Gradient-based Method Research Articles

Global Genetic Algorithm for Automating and Optimizing Petroleum Well Deployment in Complex Reservoirs

Locating petroleum-productive wells using informed geological data, a conventional means, has proven to be tedious and undesirable by reservoir engineers. The former numerical simulator required a lengthy trial-and-error process to manipulate the variables and uncertainties that lie on the reservoir to determine the best placement of the well. Hence, this paper examines the use of a global genetic algorithm (GA) to optimize the placement of wells in complex reservoirs, rather than relying on gradient-based (GB) methods. This is because GB approaches are influenced by the solution’s surface gradient and may only reach local optima, as opposed to global optima. Complex reservoirs have rough surfaces with high uncertainties, which hinders the traditional gradient-based method from converging to global optima. The explicit focus of this study was to examine the impact of various initial well placement distributions, the number of random solution sizes and the crossover rate on cumulative oil production, the optimization of the synthetic reservoir model created by CMG Builder, CMOST, and IMEX indicated that using a greater number of random solutions led to an increase in cumulative oil production. Despite the successful optimization, more generations are required to reach the optimal solution, while the application of GA on our synthetic model has proven efficient for well placement; however, different optimization algorithms such as the improved particle swarm (PSO) and grey wolf optimization (GWO) algorithms could be used to redefine well-placement optimization in CMG.

Ensemble variational Bayesian approximation for the inversion and uncertainty quantification of Darcy flows in heterogeneous porous media with random parameters

The inversion and uncertainty quantification of physical parameters are important for many science and engineering problems. For nonlinear parameter inversion problems of flows in hydrocarbon reservoirs, estimating the true posterior probability distribution function for the random parameter is difficult when the dimension of the parameter is relatively high. Inversion methods such as gradient-based or heuristic optimization methods searching for the maximum a posterior are generally point-estimate, while uncertainty quantification using MCMC is computationally expensive. In the current study, a new ensemble variational Bayesian approximation method is developed to estimate the posterior probability density using an ensemble of realizations regarded as a trial sample distribution. The objective is to optimize the trial sample distribution such that the evidence lower bound is maximized indicating that the distance between the trial and true posterior distribution is minimized. A subspace is built using principle component analysis based on finite samples to obtain a diagonal positive-definite covariance matrix, and ensemble-based data assimilation is used to optimize the trial distribution efficiently. Heterogeneous 2D and 3D test cases of transient single- and two-phase Darcy flows are presented for validation.

DL-RSM: Deep learning-integrated Response Surface Methodology for positive and negative-ideal environmental conditions estimation for crop yield

Understanding the most suitable and unsuitable environmental scenarios for crop production is critical to ensuring food security and sustainability. In this direction, the presented work proposes a novel approach, DL-RSM, to identify the optimized levels of environmental factors for wheat yield by integrating the Deep Learning technique with Response Surface Methodology (RSM). The uniqueness of this approach lies in its utilization of a 1-Dimensional Convolutional Neural Network model for response surface modelling. Additionally, the study has investigated the combination of numerical methods-based partial derivative calculation with a deep learning model. Specifically, our approach incorporates a symmetric difference quotient-based method for calculating partial derivatives, ultimately leading to the determination of optimal parameter values. Besides, multiple positive and negative ideal solutions are obtained from the modelled response surface using a modified gradient-based method. The effectiveness of our approach is illustrated through a case study on finding the optimized parameter values for the district-wise wheat yields of the Indo-Gangetic plains of India. The study results demonstrate the combinations of monthly rainfall levels and min. and max. temperature variations correspond to maximizing and minimizing wheat yield in the target region. The presented results provide significant insights into the relationship between wheat yields and the considered environmental factors that have not been sufficiently covered in the existing literature. The proposed methodology can benefit agricultural scientists, policymakers and farmers by offering an innovative approach to maximize crop yield and minimize resource utilization. Moreover, the study findings provide novel insights into the development of similar optimization strategies for other crops and systems.

Research on the Data-Driven Differential Equation-Solving Algorithm Based on Artificial Intelligence

Data-driven DEs has gained popularity in the past few years. This work proposes the new framework, named Adam Gannet Optimization Algorithm (AdamGOA), that combines Adam Optimization and Gannet Optimization Algorithm (GOA) to improve a stability, solve higher order Differential Equations (DE) and accuracy of DE. Adam is a first-order gradient-based methods, optimizes stochastic objectives using adaptive lower-order moments. In contrast, GOA represents a different distinct action of a gannets mathematically during foraging and is employed to facilitate exploitation and exploration. In addition, a Shepard Convolutional Neural Network (ShCNN) processed data to construct meta-data and estimate derivatives. After that, the unified integral form is established to determine optimal structure. Heterogeneous parameters are used to estimate and are labeled as constants or variables. Furthermore, the experimental findings showed that the AdamGOA_ ShCNN beat leading models in Accuracy, Convergence, and Mean Square Error (MSE), with values of 0.989, 4, and 0.539, respectively.

A Comprehensive Evaluation and Comparison of Enhanced Learning Methods

This paper provides a comprehensive evaluation and comparison of current reinforcement learning methods. By analyzing the strengths and weaknesses of the main methods, such as value function-based, strategy gradient-based, and value and strategy-based methods, the differences in their performances on standard problems and the applicable scenarios are explored. Meanwhile, other methods such as Monte Carlo Tree Search (MCTS) and evolutionary methods are also briefly introduced. Through the research and analysis in this paper, it provides reference and guidance for choosing appropriate reinforcement learning methods, and promotes the development and application of reinforcement learning techniques in practical applications.

Controlled State Transfer in Central Spin Models

In the recent literature, various aspects of the transfer of quantum states by spin chains have been thoroughly investigated. Part of the existing study is devoted to the problem of optimal control, with the goal of achieving a highly reliable information/state transfer for a given time T. In general, achieving this goal is not an easy task in the case of (open) quantum systems. Various approaches have been developed and applied, including Krotov’s method to study the problem. It is a gradient-based method used here to study the problem of state transfer control in central spin models. Our results show that with Krotov’s method, it is possible to find an optimal control form that allows for very-high-fidelity state transfer in the central spin models we have developed. Our results will be of interest for a better understanding of the non-trivial effects of the classical world on the quantum world, which have been discussed in the form of various new effects, including the Epstein effect, in the recent literature.

Improving cross-lingual low-resource speech recognition by Task-based Meta PolyLoss

Multilingual meta learning has emerged as a promising paradigm for transferring knowledge from source languages to facilitate the learning of low-resource target languages. Loss functions are a type of meta-knowledge that is crucial to the effective training of neural networks. However, the misalignment between the loss functions and the learning paradigms of meta learning degrades the network’s performance. To address this challenge, we propose a new method called Task-based Meta PolyLoss (TMPL) for meta learning. By regarding speech recognition tasks as normal samples and applying PolyLoss to the meta loss function, TMPL can be denoted as a linear combination of polynomial functions based on task query loss. Theoretical analysis shows that TMPL improves meta learning by enabling attention adjustment across different tasks, which can be tailored for different datasets. Experiments on three datasets demonstrated that gradient-based meta learning methods achieve superior performance with TMPL. Furthermore, our experiments validate that the task-based loss function effectively mitigates the misalignment issue.

The Explainability of Transformers: Current Status and Directions

An increasing demand for model explainability has accompanied the widespread adoption of transformers in various fields of applications. In this paper, we conduct a survey of the existing literature on the explainability of transformers. We provide a taxonomy of methods based on the combination of transformer components that are leveraged to arrive at the explanation. For each method, we describe its mechanism and survey its applications. We find out that attention-based methods, both alone and in conjunction with activation-based and gradient-based methods, are the most employed ones. A growing attention is also devoted to the deployment of visualization techniques to help the explanation process.

Quantum Control of Radical-Pair Dynamics beyond Time-Local Optimization

We realize arbitrary-wave-form-based control of spin-selective recombination reactions of radical pairs in the low-magnetic-field regime. To this end, we extend the gradient-ascent pulse engineering (GRAPE) paradigm to allow for optimizing reaction yields. This overcomes drawbacks of previously suggested time-local optimization approaches for the reaction control of radical pairs, which were limited to high biasing fields. We demonstrate how efficient time-global optimization of the recombination yields can be realized by gradient-based methods augmented by time blocking, sparse sampling of the yield, and evaluation of the central single time-step propagators and their Fréchet derivatives using iterated Trotter-Suzuki splittings. Results are shown for both a toy model, previously used to demonstrate coherent control of radical-pair reactions in the simpler high-field scenario and, furthermore, for a realistic exciplex-forming donor-acceptor system comprising 16 nuclear spins. This raises prospects for the spin control of actual radical-pair systems in ambient magnetic fields, by suppressing or boosting radical reaction yields using purpose-specific radio-frequency wave forms, paving the way for reaction-yield-dependent quantum magnetometry and potentially applications of quantum control to biochemical radical-pair reactions. We demonstrate the latter aspect for two radical pairs implicated in quantum biology. Published by the American Physical Society 2024

A new inexact gradient descent method with applications to nonsmooth convex optimization

The paper proposes and develops a novel inexact gradient method (IGD) for minimizing C 1 -smooth functions with Lipschitzian gradients, i.e. for problems of C 1 , 1 optimization. We show that the sequence of gradients generated by IGD converges to zero. The convergence of iterates to stationary points is guaranteed under the Kurdyka-Łojasiewicz (KL) property of the objective function with convergence rates depending on the KL exponent. The newly developed IGD is applied to designing two novel gradient-based methods of nonsmooth convex optimization such as the inexact proximal point methods (GIPPM) and the inexact augmented Lagrangian method (GIALM) for convex programs with linear equality constraints. These two methods inherit global convergence properties from IGD and are confirmed by numerical experiments to have practical advantages over some well-known algorithms of nonsmooth convex optimization.

Gradient-Based Empirical Risk Minimization Using Local Polynomial Regression

In this paper, we consider the widely studied problem of empirical risk minimization (ERM) of strongly convex and smooth loss functions using iterative gradient-based methods. A major goal of the existing literature has been to compare different prototypical algorithms, such as batch gradient descent (GD) or stochastic gradient descent (SGD), by analyzing their rates of convergence to ϵ-approximate solutions with respect to the number of gradient computations, which is also known as the oracle complexity. For example, the oracle complexity of GD is [Formula: see text], where n is the number of training samples and p is the parameter space dimension. When n is large, this can be prohibitively expensive in practice, and SGD is preferred due to its oracle complexity of [Formula: see text]. Such standard analyses only utilize the smoothness of the loss function in the parameter being optimized. In contrast, we demonstrate that when the loss function is smooth in the data, we can learn the oracle at every iteration and beat the oracle complexities of GD, SGD, and their variants in important regimes. Specifically, at every iteration, our proposed algorithm, Local Polynomial Interpolation-based Gradient Descent (LPI-GD), first performs local polynomial regression with a virtual batch of data points to learn the gradient of the loss function and then estimates the true gradient of the ERM objective function. We establish that the oracle complexity of LPI-GD is [Formula: see text], where d is the data space dimension, and the gradient of the loss function is assumed to belong to an η-Hölder class with respect to the data. Our proof extends the analysis of local polynomial regression in nonparametric statistics to provide supremum norm guarantees for interpolation in multivariate settings and also exploits tools from the inexact GD literature. Unlike the complexities of GD and SGD, the complexity of our method depends on d. However, our algorithm outperforms GD, SGD, and their variants in oracle complexity for a broad range of settings where d is small relative to n. For example, with typical loss functions (such as squared or cross-entropy loss), when [Formula: see text] for any [Formula: see text] and [Formula: see text] is at the statistical limit, our method can be made to require [Formula: see text] oracle calls for any [Formula: see text], while SGD and GD require [Formula: see text] and [Formula: see text] oracle calls, respectively. Funding: This work was supported in part by the Office of Naval Research [Grant N000142012394], in part by the Army Research Office [Multidisciplinary University Research Initiative Grant W911NF-19-1-0217], and in part by the National Science Foundation [Transdisciplinary Research In Principles Of Data Science, Foundations of Data Science].

Federated Label-Noise Learning with Local Diversity Product Regularization

Training data in federated learning (FL) frameworks can have label noise, since they must be stored and annotated on clients' devices. If trained over such corrupted data, the models learn the wrong knowledge of label noise, which highly degrades their performance. Although several FL schemes are designed to combat label noise, they suffer performance degradation when the clients' devices only have limited local training samples. To this end, a new scheme called federated label-noise learning (FedLNL) is developed in this paper. The key problem of FedLNL is how to estimate a noise transition matrix (NTM) accurately in the case of limited local training samples. If a gradient-based update method is used to update the local NTM on each client's device, it can generate too large gradients for the local NTM, causing a high estimation error of the local NTM. To tackle this issue, an alternating update method for the local NTM and the local classifier is designed in FedLNL, where the local NTM is updated by a Bayesian inference-based update method. Such an alternating update method makes the loss function of existing NTM-based schemes not applicable to FedLNL. To enable federated optimization of FedLNL, a new regularizer on the parameters of the classifier called local diversity product regularizer is designed for the loss function of FedLNL. The results show that FedLNL improves the test accuracy of a trained model by up to 25.98%, compared with the state-of-the-art FL schemes that tackle label-noise issues.

Symbolic Cognitive Diagnosis via Hybrid Optimization for Intelligent Education Systems

Cognitive diagnosis assessment is a fundamental and crucial task for student learning. It models the student-exercise interaction, and discovers the students' proficiency levels on each knowledge attribute. In real-world intelligent education systems, generalization and interpretability of cognitive diagnosis methods are of equal importance. However, most existing methods can hardly make the best of both worlds due to the complicated student-exercise interaction. To this end, this paper proposes a symbolic cognitive diagnosis~(SCD) framework to simultaneously enhance generalization and interpretability. The SCD framework incorporates the symbolic tree to explicably represent the complicated student-exercise interaction function, and utilizes gradient-based optimization methods to effectively learn the student and exercise parameters. Meanwhile, the accompanying challenge is that we need to tunnel the discrete symbolic representation and continuous parameter optimization. To address this challenge, we propose to hybridly optimize the representation and parameters in an alternating manner. To fulfill SCD, it alternately learns the symbolic tree by derivative-free genetic programming and learns the student and exercise parameters via gradient-based Adam. The extensive experimental results on various real-world datasets show the superiority of SCD on both generalization and interpretability. The ablation study verifies the efficacy of each ingredient in SCD, and the case study explicitly showcases how the interpretable ability of SCD works.

Root Cause Explanation of Outliers under Noisy Mechanisms

Identifying root causes of anomalies in causal processes is vital across disciplines. Once identified, one can isolate the root causes and implement necessary measures to restore the normal operation. Causal processes are often modelled as graphs with entities being nodes and their paths/interconnections as edge. Existing work only consider the contribution of nodes in the generative process, thus can not attribute the outlier score to the edges of the mechanism if the anomaly occurs in the connections. In this paper, we consider both individual edge and node of each mechanism when identifying the root causes. We introduce a noisy functional causal model to account for this purpose. Then, we employ Bayesian learning and inference methods to infer the noises of the nodes and edges. We then represent the functional form of a target outlier leaf as a function of the node and edge noises. Finally, we propose an efficient gradient-based attribution method to compute the anomaly attribution scores which scales linearly with the number of nodes and edges. Experiments on simulated datasets and two real-world scenario datasets show better anomaly attribution performance of the proposed method compared to the baselines. Our method scales to larger graphs with more nodes and edges.

Towards Efficient Verification of Quantized Neural Networks

Quantization replaces floating point arithmetic with integer arithmetic in deep neural network models, providing more efficient on-device inference with less power and memory. In this work, we propose a framework for formally verifying the properties of quantized neural networks. Our baseline technique is based on integer linear programming which guarantees both soundness and completeness. We then show how efficiency can be improved by utilizing gradient-based heuristic search methods and also bound-propagation techniques. We evaluate our approach on perception networks quantized with PyTorch. Our results show that we can verify quantized networks with better scalability and efficiency than the previous state of the art.

Feature Distribution Matching by Optimal Transport for Effective and Robust Coreset Selection

Training neural networks with good generalization requires large computational costs in many deep learning methods due to large-scale datasets and over-parameterized models. Despite the emergence of a number of coreset selection methods to reduce the computational costs, the problem of coreset distribution bias, i.e., the skewed distribution between the coreset and the entire dataset, has not been well studied. In this paper, we find that the closer the feature distribution of the coreset is to that of the entire dataset, the better the generalization performance of the coreset, particularly under extreme pruning. This motivates us to propose a simple yet effective method for coreset selection to alleviate the distribution bias between the coreset and the entire dataset, called feature distribution matching (FDMat). Unlike gradient-based methods, which selects samples with larger gradient values or approximates gradient values of the entire dataset, FDMat aims to select coreset that is closest to feature distribution of the entire dataset. Specifically, FDMat transfers coreset selection as an optimal transport problem from the coreset to the entire dataset in feature embedding spaces. Moreover, our method shows strong robustness due to the removal of samples far from the distribution, especially for the entire dataset containing noisy and class-imbalanced samples. Extensive experiments on multiple benchmarks show that FDMat can improve the performance of coreset selection than existing coreset methods. The code is available at https://github.com/successhaha/FDMat.

Fast Coherent Video Style Transfer via Flow Errors Reduction

For video style transfer, naively applying still image techniques to process a video frame-by-frame independently often causes flickering artefacts. Some works adopt optical flow into the design of temporal constraint loss to secure temporal consistency. However, these works still suffer from incoherence (including ghosting artefacts) where large motions or occlusions occur, as optical flow fails to detect the boundaries of objects accurately. To address this problem, we propose a novel framework which consists of the following two stages: (1) creating new initialization images from proposed mask techniques, which are able to significantly reduce the flow errors; (2) process these initialized images iteratively with proposed losses to obtain stylized videos which are free of artefacts, which also increases the speed from over 3 min per frame to less than 2 s per frame for the gradient-based optimization methods. To be specific, we propose a multi-scale mask fusion scheme to reduce untraceable flow errors, and obtain an incremental mask to reduce ghosting artefacts. In addition, a multi-frame mask fusion scheme is designed to reduce traceable flow errors. In our proposed losses, the Sharpness Losses are used to deal with the potential image blurriness artefacts over long-range frames, and the Coherent Losses are performed to restrict the temporal consistency at both the multi-frame RGB level and Feature level. Overall, our approach produces stable video stylization outputs even in large motion or occlusion scenarios. The experiments demonstrate that the proposed method outperforms the state-of-the-art video style transfer methods qualitatively and quantitatively on the MPI Sintel dataset.

Modeling and multi-objective optimization of forward osmosis process

In order to ensure efficient wastewater treatment and seawater desalination, adequate modeling and optimization of the forward osmosis (FO) process has the potential to be very helpful. This paper deals with the FO model parameters calibration and FO process optimization by a gradient-based optimization method. For this purpose, an upgraded FO model, which involves temperature- and agent-dependent parameters, was developed. The FO model calibration was done using NaCl as agents in draw solution, while MgCl2 was used for model validation. The agreements between simulated and measured FO performance were satisfactory; relative index of agreement are higher than 0.99. By using the proposed FO model, the optimization of FO process conditions was performed with various definitions of the objective and constraint functions. In case of maximizing the water flux, minimizing reverse solute flux, and fulfilling the required constraints, the ratio of water flux and reverse solute flux increased up to 40 % for NaCl and up to 20 % for MgCl2; meanwhile the effective osmotic pressure difference was improved 2-times for NaCl and up to 3.8-times for MgCl2. The optimization process proved to be stable and efficient and can easily be adapted or upgraded for more complex dynamic FO modeling.

Maximum likelihood localization of a network of moving agents from ranges, bearings and velocity measurements

Localization is a fundamental enabler technology for many applications, like vehicular networks, IoT, and even medicine. While Global Navigation Satellite Systems solutions offer great performance, they are unavailable in scenarios like indoor or underwater environments, and, for large networks, the instrumentation cost is prohibitive. We develop a localization algorithm from ranges and bearings, suitable for generic mobile networks. Our algorithm is built on a tight convex relaxation of the Maximum Likelihood position estimator. To serve positioning to mobile agents, a horizon-based version is developed accounting for velocity measurements at each agent. To solve the convex problem, a distributed gradient-based method is provided. This constitutes an advantage over centralized approaches, which usually exhibit high latency for large networks and present a single point of failure. Additionally, the algorithm estimates all required parameters and effectively becomes parameter-free. Our solution to the dynamic network localization problem is theoretically well-founded and still easy to understand. We obtain a parameter-free, outlier-robust and trajectory-agnostic algorithm, with nearly constant positioning error regardless of the trajectories of agents and anchors, achieving better or comparable performance to state-of-the-art methods, as our simulations show. Furthermore, the method is distributed, convex and does not require any particular anchor configuration.

Robust and accurate corneal interfaces segmentation in 2D and 3D OCT images.

Segmentation of corneal layer interfaces in optical coherence tomography (OCT) images is important for diagnostic and surgical purposes, while manual segmentation is a time-consuming and tedious process. This paper presents a novel technique for the automatic segmentation of corneal layer interfaces using customized initial layer estimation and a gradient-based segmentation method. The proposed method was also extended to three-dimensional OCT images. Validation was performed on two corneal datasets, one with 37 B-scan images of healthy human eyes and the other with a 3D volume scan of a porcine eye. The approach showed robustness in extracting different layer boundaries in the low-SNR region with lower computational cost but higher accuracy compared to existing techniques. It achieved segmentation errors below 2.1 pixels for both the anterior and posterior layer boundaries in terms of mean unsigned surface positioning error for the first dataset and 2.6 pixels (5.2 μm) for segmenting all three layers that can be resolved in the second dataset. On average, it takes 0.7 and 0.4 seconds to process a cross-sectional B-scan image for datasets one and two, respectively. Our comparative study also showed that it outperforms state-of-the-art methods for quantifying layer interfaces in terms of accuracy and time efficiency.