equations (DAEs), which may also arise from spatial discretization of partial differential equations (PDEs). The internal weights are fixed to ones while the unknown weights between the hidden and output layer are computed with Newton's iterations using the Moore-Penrose pseudo-inverse for low to medium scale and sparse QR decomposition with L 2 regularization for medium- to large-scale systems. Building on previous works on random projections, we also prove its approximation accuracy. To deal with stiffness and sharp gradients, we propose an adaptive step-size scheme and address a continuation method for providing good initial guesses for Newton iterations. The "optimal" bounds of the uniform distribution from which the values of the shape parameters of the Gaussian kernels are sampled and the number of basis functions are "parsimoniously" chosen based on bias-variance trade-off decomposition. To assess the performance of the scheme in terms of both numerical approximation accuracy and computational cost, we used eight benchmark problems (three index-1 DAEs problems, and five stiff ODEs problems including the Hindmarsh-Rose neuronal model of chaotic dynamics and the Allen-Cahn phase-field PDE). The efficiency of the scheme was compared against two stiff ODEs/DAEs solvers, namely, ode15s and ode23t solvers of the MATLAB ODE suite as well as against deep learning as implemented in the DeepXDE library for scientific machine learning and physics-informed learning for the solution of the Lotka-Volterra ODEs included in the demos of the library. A software/toolbox in Matlab (that we call RanDiffNet) with demos is also provided.

Sharing Traffic Priorities via Cyber–Physical–Social Intelligence: A Lane-Free Autonomous Intersection Management Method in Metaverse

Replacing traffic signals with roadside vehicle-to-infrastructure systems in the era of connected and autonomous vehicles (CAVs) is promising. Managing CAVs in a signal-free intersection, known as autonomous intersection management (AIM), controls the driving behavior of each intersection-traverse CAV to maximize the throughput. Although AIM improves the gross throughput, the fairness of each individual vehicle in its right of way is not seriously considered. This study sets up an AIM system in the cyber–physical–social space to trade traverse priorities quantitatively and fairly. To that end, one needs an AIM method that is optimal and stable, otherwise no convincing trades of traverse priorities could be made. This study proposes a near-optimal lane-free AIM method based on numerical optimal control, wherein log-exp functions are deployed to convexify nondifferentiable collision-avoidance constraints. Besides that, a parameterized social force model (SFM) is proposed to provide a tunable initial guess for numerical optimal control. By tuning the urgency weights in SFM, one may get cooperative trajectories in different homotopy classes, which are further utilized to decide the amount of virtual currency to reward those CAVs who tend to share their traverse priorities. The overall method improves the traverse throughput with individual fairness respected. In experiencing this system, passengers learn how to behave with politeness when they drive manually. Experiments show the efficiency and robustness of the AIM method and also show the efficacy of the overall priority-sharing system.