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Unveiling the optimization process of physics informed neural networks: How accurate and competitive can PINNs be?

JOURNAL OF COMPUTATIONAL PHYSICS 2025年 523卷

作者： Urban, Jorge F. Stefanou, Petros Pons, Jose A. Univ Alacant Dept Fis Aplicada Ap Correus 99 Alacant 03830 Comunitat Valen Spain Univ Valencia Dept Astron & Astrofis Dr Moliner 50 Valencia 46100 Comunitat Valen Spain

This study investigates the potential accuracy boundaries of physics-informed neural networks, contrasting their approach with previous similar works and traditional numerical methods. We find that selecting improved optimization algorithms significantly enhances the accuracy of the results. Simple modifications to the loss function may also improve precision, offering an additional avenue for enhancement. Despite optimization algorithms having a greater impact on convergence than adjustments to the loss function, practical considerations often favor tweaking the latter due to ease of implementation. On a global scale, the integration of an enhanced optimizer and a marginally adjusted loss function enables a reduction in the loss function by several orders of magnitude across diverse physical problems. Consequently, our results obtained using compact networks (typically comprising 2 or 3 layers of 20-30 neurons) achieve accuracies comparable to finite difference schemes employing thousands of grid points. This study encourages the continued advancement of PINNs and associated optimization techniques for broader applications across various fields.

关键词： Physics-informed neural networks optimization algorithms Non-linear PDEs

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Multiscale quantum approximate optimization algorithm

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Physical Review A 2025年第1期111卷 012427-012427页

作者： Ping Zou Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials School of Optoelectronic Science and Engineering South China Normal University Guangzhou 510006 China

The quantum approximate optimization algorithm (QAOA) is one of the canonical algorithms designed to find approximate solutions for combinatorial optimization problems on current noisy intermediate-scale quantum (NISQ) devices. The primary focus of ongoing research is to exhibit its speed advantage over classical algorithms. However, the performance of QAOA is restricted at lower depths, while higher depths are limited by current experimental techniques. We propose an algorithm that amalgamates the capabilities of QAOA and the real-space renormalization group transformation. Numerical simulations indicate that our proposed algorithm can deliver precise solutions for specific randomly generated instances using QAOA at shallow depths, even at the lowest depth. This algorithm is particularly suitable for current NISQ devices, offering the potential to demonstrate a quantum advantage.

关键词： optimization algorithms

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Data-driven optimization reveals the impact of Urban Heat Island effect on the retrofit potential of building envelopes

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BUILDING AND ENVIRONMENT 2025年 269卷

作者： Li, Renge Huang, Chenyu Xin, Weilin Ye, Jiahong Zhang, Xue Qu, Rong Wang, Jinyu Yuan, Liang Yao, Jiawei China Construct Sci & Ind Corp LTD Shenzhen Peoples R China Tongji Univ Coll Architecture & Urban Planning Shanghai Peoples R China Natl Univ Singapore Dept Architecture Singapore Singapore

The urban heat island (UHI) effect significantly impacts building energy consumption, but its effect on energy retrofit potential remains unclear. Here, we propose a data-driven surrogate optimization framework to assess the energy-saving potential of improving building envelope thermal performance in 101 public buildings in Shenzhen. The framework integrates batch building energy modeling, ensemble learning surrogate model training, and multi-objective optimization. The potential changes in building loads resulting from different parameter combinations are defined as energy-saving potential. We use the Urban Weather Generator to adjust typical meteorological year data and account for UHI effects in energy modeling. The results indicate that neglecting the UHI effect in Shenzhen overestimates the potential for building energy retrofitting by approximately 25.2 % (office buildings:-8.96 %, commercial buildings: 60.7 %). Among the nine thermal retrofitting parameters, the heat transfer coefficient of windows contributes the most to the energy-saving potential. Considering the UHI effect or not leads to significant differences in retrofitting strategies and optimal retrofitting parameter configurations. These findings underscore the importance of considering the UHI effect and interactions between buildings in energy retrofit modeling and decision-making processes to formulate precise retrofit strategies and schemes.

关键词： Urban heat island effect Building energy retrofit Machine learning optimization algorithms

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Modeling and optimization of anaerobic digestion technology: Current status and future outlook

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PROGRESS IN ENERGY AND COMBUSTION SCIENCE 2025年 106卷

作者： Kegl, Tina Jimenez, Eloisa Torres Kegl, Breda Kralj, Anita Kovac Kegl, Marko Univ Maribor Fac Chem & Chem Engn Maribor Slovenia Univ Jaen Dept Mech & Min Engn Jaen Spain Univ Maribor Fac Mech Engn Maribor Slovenia

Anaerobic digestion (AD) is an important technology that can be engaged to produce renewable energy and valuable products from organic waste while reducing the net greenhouse gas emissions. Due to the AD process complexity, further development of AD technology goes hand in hand with the advancement of underlying mathematical models and optimization techniques. This paper presents a comprehensive and critical review of current AD process modeling and optimization techniques as well as various aspects of further processing of AD products. The most important mechanistically inspired, kinetic, and phenomenological AD models and the most frequently used deterministic and stochastic methods for AD process optimization are addressed. The foundations, properties, and features of these models and methods are highlighted, discussed, and compared with respect to advantages, disadvantages, and various performance metrics;the models are also ranked with respect to adequately introduced criteria. Since AD process optimization affects heavily the required treatment and utilization of AD products, biogas and digestate utilization in the production of renewable energy and other valuable products is also addressed. Furthermore, special attention is devoted to the challenges and future research needs related to AD modeling and optimization, such are modeling issues related to foaming and microbial activities, AD model parameters calibration, CFD simulation challenges, availability of experimental data, and optimization of the AD process with respect to further biogas and digestate utilizations. As current research results indicate, further progress in these areas could notably improve AD modeling robustness and accuracy as well as AD optimization performance.

关键词： Renewable energy Anaerobic digestion Biogas plant Mathematical models optimization algorithms Products utilization

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A two-stage optimization strategy for VPP trading in multi-market considering setting method and marginal revenue and expenditure of standby capacity

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JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 2025年第1期17卷

作者： Wang, Yongli Jiang, Sichong Zhou, Hanzhi Zhu, Mingyang Zhang, Yunfei North China Elect Power Univ Sch Econ & Management Beijing 102206 Peoples R China

Virtual power plant (VPP) with a high percentage of flexibility resources has issues that need to be addressed, such as high source-load volatility and limited scope to participate in multi-market bids. Therefore, this paper proposes a VPP standby capacity setting method based on normal distribution framework and Bayesian parameter optimization. Through the marginal revenue and expenditure of standby capacity analysis, this paper constructs a two-stage optimization strategy for VPP trading in multi-market considering double uncertainty, which is solved by the Improved Multi-Objective Squirrel Search Algorithm (IMSSA). Compared to the traditional program, the VPP's participation in the day-ahead spot bidding increased by 5.97% and 2.48%, respectively, total revenue increased by 17.41% and 12.97%, respectively, reliability increased by 0.21%, and overall energy efficiency increased by 10%. Compared to Squirrel Search Algorithm and Particle Swarm optimization Algorithm, IMSSA improves the optimal revenue by 1.03% and 1.91%, and the convergence speed by 24.24% and 38.01%, respectively.

关键词： optimization algorithms

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An enhanced Kepler optimization algorithm with global attraction model and dynamic neighborhood search for global optimization and engineering problems

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Mathematics and Computers in Simulation 2025年 237卷 107-144页

作者： Liang, Ziyuan Wang, Zhenlei Key Laboratory of Smart Manufacturing in Energy Chemical Process Ministry of Education East China University of Science and Technology Shanghai200237 China

The Kepler optimization algorithm (KOA) is a recently proposed physics-based algorithm inspired by Kepler's laws. Despite the strong competitiveness of KOA relative to established algorithms, it faces challenges such as limited search capability, premature convergence, and low convergence accuracy in solving complex optimization problems. To address these shortcomings, we propose an enhanced KOA (EKOA) that integrates a global attraction model, a dynamic neighborhood search operator, and a local update strategy with multi-elite guided differential mutation. Firstly, EKOA introduces an innovative global attraction model to facilitate information exchange among individuals, aiming to extend the search space and improve search efficiency. Secondly, a dynamic neighborhood search operator is designed to weaken the influence of the best individual on the current position updates, thereby mitigating premature convergence. Finally, a local update strategy with multi-elite guided differential mutation is developed to provide new evolutionary opportunities for individuals, ensure evolution in a more favorable direction, and prevent stagnation of the optimal solution during the optimization process. The performance of EKOA is evaluated by comparing it with 12 state-of-the-art algorithms using the CEC2017, CEC2020, and CEC2022 benchmark test suites. Experimental results and statistical analysis substantiate the superiority of EKOA. Additionally, the practical applicability of EKOA is demonstrated through four real-world engineering problems. In conclusion, EKOA not only effectively enhances the performance of the original KOA but also emerges as a powerful and promising algorithm for solving complex engineering problems. © 2025 International Association for Mathematics and Computers in Simulation (IMACS)

关键词： optimization algorithms

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Improved Multi-Objective Coati optimization Algorithm for Optimizing Energy Efficiency and Thermal Comfort in Chilled Water Systems

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Journal of Thermal Science and Engineering Applications 2025年第4期17卷 041009页

作者： Feng, Zengxi Liu, Xuefeng Zhang, Xian Lu, Shuai Wang, Bo Liu, Li Quan, Wei An, Jianhu Wang, Chang Kang, Limin School of Building Services Science and Engineering Xi’an University of Architecture and Technology Xi'an Shaanxi 710055 China State Grid Xi’an Electric Power Supply Company Xi'an Shaanxi 710032 China College of Information and Control Engineering Xi’an University of Architecture and Technology Xi'an Shaanxi 710311 China

As the main energy consumption part of the central air-conditioning systems, the energy saving of the chilled water system is particularly crucial. This system realizes heat exchange with indoor air by delivering chilled water to air-conditioning units, effectively regulating indoor temperature and humidity to ensure thermal comfort. In this article, an improved multi-objective coati optimization algorithm (IMOCOA) is used to optimize the operating parameters and thermal comfort environment parameters of chilled water systems to improve thermal comfort and reduce energy consumption. The algorithm introduces chaotic mapping to enhance search diversity, balances global and local search capabilities through Levy flight and Gauss variation strategies, and uses location greedy choices to help coatis jump out of local optima. To verify the optimization effect of IMOCOA, a multi-objective optimization model was established, combining the energy consumption model of the chilled water system and the simplified thermal comfort model. Key parameters, including chilled water supply temperature, pump speed ratio, indoor temperature, and relative humidity, are optimized. The simulation results from the experiments show that the average energy-saving rate of the chilled water system using IMOCOA is 7.8% and thermal comfort is improved by 19.6%. Compared to other optimization algorithms, this method demonstrates a better optimization effect.

关键词： multi-objective coati optimization algorithm optimization algorithms Energy consumption energy efficiency Water algorithms Flight indoor thermal comfort Modeling Temperature chilled water system parameter optimization optimization Pareto optimization energy systems thermal systems Air conditioning Pumps Energy efficiency

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A Julia Package for Polyhedral Omega and Applications

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ACM Communications in Computer Algebra 2025年第2期58卷 39-42页

作者： Ayylldlz, Tülay Demirel, Deniz Naz Tapan, Ismail Zafeirakopoulos, Zafeirakis Department of Computer Engineering Gebze Technical University Gebze Kocaeli Turkey Department of Philosophy Middle East Technical University Ankara Turkey Section of Mathematics University of Geneva Geneva Switzerland

This paper introduces a Julia package for tackling linear Diophantine systems and related optimization problems using the Polyhedral Omega algorithm. The package integrates partition analysis and polyhedral geometry to offer efficient solutions. *** package implements the Polyhedral Omega algorithm, and *** provides optimization enhancements. © 2025 Copyright is held by the owner/author(s).

关键词： optimization algorithms

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Research on Information Dissemination and Monitoring of Online Public Opinion Under an Intelligent Algorithm

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International Journal of Network Security 2025年第2期27卷 330-337页

作者： Zhang, Huidan Li, Qingjuan Shen, Hongyan Xia Qing Communication School Handan University No. 530 North College Road Hanshan District Hebei Handan056000 China School of Chinese and History Handan University Hebei Handan056005 China Departpment of Propaganda Handan University Hebei Handan056005 China

Under the influence of network popularization, the information dissemination speed of online public opinion is faster, and public opinion events appear more frequently. It is necessary to effectively monitor them. This paper firstly analyzed the information dissemination of online public opinion, selected some relevant indicators, and designed an improved sooty tern optimization algorithm-back propagation neural network (ISTOABPNN) algorithm to realize online public opinion monitoring. Through tests on three test functions, it was found that compared with the SOA, GWO, and other optimization algorithms, the ISTOA obtained better solutions, which verified its optimization ability. Through a case analysis, it was found that compared with the support vector machine and BPNN algorithms, the output result of the ISTOA-BPNN algorithm was in better agreement with the expected output. The accuracy of the ISTOA was 95% for 20 test samples. The experimental results verify that the ISTOA-BPNN algorithm is reliable in online public opinion monitoring and can be applied in practice. © (2024), (Femto Technique Co. Ltd.). All Rights Reserved.

关键词： optimization algorithms

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Accelerated Distributed Aggregative optimization

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IEEE Transactions on Automatic Control 2025年

作者： Liu, Jiaxu Chen, Song Cai, Shengze Xu, Chao Chu, Jian Zhejiang University School of Mathematical Sciences Zhejiang Hangzhou310027 China Zhejiang University State Key Laboratory of Industrial Control Technology Institute of Cyber-Systems and Control Zhejiang Hangzhou310027 China

This paper delves into the investigation of a distributed aggregative optimization problem within a network. In this scenario, each agent possesses its own local cost function, which relies not only on the local state variable but also on an aggregated function of state variables from all agents. To expedite the optimization process, we amalgamate the heavy ball and Nesterov's accelerated method with distributed aggregative gradient tracking, resulting in the proposal of two innovative algorithms, aimed at resolving the distributed aggregative optimization problem. Our analysis demonstrates that the proposed algorithms can converge to an optimal solution at a global linear convergence rate when the objective function is strongly convex with the Lipschitz-continuous gradient, and when the parameters (e.g., step size and momentum coefficients) are chosen within specific ranges. Additionally, we present several numerical experiments to verify the effectiveness, robustness and superiority of our proposed algorithms. © 2025 IEEE.

关键词： optimization algorithms

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