Nonlinear Gradient Research Articles

Multi-objective reinforcement learning based on nonlinear scalarization and long-short-term optimization

PurposeMany practical control problems require achieving multiple objectives, and these objectives often conflict with each other. The existing multi-objective evolutionary reinforcement learning algorithms cannot achieve good search results when solving such problems. It is necessary to design a new multi-objective evolutionary reinforcement learning algorithm with a stronger searchability.Design/methodology/approachThe multi-objective reinforcement learning algorithm proposed in this paper is based on the evolutionary computation framework. In each generation, this study uses the long-short-term selection method to select parent policies. The long-term selection is based on the improvement of policy along the predefined optimization direction in the previous generation. The short-term selection uses a prediction model to predict the optimization direction that may have the greatest improvement on overall population performance. In the evolutionary stage, the penalty-based nonlinear scalarization method is used to scalarize the multi-dimensional advantage functions, and the nonlinear multi-objective policy gradient is designed to optimize the parent policies along the predefined directions.FindingsThe penalty-based nonlinear scalarization method can force policies to improve along the predefined optimization directions. The long-short-term optimization method can alleviate the exploration-exploitation problem, enabling the algorithm to explore unknown regions while ensuring that potential policies are fully optimized. The combination of these designs can effectively improve the performance of the final population.Originality/valueA multi-objective evolutionary reinforcement learning algorithm with stronger searchability has been proposed. This algorithm can find a Pareto policy set with better convergence, diversity and density.

Deriving Input Variables through Applied Machine Learning for Short-Term Electric Load Forecasting in Eskilstuna, Sweden

As the demand for electricity, electrification, and renewable energy rises, accurate forecasting and flexible energy management become imperative. Distribution network operators face capacity limits set by regional grids, risking economic penalties if exceeded. This study examined data-driven approaches of load forecasting to address these challenges on a city scale through a use case study of Eskilstuna, Sweden. Multiple Linear Regression was used to model electric load data, identifying key calendar and meteorological variables through a rolling origin validation process, using three years of historical data. Despite its low cost, Multiple Linear Regression outperforms the more expensive non-linear Light Gradient Boosting Machine, and both outperform the “weekly Naïve” benchmark with a relative Root Mean Square Errors of 32–34% and 39–40%, respectively. Best-practice hyperparameter settings were derived, and they emphasize frequent re-training, maximizing the training data size, and setting a lag size larger than or equal to the forecast horizon for improved accuracy. Combining both models into an ensemble could the enhance accuracy. This paper demonstrates that robust load forecasts can be achieved by leveraging domain knowledge and statistical analysis, utilizing readily available machine learning libraries. The methodology for achieving this is presented within the paper. These models have the potential for economic optimization and load-shifting strategies, offering valuable insights into sustainable energy management.

Ambrosetti-Prodi type results for elliptic equations with nonlinear gradient terms on an exterior domain

The aim of this paper is to establish an Ambrosetti-Prodi type result for the problem where is a parameter, is continuous and satisfies is continuous. with .

Practical utilization of nonlinear spatial encoding: Fast field mapping and FRONSAC-wave.

To study the additional value of FRONSAC encoding in 2D and 3D wave sequences, implementing a simple strategy to trajectory mapping for FRONSAC encoding gradients. The nonlinear gradient trajectory for each voxel was estimated by exploiting the sparsity of the point spread function in the frequency domain. Simulations and in-vivo experiments were used to analyze the performance of combinations of wave and FRONSAC encoding. Field mapping using the simplified approach produced similar image quality with much shorter calibration time than the comprehensive mapping schemes utilized in previous work. In-vivo human brain images showed that the addition of FRONSAC encoding could improve wave image quality, particularly at very high undersampling factors and in the context of limited wave amplitudes. These results were further supported by g-factor maps. Results show that FRONSAC can be used to improve image quality of wave at very high undersampling rates or in slew-limited acquisitions. Our study illustrates the potential of the proposed fast field mapping approach.

Boundary and distributed optimal control for a population dynamics PDE model with discontinuous in time Galerkin FEM schemes

We consider fully discrete finite element approximations for a semilinear optimal control system of partial differential equations in two cases: for distributed and Robin boundary control. The ecological predator-prey optimal control model is approximated by conforming finite element methods mimicking the spatial part, while a discontinuous Galerkin method is used for the time discretization. We investigate the sensitivity of the solution distance from the target function, in cases with smooth and rough initial data. We employ low, and higher-order polynomials in time and space whenever proper regularity is present. The approximation schemes considered are with and without control constraints, driving efficiently the system to desired states realized using non-linear gradient methods.

On Liouville-type theorems for 𝑘-Hessian equations with gradient terms

In this paper, we investigate several Liouville-type theorems related to k k -Hessian equations with non-linear gradient terms. More specifically, we study non-negative solutions to S k [ D 2 u ] ≥ h ( u , | D u | ) S_k[D^2u]\ge h(u,|Du|) in R n \mathbb {R}^n . The results depend on some qualified growth conditions of h h at infinity. A Liouville-type result to subsolutions of a prototype equation S k [ D 2 u ] = f ( u ) + g ( u ) ϖ ( | D u | ) S_k[D^2u]=f(u)+g(u)\varpi (|Du|) is investigated. A necessary and sufficient condition for the existence of a non-trivial non-negative entire solution to S k [ D 2 u ] = f ( u ) + g ( u ) | D u | q S_k[D^2u]=f(u)+g(u)|Du|^q for 0 ≤ q > k + 1 0\le q>k+1 is also given.

Macroscopic Polarization from Nonlinear Gradient Couplings.

We show that a lattice mode of arbitrary symmetry induces a well-defined macroscopic polarization at first order in the momentum and second order in the amplitude. We identify a symmetric flexoelectric-like contribution, which is sensitive to both the electrical and mechanical boundary conditions, and an antisymmetric Dzialoshinskii-Moriya-like term, which is unaffected by either. We develop the first-principles methodology to compute the relevant coupling tensors in an arbitrary crystal, which we illustrate with the example of the antiferrodistortive order parameter in SrTiO_{3}.

Fractal study on the nonlinear seepage mechanism during low-permeability coal water injection

In the initial stage of coal seam water injection, due to the high density and low permeability of coal bodies, an obvious startup pressure gradient is observed in relation to water seepage; this phenomenon leads to low-velocity nonlinear seepage. In this paper, we study the nonlinear seepage law and the main influencing parameters of the water injection process. First, based on the startup pressure gradient, the nonlinear seepage equation, and the fractal theory, we formulated a nonlinear seepage model of coal seam water injection that considered the fractal characteristics of a complex coal structure. Subsequently, we carried out coal seam water injection and gas radial seepage experiments under a high overburden pressure, obtaining the startup pressure gradient according to the seepage characteristics and the changes of dynamic parameters. Then, the dynamic parameters of water injection, the structural parameters of the coal samples, the physical parameters, and the fractal dimension were substituted into the theoretical model to obtain the theoretically calculated value. Finally, through comparative analysis of theoretical and experimental startup pressure gradient calculation results, it is found that with the increase in the overburden pressure, the permeability of coal and the connectivity effect are reduced, while the fracture tortuosity and the startup pressure gradient increase. Moreover, coal seam permeability does not seem to be the single decisive factor for the nonlinear startup pressure gradient.

The existence of radial solutions for a class of k-Hessian systems with the nonlinear gradient terms

The existence of radial solutions for a class of k-Hessian systems with the nonlinear gradient terms

Photovoltaic module temperature prediction using various machine learning algorithms: Performance evaluation

This paper presents data-driven models for photovoltaic module temperature prediction and analyzes the relation and effects of ambient conditions to module temperature. A total of 12 different machine learning and regression algorithms are implemented, with a large experimental dataset of 345,600 × 7. Prior to implementing those algorithms, data preprocessing is performed to prepare the datasets and determine the informative attributes for the models. Using PCA with module temperature as target to predict, the selected features for models' inputs were determined to be ambient temperature, solar radiation, wind speed, and relative humidity, and each algorithm is cross-validated and tuned with optimal performance parameters. Results show that while relative humidity is more likely to introduce less information to the model, other aforementioned features are the important parameters to predict the module temperature. While for linear modeling, LASSO algorithm provided the best performance, the ANN model demonstrated the best overall results as it produced the most accurate predictions with lowest errors. A similar performance is attained by the proposed non-linear model, KRR and Gradient Boosting algorithm, with a slight advantage to the KRR model. Furthermore, in comparison to experimental data, the ANN model and the proposed non-linear model provided an R2 values of 0.986 and 0.981, with a MAE of 0.982 and 1.476, and MSE of 2.181and 3.464, respectively. Moreover, the proposed model supplied accurate results when compared to models from literature in an out-of-sample testing, it also proven to be robust and accurate when used to predict the PV power output.

Reduced membrane model for liquid crystal polymer networks: Asymptotics and computation

We examine a reduced membrane model of liquid crystal polymer networks (LCNs) via asymptotics and computation. This model requires solving a minimization problem for a non-convex stretching energy. We show a formal asymptotic derivation of the 2D membrane model from 3D rubber elasticity. We construct approximate solutions with point defects. We design a finite element method with regularization, and propose a nonlinear gradient flow with Newton inner iteration to solve the non-convex discrete minimization problem. We present numerical simulations of practical interests to illustrate the ability of the model and our method to capture rich physical phenomena.

Generalized variational framework with minimax optimization for parametric blind deconvolution

Blind deconvolution (BD), which aims to separate unknown convolved signals, is a fundamental problem in signal processing. Due to the ill-posedness and underdetermination of the convolution system, it is a challenging nonlinear inverse problem. This paper is devoted to the algorithmic studies of parametric BD, which is typically applied to recover images from ad hoc optical modalities. We propose a generalized variational framework for parametric BD with various priors and potential functions. By using the conjugate theory in convex analysis, the framework can be cast into a nonlinear saddle point problem. We employ the recent advances in minimax optimization to solve the parametric BD by the nonlinear primal-dual hybrid gradient method, with all subproblems admitting closed-form solutions. Numerical simulations on synthetic and real datasets demonstrate the compelling performance of the minimax optimization approach for solving parametric BD.

Neutral Axis-Based Anomaly Detection for Local Damage to Girders Affected by Nonlinear Temperature Gradients

Neutral Axis-Based Anomaly Detection for Local Damage to Girders Affected by Nonlinear Temperature Gradients

Temporal convex combination‐based secure distributed estimation against cyberattacks and noisy input

AbstractThis paper proposes a new secure distributed estimation for cyber‐physical systems against adversarial attacks with noisy input. To mitigate the effect of attacks, a novel distributed attack detection based on a reliable reference estimation obtained by temporal convex combination is proposed. Furthermore, for more effective and robust performance, an adaptation rule to adjust convex combination weights is presented, in which the generalized correntropy method with nonlinear loss function and stochastic gradient descent are utilized. Besides, to eliminate input noise, a bias‐compensation method in local adaptation of the secure distributed estimation is proposed. Simulations show superior dynamic and real‐time adaptability of the proposed algorithm under complex attacking scenarios.

Continuous Zonal Gradients Characterize Epipelagic Plankton Assemblages and Hydrography in the Subtropical North Atlantic

The subtropical North Atlantic is a key region for understanding climate impact in the ocean. Plankton studies in this region have been generally framed in biogeographic provinces or focused on latitudinal gradients. In this study, we demonstrate the benefits of using empirically constructed continuous gradients versus the use of average values for biogeographical provinces to characterize plankton assemblages along a longitudinal transect at 24.5° N using an unprecedented array of stations including hydrographic observations, abundance of phytoplankton and zooplankton, and plankton size spectra in the epipelagic layer (0–200 m). In addition, the variability of zooplankton assemblages was analyzed using detailed taxonomic identification at selected stations. We found significant gradients in most hydrographic and plankton variables. The former, including surface temperature and salinity, the depth of the upper mixing layer, and the depth of the chlorophyll maximum, displayed non-linear gradients with maximum or minimum values near the center of the transect. In contrast, most plankton variables showed linear zonal gradients. Phytoplankton, microzooplankton (<100 µm), and the slope and the intercept of the size spectra increased (and Trichodesmium decreased) to the west. Total mesozooplankton (>200 µm) did not show any significant zonal pattern, but the taxonomic assemblages were characterized by a gradual replacement of large Calanoids by small-bodied Cyclopoid copepods from east to west. The use of continuous gradients provides more detailed information on the zonal structure of subtropical plankton than the classical approach using discrete areas.

Temporal Regularity of Symmetric Stochastic p-Stokes Systems

We study the symmetric stochastic p-Stokes system, p∈(1,∞)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p \\in (1,\\infty )$$\\end{document}, in a bounded domain. The results are two-fold: First, we show that in the context of analytically weak solutions, the stochastic pressure—related to non-divergence free stochastic forces—enjoys almost -1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-1/2$$\\end{document} temporal derivatives on a Besov scale. Second, we verify that the velocity u of strong solutions obeys 1/2 temporal derivatives in an exponential Nikolskii space. Moreover, we prove that the non-linear symmetric gradient V(ϵu)=(κ+ϵu)(p-2)/2ϵu\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V(\\mathbb {\\epsilon } u) = (\\kappa + \\left| \\mathbb {\\epsilon } u\\right| )^{(p-2)/2} \\mathbb {\\epsilon } u$$\\end{document}, κ≥0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa \\ge 0$$\\end{document}, which measures the ellipticity of the p-Stokes system, has 1/2 temporal derivatives in a Nikolskii space.

On anisotropic parabolic equation with nonstandard growth order

ABSTRACT In this paper, the existence and the uniqueness of an evolutionary anisotropic p i ( x ) -Laplacian equation with a damping term are studied. If the damping term is with a subcritical index, by the Di Giorgi iteration technique, the L ∞ -estimate of the weak solutions can be obtained. The existence of weak solution is proved by the renormalized solution method, and how the anisotropic characteristic of the considered equation affect the L ∞ -estimate of the weak solutions is revealed. The uniqueness is true strongly depending on subcritical index of the damping term, and this result goes beyond previous efforts in the literature (Bertsch M, Dal Passo R, Ughi M: Discontinuous viscosity solutions of a degenerate parabolic equation. Trans Amer Math Soc. 1990;320:779–798; Li Z, Yan B, Gao W. Existence of solutions to a parabolic p ( x ) − Laplace equation with convection term via L ∞ − Estimates. Electron J Differ Equ. 2015;46:1–21; Zhang Q, Shi P. Global solutions and self-similar solutions of semilinear parabolic equations with nonlinear gradient terms. Nonlinear Anal. 2010;72:2744–2752; Zhou W, Cai S. The continuity of the viscosity of the Cauchy problem of a degenerate parabolic equation not in divergence form. J Jilin University (Natural Sci.). 2004;42:341–345), etc.

Nonlinear gradient term effects on the stability of localized structures in parametrically forced extended dissipative systems

Nonlinear gradient term effects on the stability of localized structures in parametrically forced extended dissipative systems

Nonlinear Seepage Mechanism and Evolution Law of CO2 Enhancing Coalbed Methane Recovery

China’s coal seam permeability is low, and the original coal seam gas extraction is difficult. CO2 displacement of coal seam CH4 technology is an effective gas extraction technology. CO2 is injected into the coal seam under pressure, and competitive adsorption occurs with CH4 in the pores. The gas composition is nonuniformly distributed, and its viscosity μ is the dynamic parameter. As the gas is compressible, the pressure drops, and migration distance does not satisfy a linear relationship. Therefore, the gas transport does not conform to Darcy’s law. The mass transfer process and a multicomponent gas competitive adsorption were investigated theoretically and experimentally. The adsorption characteristics and gas compressibility determine the distribution of the gas components in pores and change the gas dynamic viscosity in different regions. The change in the gas dynamic viscosity in the channel is the direct reason for the nonlinear pressure gradient and gas flow curve. The permeability and gas component affect the degree of nonlinear deviation of the gas flow and pressure gradient curve. This affects the nonlinear deviation degree of the curve by changing the gas dynamic viscosity in the pore channel during displacement. The reasonable displacement pressure is the critical pressure (PO) through experimental and theoretical analysis.

Polygon model for solution of non-linear velocity gradient of interface and asymmetric break-up of droplet

In this study, a novel model is proposed to accurately depict the changes in the droplet-matrix interface as a function of the velocity gradient at different times. Using the iteration method and drawing the droplet shape, the interface velocity gradient-matrix shear rate non-linear equation is simultaneously solved. The initial droplet shape is assumed to be a polygon, with each side independently undergoing modifications under stress. By sequentially adjusting each side at different time points, the overall shape of the droplet is reconstructed. The experimental section examines droplets consisting of alcohols (polyvinyl alcohol and polyethylene glycol) in water-soluble form with different concentrations and glycerol. The matrix material used is poly dimethyl siloxane. The viscosity ratio between the droplet and matrix falls within the range of 0.18–3.08. The experimental findings show two types of droplet breakup: a single-end bulb and two non-uniform end bulbs of different sizes. The simulation results from the model align well with the experimental observations, accurately capturing the dimensions and volume of the droplets and the aspect ratio of the bulbs. The model also predicts the aspect ratio, lateral area, and rotation of the droplets before breakup with minimal deviation from the experimental data.