Adaptive Step Research Articles

Adaptive time step selection for spectral deferred correction

AbstractSpectral Deferred Correction (SDC) is an iterative method for the numerical solution of ordinary differential equations. It works by refining the numerical solution for an initial value problem by approximately solving differential equations for the error, and can be interpreted as a preconditioned fixed-point iteration for solving the fully implicit collocation problem. We adopt techniques from embedded Runge-Kutta Methods (RKM) to SDC in order to provide a mechanism for adaptive time step size selection and thus increase computational efficiency of SDC. We propose two SDC-specific estimates of the local error that are generic and do not rely on problem specific quantities. We demonstrate a gain in efficiency over standard SDC with fixed step size and compare efficiency favorably against state-of-the-art adaptive RKM.

Research on APF-Bi-RRT Algorithm of Adaptive Step Strategy for Robot Path Planning

Research on APF-Bi-RRT Algorithm of Adaptive Step Strategy for Robot Path Planning

A multi-strategy improved sparrow search algorithm for indoor AGV path planning

To address the problems of weak search ability, easily falling into local optimal solutions and poor path quality of sparrow search algorithm in AGV path planning, a multi-strategy improved sparrow search algorithm (MISSA) is proposed in this paper. MISSA improves the global search ability by improving the discoverer position update operator and introducing the sine cosine algorithm; adopts the adaptive number of vigilantes and adaptive adjustment step size to improve the convergence speed; introduces the Levy flight variation strategy to reduce the probability of falling into any local optimal solution; optimizes the boundary handling mechanism to prevent the loss of population diversity at a later stage; finally, uses the large-scale neighborhood search strategy and path smoothing mechanism for path optimization to further improve the path quality. The superiority-seeking ability of MISSA was verified by 12 standard test functions, and then 30 simulation experiments were conducted in grid maps with two specifications of 20×20 and 30×30. The experimental results showed that, by using MISSA, the path length was reduced by 44.1% and 63.1%, the number of turns was reduced by 68.4% and 78.4%, and the risk degree was reduced by 61.3% and 77.2%, which verifies the superiority of MISSA in path planning. Finally, MISSA was ported to the QBot2e mobile robot for physical verification to prove its feasibility in practical applications.

Robust variable step size least mean fourth with quotient form-based control scheme for DVR operation

ABSTRACT A robust variable step size least mean fourth with a quotient form control scheme (RVSSLMFQ) is implemented for addressing power quality concerns and delivering clean voltage to sensitive loads through a dynamic voltage restorer (DVR). This method estimates the fundamental components from distorted grid voltages, featuring an automated process with adaptive time-varying step sizes and utilizing a quotient structure to reduce mean squared error (MSE) effectively. The suggested control scheme overcomes the stability and performance issues of the least mean fourth (LMF) algorithm by improving convergence and adapting well to varying step sizes. Furthermore, RVSSLMFQ achieves remarkable results with reduced settling time and fewer peak overshoots compared to the least mean square (LMS) and LMF control algorithms. For tuning the load voltage and DC-link voltage proportional-integral (PI) controllers, the improved grey wolf optimization technique (I-GWO) is applied. The results are evaluated through MATLAB simulations.

Optimization of a Hydrogen-Fueled Parametric Strut Injector Using an Automated Workflow Computational Fluid Dynamics Method

Abstract A strut injector for burning hydrogen has been optimized using an automated workflow system. In order to choose the optimal set of injectors to cover the design space, an optimized design of experiments (DOE) method was used to automatically choose the parameters that best spanned the design space. One hundred candidate designs were chosen, and a script was used to generate a series of stereolithography (STL) files for each design. The STL files were then uploaded to a supercomputer for computational fluid dynamics analysis. For each of the 100 designs, a four step process was followed to generate the required data, and this included an automated mesh generation step, a field initialization step, a mesh adaptation step, and finally an large eddy simulation all within the yales2 numerical framework. In order to reduce the time required for postprocessing and the amount of data required, the simulations relied heavily on an on-the-fly postprocessing methodology, which reduced the complex time-unsteady flow fields to a small number of quantified outputs of interest that measured the suitability of each design such as the pressure drop across the injector and the efficiency of the mixing process. At the conclusion of these simulations, automated scripts translated these outputs into a smaller set of parameters that could be used to compare each design and allow subsequent optimization and surrogate modeling. Several surrogate modeling methods were attempted with mixed results; however, a simple classification methodology quickly identified the parameters of interest.

Simple and efficient step detection algorithm for foot-mounted IMU

Abstract This paper presents a concise, efficient, and adaptive step detection algorithm based on foot-mounted inertial measurement unit sensors. The proposed method maps the temporal values of pedestrian motion and gait diversity into two variables: the distance between peaks and valleys, and the slope. Compared to traditional sliding window methods, this approach amplifies the differences between normal and abnormal steps, allowing it to adapt to various indoor activities such as fast walking, slow walking, running, jogging, standing still, and turning. By incorporating adaptive factors, it addresses the challenge of detecting steps while going up and down stairs. The proposed algorithm overcomes the limitations of traditional adaptive threshold methods that require different temporal and peak thresholds for various gait conditions. By utilizing the significant differences in distance and slope, it effectively resolves the issue of detecting steps during stationary periods. Unlike neural network-based gait classifiers, this algorithm does not need to account for multiple gait conditions, thereby simplifying the training process. Experimental results demonstrate that the algorithm achieves an average accuracy of over 99% under mixed indoor walking conditions and over 98% accuracy in long-term outdoor walking conditions.

Performance Analysis and Parallel Scalability of Numerical Methods for Fractional-in-Space Diffusion Problems with Adaptive Time Stepping

We study numerical methods and algorithms for time-dependent fractional-in-space diffusion problems. The considered anomalous diffusion is modelled by the fractional Laplacian (−Δ)α, 0<α<1, following the integral definition. Fractional diffusion is non-local, and the finite element method (FEM) discretization in space leads to a dense stiffness matrix. It is well known that numerically solving such non-local boundary value problems is expensive. Difficulties increase significantly when the problem is time-dependent. The aim of the article is to develop computationally efficient methods and algorithms. There are two main features of our approach. Hierarchical semi-separable (HSS) compression is applied for an approximate solution of the arising linear systems. For time discretization, we use an adaptive forward–backward Euler scheme. The properties of the composite algorithm thus obtained are investigated. In particular, the block representation of HSS compression allowed us to upgrade the HSS solver to efficiently handle varying diagonally perturbed transition matrices corresponding to changing time steps. The contribution of the paper is threefold. The methods are completely constructive, which allows for a clearly structured description of the algorithms. A theoretical estimate of the computational complexity is presented. It shows the advantages of the adaptive time stepping in combination with the HSS solver. Theoretical results are supported by representative numerical experiments. Both sequential and parallel scalability and efficiency are analyzed. The presented results provide convincing proof of the concept of the proposed methods and algorithms.

Translation Efficiency Test Using Polysome Profiles Under Heat Stress.

Translational control of different genes under heat stress is a critical step for plant adaptation to the environment. Assessing the translational activities of various genes can help us understand the molecular mechanisms underlying plant resilience, contributing to the development of crops with enhanced stress tolerance in the face of global climate change. This paper presents a detailed methodology for assessing translation efficiency through polysome profiling in plants exposed to heat stress. The procedure is divided into three parts: heat stress treatment for Arabidopsis, translation efficiency test using polysome profiles, and calculation of translation efficiency by isolating non-polysomal and polysomal RNA based on the profile. In the first part, Arabidopsis plants are subjected to controlled heat stress conditions to mimic environmental challenges. The treatment involves exposing the plants to high temperatures for specified durations, ensuring consistent and reproducible stress induction. This step is crucial for studying the plant's physiological and molecular responses to heat stress. The second part involves the translation efficiency test using polysome profiling. Polysomes are extracted through sucrose gradient centrifugation, which separates mRNAs based on ribosomal loading. This allows for the examination of ribosome occupancy on mRNAs, providing insights into the translational control mechanisms under stress conditions. In the third part, RNA is isolated from both polysomal and non-polysomal fractions. Spike-in RNA is used to accurately measure the amount of RNA in each fraction. The calculation of translation efficiency is performed by comparing the distribution of mRNAs across these fractions under normal and heat stress conditions. The translation activities of specific genes are further assessed by performing quantitative real-time PCR (qRT-PCR) with ribosome-associated RNA and total RNA. This methodology focuses exclusively on the effects of heat stress, providing a detailed protocol for analyzing translational regulation in plants.

Investigating Transfer Learning in Noisy Environments: A Study of Predecessor and Successor Features in Spatial Learning Using a T-Maze.

In this study, we investigate the adaptability of artificial agents within a noisy T-maze that use Markov decision processes (MDPs) and successor feature (SF) and predecessor feature (PF) learning algorithms. Our focus is on quantifying how varying the hyperparameters, specifically the reward learning rate (αr) and the eligibility trace decay rate (λ), can enhance their adaptability. Adaptation is evaluated by analyzing the hyperparameters of cumulative reward, step length, adaptation rate, and adaptation step length and the relationships between them using Spearman's correlation tests and linear regression. Our findings reveal that an αr of 0.9 consistently yields superior adaptation across all metrics at a noise level of 0.05. However, the optimal setting for λ varies by metric and context. In discussing these results, we emphasize the critical role of hyperparameter optimization in refining the performance and transfer learning efficacy of learning algorithms. This research advances our understanding of the functionality of PF and SF algorithms, particularly in navigating the inherent uncertainty of transfer learning tasks. By offering insights into the optimal hyperparameter configurations, this study contributes to the development of more adaptive and robust learning algorithms, paving the way for future explorations in artificial intelligence and neuroscience.

A novel hybrid GMPPT method for PV systems to mitigate power oscillations and partial shading detection

The Maximum Power Point Tracking (MPPT) algorithm plays a crucial role in maximizing the power output of a PV system. While uniform shading conditions (USCs) present challenges related to dynamic changes in irradiance, partial shading conditions (PSCs) introduce the complexity of multiple local maxima and rapidly changing shading patterns. Conventional algorithms often struggle to effectively track the global maximum power point (GMPP) during PSCs leading to power losses and oscillations around the MPP. In contrast, advanced algorithms are more complex and require additional computational time causing the algorithm to unnecessarily scan the entire PV curve during USCs, thereby extending the tracking time. This paper proposes a hybrid approach that combines the Modified Perturb and Observe (MP&O) and Modified Coot Optimization Algorithm (MCOA) methods termed as MP&O-MCOA as a robust real time MPPT algorithm. The MP&O method with trapezoidal rule and adaptive step size is employed under USCs, while the MCOA with only one tuning parameter and fewer random numbers is utilized during PSCs to rapidly identify varying conditions. Experimental validation using a boost converter has demonstrated the effectiveness of the proposed method, achieving the fastest average tracking times of 0.24 s under USCs and 0.73 s under PSCs and highest average tracking accuracy above 99 % for all operating conditions tested. The proposed method has proven to outperform other existing MPPT methods under various weather conditions due to its ability to distinguish between USCs and PSCs at exceptional speed and accuracy.

A Numerical Integrator for Kinetostatic Folding of Protein Molecules Modeled as Robots with Hyper Degrees of Freedom

The kinetostatic compliance method (KCM) models protein molecules as nanomechanisms consisting of numerous rigid peptide plane linkages. These linkages articulate with respect to each other through changes in the molecule dihedral angles, resulting in a kinematic mechanism with hyper degrees of freedom. Within the KCM framework, nonlinear interatomic forces drive protein folding by guiding the molecule’s dihedral angle vector towards its lowest energy state in a kinetostatic manner. This paper proposes a numerical integrator that is well suited to KCM-based protein folding and overcomes the limitations of traditional explicit Euler methods with fixed step size. Our proposed integration scheme is based on pseudo-transient continuation with an adaptive step size updating rule that can efficiently compute protein folding pathways, namely, the transient three-dimensional configurations of protein molecules during folding. Numerical simulations utilizing the KCM approach on protein backbones confirm the effectiveness of the proposed integrator.

Modelling of wall-bounded cavitating flow and spray mixing in multi-component environments using the PC-SAFT equation of state

This work introduces a numerical multiphase model for multi-component mixtures, utilizing tabulated data for physical and transport properties across a spectrum of conditions from near-vacuum pressures to supercritical states. The property data are derived using Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT), vapor-liquid equilibrium (VLE) calculations, entropy scaling methodologies, and Group Contribution (GC) methods. These techniques accurately reflect the thermodynamic behaviors of real fluids, avoiding the empirical estimation of Equation of State (EoS) input parameters. Implemented in OpenFOAM, the fluid dynamics solver is designed to address the three-dimensional Navier-Stokes equations for multi-component mixtures. The methodology integrates operator splitting to manage hyperbolic and parabolic steps distinctively. Hyperbolic terms are solved using the HLLC (Harten-Lax-van Leer-Contact) solver with temporal integration performed via a third-order Strong-Stability-Preserving Runge–Kutta (SSP-RK3) method. Viscous stress tensor contributions in the momentum equation are handled through an implicit velocity correction equation, while parabolic terms in the energy equation are explicitly solved. The simulation efficiency is further enhanced by adaptive Local Time Stepping and the Immersed Boundary (IB) method, which addresses interactions between the fluid and solid boundaries. Turbulence is resolved using the Wall Adaptive Large Eddy (WALE) model. Applied to high-pressure diesel fuel spray injections into non-reacting (nitrogen) gas environments, the model has been validated against Engine Combustion Network (ECN) data for the Spray-C configuration, featuring a fully cavitating multi-hole orifice. Results demonstrate that the model achieves accurate predictions across a broad range of tested conditions without the need for tuning or calibration parameters.

Suppression of cross-interference in the absorption spectra of gas mixtures

In the quantitative analysis of mixed gases by tunable diode laser absorption spectroscopy, the overlapping of absorption spectra and mutual interference of multi-component gases can lead to problems of large measurement errors and low analysis accuracy. In this paper, an improved firefly algorithm is proposed and applied to the support vector machine regression model to solve this problem. The specific method includes introducing an adaptive step size to balance the local and global searches and using the gradient descent method to accelerate the parameter optimization process so as to improve the model’s generalization ability and prediction accuracy. The experimental results show that the maximum errors of the improved algorithm in the prediction of CH4 and CO gas concentrations are no more than 0.0443 % and 2 ppm, with coefficients of determination, R2, of 0.9994 and 0.99815. The promising results obtained by the system provide theoretical support for the realization of high-precision detection of multicomponent gases with a single source of light, and also demonstrate the high efficiency and feasibility of the method in practical detection.

Painless Stochastic Conjugate Gradient for Large-Scale Machine Learning.

Conjugate gradient (CG), as an effective technique to speed up gradient descent algorithms, has shown great potential and has widely been used for large-scale machine-learning problems. However, CG and its variants have not been devised for the stochastic setting, which makes them extremely unstable, and even leads to divergence when using noisy gradients. This article develops a novel class of stable stochastic CG (SCG) algorithms with a faster convergence rate via the variance-reduced technique and an adaptive step size rule in the mini-batch setting. Actually, replacing the use of a line search in the CG-type approaches which is time-consuming, or even fails for SCG, this article considers using the random stabilized Barzilai-Borwein (RSBB) method to obtain an online step size. We rigorously analyze the convergence properties of the proposed algorithms and show that the proposed algorithms attain a linear convergence rate for both the strongly convex and nonconvex settings. Also, we show that the total complexity of the proposed algorithms matches that of modern stochastic optimization algorithms under different cases. Scores of numerical experiments on machine-learning problems demonstrate that the proposed algorithms outperform state-of-the-art stochastic optimization algorithms.

MCEND: an open-source program for quantum electron-nuclear dynamics

The software MCEND (Multi-Configuration Electron-Nuclear Dynamics) is a free open-source program package which simulates the quantum dynamics of electron-nuclei simultaneously for diatomic molecules. Its formulation, implementation, and usage are described in detail. MCEND uses a grid-based basis representation for the nuclei, and the electronic basis is derived from standard electronic structure basis sets on the nuclear grid. The wave function is represented as a sum over products of electronic and nuclear wave functions, thus capturing correlation effects between electrons, nuclei, and electrons and nuclei. The LiH molecule was used as an example for simulating the molecular properties such as the dipole moment and absorption spectrum. Program summaryProgram Title: MCEND, v.2.6.0CPC Library link to program files:https://doi.org/10.17632/tkb9dwf85t.1Developer's repository link:https://github.com/MCEND-hub/MCEND (https://github.com/MCEND-hub/MCEND-library and https://github.com/MCEND-hub/MCEND-tools are git submodules of MCEND)Licensing provisions: MITProgramming language: Fortran 90 and Python 3External routines/libraries: FFTW, OpenMP, BLAS, LAPACK, PSI4, Matplotlib, mendeleev, NumPy, Pandas, SciPy, PyTablesNature of problem: MCEND is to simulate the quantum dynamics of electrons and nuclei simultaneously at multiconfiguration levels.Solution method: The presented program package solves the time-dependent Schrödinger equation with the wave function represented as sum over configuration products using an 8th-order adaptive step size Runge-Kutta ordinary differential equation (ODE) solver. The software can be extended by supplementing modules on the existing infrastructure.

A numerical study of vortex nucleation in 2D rotating Bose–Einstein condensates

This article implements a numerical method for the minimization under constraints of a discrete energy modelling multicomponents rotating Bose–Einstein condensates in the regime of strong confinement and with rotation. Moreover, this method allows to consider both segregation and coexistence regimes between the components. The method includes a discretization of a continuous energy in space dimension 2 and a gradient algorithm with adaptive time step and projection for the minimization. It is well known that, depending on the regime, the minimizers may display different structures, sometimes with vorticity (from singly quantized vortices, to vortex sheets and giant holes). The goal of this paper is to study numerically the structures of the minimizers. In order to do so, we introduce a numerical algorithm for the computation of the indices of the vortices, as well as an algorithm for the computation of the indices of vortex sheets. Several computations are carried out, to illustrate the efficiency of the method, to cover different physical cases, to validate recent theoretical results as well as to support conjectures. Moreover, we compare this method with an alternative method from the literature.

Achieving an adaptive learner

This essay was invited upon the receipt of the American Psychological Association Division 15’s Career Achievement Award for Distinguished Psychological Contributions to Education in 2021. I propose that modern education should prepare students to continue learning so they can adapt to changing times, circumstances, and knowledge bases. A key step in adaptation is recognizing that there is something new. I review evidence from three sets of previous studies that show traditional instruction succeeds in helping students complete routine tasks but falls well short of preparing students to learn from new information and adapt it to novel situations. I try to understand these results from three levels of analysis: The overarching goals of instruction; the psychological assumptions underlying the instruction; and the in situ demands and natural responses of classroom learners. Given these analyses, I motivate four instructional design principles that emphasize helping students innovate new ideas and solutions, which in turn, leads them to focus on new information and prepares them to adapt and learn from future situations.

Limited population structure but signals of recent selection in introduced African Fig Fly (Zaprionus indianus) in North America.

Invasive species have devastating consequences for human health, food security, and the environment. Many invasive species adapt to new ecological niches following invasion, but little is known about the early steps of adaptation. Here we examine population genomics of a recently introduced drosophilid in North America, the African Fig Fly, Zaprionus indianus. This species is likely intolerant of subfreezing temperatures and recolonizes temperate environments yearly. We generated a new chromosome-level genome assembly for Z. indianus. Using resequencing of over 200 North American individuals collected over four years in temperate Virginia, plus a single collection from subtropical Florida, we tested for signatures of recolonization, population structure, and adaptation within invasive populations. We show founding populations are sometimes small and contain close genetic relatives, yet temporal population structure and differentiation of populations is mostly absent across recurrent recolonization events. Although we find limited signals of genome-wide spatial or temporal population structure, we identify haplotypes on the X chromosome that are repeatedly differentiated between Virginia and Florida populations. These haplotypes show signatures of natural selection and are not found in African populations. We also find evidence for several large structural polymorphisms segregating within North America populations and show X chromosome evolution in invasive populations is strikingly different from the autosomes. These results show that despite limited population structure, populations may rapidly evolve genetic differences early in an invasion. Further uncovering how these genomic regions influence invasive potential and success in new environments will advance our understanding of how organisms evolve in changing environments.

A Statistical Approach for Functional Reach-to-Grasp Segmentation Using a Single Inertial Measurement Unit.

The aim of this contribution is to present a segmentation method for the identification of voluntary movements from inertial data acquired through a single inertial measurement unit placed on the subject's wrist. Inertial data were recorded from 25 healthy subjects while performing 75 consecutive reach-to-grasp movements. The approach herein presented, called DynAMoS, is based on an adaptive thresholding step on the angular velocity norm, followed by a statistics-based post-processing on the movement duration distribution. Post-processing aims at reducing the number of erroneous transitions in the movement segmentation. We assessed the segmentation quality of this method using a stereophotogrammetric system as the gold standard. Two popular methods already presented in the literature were compared to DynAMoS in terms of the number of movements identified, onset and offset mean absolute errors, and movement duration. Moreover, we analyzed the sub-phase durations of the drinking movement to further characterize the task. The results show that the proposed method performs significantly better than the two state-of-the-art approaches (i.e., percentage of erroneous movements = 3%; onset and offset mean absolute error < 0.08 s), suggesting that DynAMoS could make more effective home monitoring applications for assessing the motion improvements of patients following domicile rehabilitation protocols.

A modified inertial shrinking projection algorithm with adaptive step size for solving split generalized equilibrium, monotone inclusion and fixed point problems

A modified inertial shrinking projection algorithm with adaptive step size for solving split generalized equilibrium, monotone inclusion and fixed point problems