Gradient Constraint Research Articles

Transverse shrinking and swelling of rattan: Hygro-deformation under simultaneous gradient constraints and shape

Transverse shrinking and swelling of rattan: Hygro-deformation under simultaneous gradient constraints and shape

Optimal Consumption and Investment with Income Adjustment and Borrowing Constraints

In this paper, we address the utility maximization problem of an infinitely lived agent who has the option to increase their income. The agent can increase their income at any time, but doing so incurs a wealth cost proportional to the amount of the increase. To prevent the agent from infinitely increasing their income and borrowing against future income, we additionally consider a non-negative wealth constraint that prohibits borrowing based on future income. This utility maximization problem is a mixture of stochastic control, where the agent chooses consumption and investment, and singular control, where the agent chooses a non-decreasing income process. To solve this non-trivial and challenging problem, we derive the Hamilton–Jacobi–Bellman (HJB) equation with a gradient constraint using the dynamic programming principle (DPP). Then, using the guess-and-verify method and a linearization technique, we obtain a closed-form solution to the HJB equation and, based on this, find the optimal strategy.

Exploring the supply-demand match and drivers of blue-green spaces cooling in Wuhan Metropolis

This study explores the spatial evolution and driving factors of cooling supply and demand matching in blue-green spaces (BGSs) to alleviate urban heat island effects. Using Wuhan Metropolis as a case study, the cooling supply index (CSI) and cooling demand index (CDI) were utilized to assess the BGSs' cooling supply capacity and demand levels in 2014, 2018 and 2022. The relationship between them was then examined applying spatial gradient analysis and constraint effect analysis. Subsequently, the coupled coordination degree (CCD) of cooling supply-demand and its built environment-driven explanatory power was investigated. Ultimately, areas with supply-demand mismatches were identified, and tailored cooling strategies were devised to rectify these discrepancies. The results indicated that: (1) Wuhan Metropolis experienced a decline in BGSs' cooling supply capacity and an increase in cooling demand level between 2014 and 2022. (2) There is a significant correlation between the cooling supply capacity and demand level of BGSs in Wuhan Metropolis, with a spatial gradient effect and a constraint effect (CSI values = 0–0.2). (3) The CCD of cooling supply-demand in Wuhan Metropolis decreased from 2014 to 2022, with building density being the dominant built environment factors (q-value = 0.83–0.86). (4) The number of mismatched cooling supply-demand units significantly increased in Wuhan Metropolis from 2014 to 2022, indicating an imperative need to alleviate urban high temperatures. To address this issue, the study proposes a mismatch mechanism-based regulatory strategy aimed at mitigating the heat from residential, transportation, and industrial areas.

Image smoothing method based on global gradient sparsity and local relative gradient constraint optimization

Removing texture while preserving the main structure of an image is a challenging task. To address this, this paper propose an image smoothing method based on global gradient sparsity and local relative gradient constraints optimization. To reduce the interference of complex texture details, adopting a multi-directional difference constrained global gradient sparsity decomposition method, which provides a guidance image with weaker texture detail gradients. Meanwhile, using the luminance channel as a reference, edge-aware operator is constructed based on local gradient constraints. This operator weakens the gradients of repetitive and similar texture details, enabling it to obtain more accurate structural information for guiding global optimization of the image. By projecting multi-directional differences onto the horizontal and vertical directions, a mapping from multi-directional differences to bi-directional gradients is achieved. Additionally, to ensure the consistency of measurement results, a multi-directional gradient normalization method is designed. Through experiments, we demonstrate that our method exhibits significant advantages in preserving image edges compared to current advanced smoothing methods.

A Level-Set-Based Density Method for Buckling Optimization of Structure with Curved Grid Stiffeners

Curved grid stiffeners, compared to straight stiffeners, offer greater flexibility in adjusting the force transmission paths and give better structural performance. In this paper, a level-set-based density method is employed to generate layouts of curved grid stiffeners so that the critical buckling load factor (BLF) of the stiffened structures is improved. During the optimization process, volume constraint is incorporated to control material utilization, and gradient constraints are employed to maintain uniformity in the width of the stiffeners. Finally, the proposed method is demonstrated through several numerical examples.

A Water Demand Forecasting Model Based on Generative Adversarial Networks and Multivariate Feature Fusion

Accurate long-term water demand forecasting is beneficial to the sustainable development and management of cities. However, the randomness and nonlinear nature of water demand bring great challenges to accurate long-term water demand forecasting. For accurate long-term water demand forecasting, the models currently in use demand the input of extensive datasets, leading to increased costs for data gathering and higher barriers to entry for predictive projects. This situation underscores the pressing need for an effective forecasting method that can operate with a smaller dataset, making long-term water demand predictions more feasible and economically sensible. This study proposes a framework to delineate and analyze long-term water demand patterns. A forecasting model based on generative adversarial networks and multivariate feature fusion (the water demand forecast-mixer, WDF-mixer) is designed to generate synthetic data, and a gradient constraint is introduced to overcome the problem of overfitting. A multi-feature fusion method based on temporal and channel features is then derived, where a multi-layer perceptron is used to capture temporal dependencies and non-negative matrix decomposition is applied to obtain channel dependencies. After that, an attention layer receives all those features associated with the water demand forecasting, guiding the model to focus on important features and representing correlations across them. Finally, a fully connected network is constructed to improve the modeling efficiency and output the forecasting results. This approach was applied to real-world datasets. Our experimental results on four water demand datasets show that the proposed WDF-mixer model can achieve high forecasting accuracy and robustness. In comparison to the suboptimal models, the method introduced in this study demonstrated a notable enhancement, with a 62.61% reduction in the MSE, a 46.85% decrease in the MAE, and a 69.15% improve in the R2 score. This research could support decision makers in reducing uncertainty and increasing the quality of water resource planning and management.

Bio-inspired foveal super-resolution method for multi-focal-length images based on local gradient constraints

Most existing super-resolution (SR) imaging systems, inspired by the bionic compound eye, utilize image registration and reconstruction algorithms to overcome the angular resolution limitations of individual imaging systems. This article introduces a multi-aperture multi-focal-length imaging system and a multi-focal-length image super-resolution algorithm, mimicking the foveal imaging of the human eye. Experimental results demonstrate that with the proposed imaging system and an SR imaging algorithm inspired by the human visual system, the proposed method can enhance the spatial resolution of the foveal region by up to 4 × compared to the original acquired image. These findings validate the effectiveness of the proposed imaging system and computational imaging algorithm in enhancing image texture and spatial resolution.

The best approximation of a given function in L 2-norm by Lipschitz functions with gradient constraint

Abstract The starting point of this paper is the study of the asymptotic behavior, as p → ∞ {p\to\infty} , of the following minimization problem: min ⁡ { 1 p ⁢ ∫ Ω | ∇ ⁡ v | p + 1 2 ⁢ ∫ Ω ( v - f ) 2 , v ∈ W 1 , p ⁢ ( Ω ) } . \min\biggl{\{}\frac{1}{p}\int_{\Omega}|\nabla v|^{p}+\frac{1}{2}\int_{\Omega}(% v-f)^{2},\quad v\in W^{1,p}(\Omega)\biggr{\}}. We show that the limit problem provides the best approximation, in the L 2 {L^{2}} -norm, of the datum f among all Lipschitz functions with Lipschitz constant less or equal than one. Moreover, such an approximation verifies a suitable PDE in the viscosity sense. After the analysis of the model problem above, we consider the asymptotic behavior of a related family of nonvariational equations and, finally, we also deal with some functionals involving the ( N - 1 ) {(N-1)} -Hausdorff measure of the jump set of the function.

Elimination of Irregular Boundaries and Seams for UAV Image Stitching with a Diffusion Model

Unmanned aerial vehicle (UAV) image stitching refers to the process of combining multiple UAV images into a single large-format, wide-field image, and the stitched image often contains large irregular boundaries and multiple stitching seams. Usually, irregular boundaries are addressed using grid-constrained methods, while seams are optimized through the design of energy functions and penalty terms applied to the pixels at the seams. The above-mentioned two solutions can only address one of the two issues individually and are often limited to pairwise stitching of images. To the best of our knowledge, there is no unified approach that can handle both seams and irregular boundaries in the context of multi-image stitching for UAV images. Considering that addressing irregular boundaries involves completing missing information for regularization and that mitigating seams involves generating images near the stitching seams, both of these challenges can be viewed as instances of a mask-based image completion problem. This paper proposes a UAV image stitching method based on a diffusion model. This method uniformly designs masks for irregular boundaries and stitching seams, and the unconditional score function of the diffusion model is then utilized to reverse the process. Additional manifold gradient constraints are applied to restore masked images, eliminating both irregular boundaries and stitching seams and resulting in higher perceptual quality. The restoration maintains high consistency in texture and semantics. This method not only simultaneously addresses irregular boundaries and stitching seams but also is unaffected by factors such as the number of stitched images, the shape of irregular boundaries, and the distribution of stitching seams, demonstrating its robustness.

A Combined Model of Diffusion Model and Enhanced Residual Network for Super-Resolution Reconstruction of Turbulent Flows

In this study, we introduce a novel model, the Combined Model, composed of a conditional denoising diffusion model (SR3) and an enhanced residual network (EResNet), for reconstructing high-resolution turbulent flow fields from low-resolution flow data. The SR3 model is adept at learning the distribution of flow fields. The EResNet architecture incorporates a long skip connection extending from the input directly to the output. This modification ensures the preservation of essential features learned by the SR3, while simultaneously enhancing the accuracy of the flow field. Additionally, we incorporated physical gradient constraints into the loss function of EResNet to ensure that the flow fields reconstructed by the Combined Model are consistent with the direct numerical simulation (DNS) data. Consequently, the high-resolution flow fields reconstructed by the Combined Model exhibit high conformity with the DNS results in terms of flow distribution, details, and accuracy. To validate the effectiveness of the model, experiments were conducted on two-dimensional flow around a square cylinder at a Reynolds number (Re) of 100 and turbulent channel flow at Re = 4000. The results demonstrate that the Combined Model can reconstruct both high-resolution laminar and turbulent flow fields from low-resolution data. Comparisons with a super-resolution convolutional neural network (SRCNN) and an enhanced super-resolution generative adversarial network (ESRGAN) demonstrate that while all three models perform admirably in reconstructing laminar flows, the Combined Model excels in capturing more details in turbulent flows, aligning the statistical outcomes more closely with the DNS results. Furthermore, in terms of L2 norm error, the Combined Model achieves an order of magnitude lower error compared to SRCNN and ESRGAN. Experimentation also revealed that SR3 possesses the capability to learn the distribution of flow fields. This work opens new avenues for high-fidelity flow field reconstruction using deep learning methods.

Scalable Motion Style Transfer with Constrained Diffusion Generation

Current training of motion style transfer systems relies on consistency losses across style domains to preserve contents, hindering its scalable application to a large number of domains and private data. Recent image transfer works show the potential of independent training on each domain by leveraging implicit bridging between diffusion models, with the content preservation, however, limited to simple data patterns. We address this by imposing biased sampling in backward diffusion while maintaining the domain independence in the training stage. We construct the bias from the source domain keyframes and apply them as the gradient of content constraints, yielding a framework with keyframe manifold constraint gradients (KMCGs). Our validation demonstrates the success of training separate models to transfer between as many as ten dance motion styles. Comprehensive experiments find a significant improvement in preserving motion contents in comparison to baseline and ablative diffusion-based style transfer models. In addition, we perform a human study for a subjective assessment of the quality of generated dance motions. The results validate the competitiveness of KMCGs.

Inverse dynamic design for motion control of soft machines driven by dielectric elastomer actuators

Dielectric elastomers (DEs) are a sort of electroactive polymers with large and fast responses, light masses and high energy densities. Hence, they are regarded as one of the most potential materials for artificial muscles and soft robots. Previous researches on DEs focused mainly on experimental prototypes and property optimization in a component level, while the system-level design and control of dynamic motions of DE actuators are still open problems. In this study, the computational method of inverse dynamic design (IDD) for input voltages of DE actuators is proposed by taking the electromechanical coupling mechanics and the effects of rigid-body motions into account. The proposed inverse dynamic design with nonlinear finite elements enables one to realize the high-precision modeling of soft actuators and to derive the dynamic voltages for desired trajectories in a system level. To describe the overall motions and deformations of DE actuators, the gradient constraints of the dynamic configurations of the actuators are introduced upon the assumption of time-varying uniform curvatures for the desired deformation. And then, based on the principle of energy equivalence, the dynamic voltages for the target deformations in motions are computed inversely from the Lagrange multipliers of the desired trajectories. In addition, the forward simulations by removing the constraints and applying the voltages are further conducted to validate and predict the final configurations. Finally, five numerical case studies and demonstrative experiments are presented to validate the effectiveness of the proposed method. This study endeavors to establish a universal inverse dynamic design method for the motion control of soft DE actuators, allowing for the application of theoretical methodology to engineering problems.

Steering Kernel Weighted Guided Image Filtering with Gradient Constraint

In order to make the weighted guided image filter (WGIF) more fully utilize the edge direction of the image, a steering kernel weighted guided image filter (SKWGIF) is proposed by employing the steering kernel to learn the edge direction and incorporating the learning results into the WGIF. However, SKWGIF does not provide a good compromise between the two possibly contradictory objectives of edge-preserving and smoothing, where the image edges are inevitably smoothed. To overcome the drawback, a SKWGIF with gradient constraint (GC-SKWGIF) is proposed by introducing the gradient constraints into the SKWGIF. The gradient constraints allow the filter to take into account the gradient variation of the edges in the filtering process, and therefore the image edges can be better preserved. To verify the effectiveness of the proposed filter, the GC-SKWGIF is applied to edge-aware smoothing, tone mapping of high range dynamic images, image denoising and haze removal. Both theoretical analysis and experimental results show that the proposed filter can produce good resultant images.

Variational Inequalities on Unbounded Domains for Zero-Sum Singular Controller vs. Stopper Games

We study a class of zero-sum games between a singular controller and a stopper over a finite-time horizon. The underlying process is a multidimensional (locally nondegenerate) controlled stochastic differential equation (SDE) evolving in an unbounded domain. We prove that such games admit a value and provide an optimal strategy for the stopper. The value of the game is shown to be the maximal solution in a suitable Sobolev class of a variational inequality of min-max type with an obstacle constraint and a gradient constraint. Although the variational inequality and the game are solved on an unbounded domain, we do not require boundedness of either the coefficients of the controlled SDE or of the cost functions in the game. Funding: A. Bovo was partially supported by the Doctoral Studentship from the University of Leeds.

A gradient descent akin method for constrained optimization: algorithms and applications

We present a ‘gradient descent akin’ method (GDAM) for constrained optimization problem, i.e. the search direction is computed using a linear combination of the negative and normalized objective and constraint gradient. We give fundamental theoretical guarantees on the global convergence of the method. This work focuses on the algorithms and applications of GDAM. We present computational algorithms that adapt common strategies for the gradient descent method. We demonstrate the potential of the method using two engineering applications, shape optimization and sensor network localization. When practically implemented, GDAM is robust and very competitive in solving the considered large and challenging optimization problems.

Density Prediction From Full Waveform Inversion With Gravity Gradient Constraints

Density Prediction From Full Waveform Inversion With Gravity Gradient Constraints

A fast stereo-matching method for a speckle pattern based on grid and gradient constraints

In the existing binocular stereo-matching methods for a speckle pattern, the pixel-by-pixel correlation weight calculation across the entire global disparity range is time-consuming. To address this issue, this paper presents a fast stereo-matching method for a speckle pattern based on grid and gradient constraints. The grid pattern is projected onto the measured object. The grid features are extracted to form the local disparity constraints, which narrow the search ranges. Moreover, the image gradient is used in selecting the pixels involved in the correlation weight calculation, which reduces the redundant computations. 3D reconstruction experiments of paper and plaster models were employed to evaluate the matching accuracy and speed of the proposed method. Furthermore, the experiments of measuring displacement were designed to validate the accuracy of our method. In contrast to the existing methods, our approach increased the matching speed by 66% on average while ensuring the matching accuracy.

Nonlocal Lagrange multipliers and transport densities

We prove the existence of generalized solutions of the Monge–Kantorovich equations with fractional [Formula: see text]-gradient constraint, [Formula: see text], associated to a general, possibly degenerate, linear fractional operator of the type, [Formula: see text] with integrable data, in the space [Formula: see text], which is the completion of the set of smooth functions with compact support in a bounded domain [Formula: see text] for the [Formula: see text]-norm of the distributional Riesz fractional gradient [Formula: see text] in [Formula: see text] (when [Formula: see text], [Formula: see text] is the classical gradient). The transport densities arise as generalized Lagrange multipliers in the dual space of [Formula: see text] and are associated to the variational inequalities of the corresponding transport potentials under the constraint [Formula: see text]. Their existence is shown by approximating the variational inequality through a penalization of the constraint and nonlinear regularization of the linear operator [Formula: see text]. For this purpose, we also develop some relevant properties of the spaces [Formula: see text], including the limit case [Formula: see text] and the continuous embeddings [Formula: see text], for [Formula: see text]. We also show the localization of the nonlocal problems ([Formula: see text]), to the local limit problem with classical gradient constraint when [Formula: see text], for which most results are also new for a general, possibly degenerate, partial differential operator [Formula: see text] with coefficients only integrable and bounded gradient constraint.

Understanding ecological restoration potential: The role of water resources and slope gradient limits

Ecological restoration is one of the most feasible ways to mitigate climate change and conserve ecosystems. However, the scope, intensity, effectiveness, and future potential of ecological restoration are restricted by unfavorable environmental conditions, especially limited water resources and complex topography. This paper proposes an assessment framework of ecological restoration potential under the coupled limits of water resources and slope gradient to quantitatively assess ecological restoration potential (ERP) under these two limiting factors. Results indicate that the current vegetation plantation in 20%, 0.19% and 32% areas of China's 31 provinces are larger, equal, and lower than the vegetation threshold permitted by local water resources respectively, which represents about 0.299 billion ha potential for additional restoration area. The ecological restoration potential under the integrated water resources and slope gradient constraints is 0.4 Pg C, less than half (47%) of the potential under the single limit of water resources (0.856 Pg C). However, this potential and China's existing carbon sink capacity related to terrestrial ecosystems is estimated to offset up to 8% of its current carbon dioxide emissions. Ecological restoration programs in areas with slope >5° will require additional economic investment to support Soil and Water Conservation programs, estimated to average about 212 trillion yuan. Succinctly, it is critical to integrate field investigations, process-based assessments and landscape design for sustainable ecological restoration. This work can provide techniques support for quantitative measurement of ecological restoration potential considering multiple limiting factors and guidance for sustainable implementation of ecological restoration programs.

Assimilation as the Residue of AGREE

An Optimality Theoretic approach to assimilation is proposed where all assimilation processes result from the interaction of a single syntagmatic markedness constraint that requires sequences of sounds to AGREE in all feature specifications with a variety of faithfulness constraints that seek to IDENT input feature specifications. Assimilation or the lack of it is the residue of AGREE after satisfaction of higher ranked IDENT constraints. AGREE is analyzed as a single gradient constraint rather than a set of categorical constraints each obligating agreement in a specific feature. The study concludes that a gradient interpretation of AGREE is theoretically appropriate since it meets the general principle of economy in the structure of our language faculty and also supports the general move towards convergence rather than divergence in linguistic analysis. The outcomes of the study also prove to be practically appropriate in handling various assimilation processes from different languages.