Bettine G. van Willigen , Nick van Osta , M. Beatrijs van der Hout-van der Jagt , Frans N. van de Vosse , Wouter Huberts
{"title":"A virtual population cohort approach for fetal cardiac valve modeling","authors":"Bettine G. van Willigen , Nick van Osta , M. Beatrijs van der Hout-van der Jagt , Frans N. van de Vosse , Wouter Huberts","doi":"10.1016/j.jocs.2025.102606","DOIUrl":"10.1016/j.jocs.2025.102606","url":null,"abstract":"<div><h3>Introduction:</h3><div>Mathematical models of fetal cardiovascular physiology provide valuable insights when studying the fetal circulatory system. In 0D and 1D models, fetal cardiac valves are often represented as diodes, offering simplicity and scalability but failing to capture realistic valvular behavior and can result in unrealistic pressure drops. More accurate models based on the Bernoulli equation capture valvular dynamic behavior more realistically, but they require constant tuning for specific cases, challenging simulation of fetal cardiac growth.</div></div><div><h3>Method:</h3><div>This study introduces a virtual population cohort approach informed by Bayesian inference as a solution to this challenge. By applying this method to a standardized aortic valve model of a 40-week-old fetus, it demonstrates its effectiveness in identifying input parameter distributions that reflect healthy fetal aortic valve behavior.</div></div><div><h3>Results:</h3><div>The approach involves defining a template model and determining an appropriate parameter space to simulate physiological behavior. Bayesian inference method facilitates identification of these parameters, resulting in a virtual population cohort that closely represents real physiological relevant fetal aortic valve conditions.</div></div><div><h3>Conclusion:</h3><div>The findings show that this approach successfully identifies a virtual population cohort of the fetal aortic valve model, including uncertainty of model parameters and their correlations with model outcomes. This approach offers a widely applicable framework with potential for models that can adapt to the evolving physiological conditions of fetal growth.</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"88 ","pages":"Article 102606"},"PeriodicalIF":3.1,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143917202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Error-based correlation coefficient: An alternative to combine error and coefficient of correlation and its application in geophysical data","authors":"Waskito Pranowo , Adhitya Ryan Ramadhani","doi":"10.1016/j.jocs.2025.102611","DOIUrl":"10.1016/j.jocs.2025.102611","url":null,"abstract":"<div><div>The coefficient of correlation and error values are two standard metrics for determining the similarity between two data sets. Correlated errors in experimental data are a common problem that is often overlooked. In addition, traditional error estimation approaches do not consider pattern similarity. An error-based method for estimating correlation coefficients is proposed, combining the fundamental principles of ' 'Pearson's correlation coefficient and error. This method represents a generalised form of the concordance correlation coefficient (CCC). The experiment with synthetic geophysical data pairs demonstrates that the suggested method effectively evaluates pattern and amplitude similarity. The proposed error-based correlation coefficient is comparable to the concordance coefficient of correlation but with some modifications. These modifications increase the new method's sensitivity to scale shifting, a vital element in geophysical data processing and analysis.</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"88 ","pages":"Article 102611"},"PeriodicalIF":3.1,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143899651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Carlos Carrillo, Tomàs Margalef, Antonio Espinosa, Ana Cortés
{"title":"Edge computing driven forest fire spread simulation: An energy-aware study","authors":"Carlos Carrillo, Tomàs Margalef, Antonio Espinosa, Ana Cortés","doi":"10.1016/j.jocs.2025.102605","DOIUrl":"10.1016/j.jocs.2025.102605","url":null,"abstract":"<div><div>An accurate and fast prediction of forest fire evolution is a crucial issue to minimize its impact. One of the challenges facing forest fire spread simulators is the uncertainty surrounding the input data. While high-performance computing (HPC) platforms help reduce these uncertainties, their accessibility during emergencies is limited due to infrastructure constraints. real time data collection using sensors onboard Unmanned Aerial Vehicles (UAVs) in real time can significantly reduce their uncertainty. However, transmitting this data to HPC environments and returning the results to firefighters remains difficult, especially in areas with poor connectivity. We propose using Edge Computing to address these challenges, leveraging low-consumption GPU-accelerated embedded systems for <em>in situ</em> data processing and wildfire spread simulation. For simulation purposes, the FARSITE forest fire spread simulator has been used. This work aims to demonstrate the feasibility of leveraging Embedded Systems with low-consumption GPUs to simulate <em>short-term</em> forest fire spread evolution (up to 5 hours) at high resolution (5 meters). The obtained results highlight that these devices can gather data, simulate the hazard, and deliver prediction results <em>in situ</em>, even without connectivity, opening up the possibility of monitoring and predicting fire behavior at high resolution without employing HPC platforms.</div><div>(This paper is an extension version of the best poster paper award in ICCS-2024 entitled “From HPC to Edge Computing: A new Paradigm in Forest Fire Spread Simulation”.)</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"88 ","pages":"Article 102605"},"PeriodicalIF":3.1,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143903471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"New globally Lipschitz no-equilibrium fractional order systems and control of hidden memory chaotic attractors","authors":"Bichitra Kumar Lenka, Ranjit Kumar Upadhyay","doi":"10.1016/j.jocs.2025.102603","DOIUrl":"10.1016/j.jocs.2025.102603","url":null,"abstract":"<div><div>In continuous-time no-equilibrium nonlinear fractional order systems, bounded attractors are often termed as hidden memory attractors that can provide very complicated dynamics, and their localization seems crucial. In many engineering applications of interest, a famous problem deals with the identification of globally Lipschitz no-equilibrium nonlinear fractional order systems that can produce hidden memory chaotic attractors that remain unknown. We address two new no-equilibrium 3-state variables nonlinear fractional order systems; one is non-autonomous and another is autonomous, where both systems nonlinearity satisfy the global Lipschitz condition. It has been discovered that such a non-autonomous system gives rise to a globally Lipschitz hidden memory chaotic attractor when system orders <span><math><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>998</mn><mo>,</mo><msub><mrow><mi>δ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>997</mn><mo>,</mo><msub><mrow><mi>δ</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>999</mn></mrow></math></span>, also when <span><math><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>999</mn><mo>,</mo><msub><mrow><mi>δ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>999</mn><mo>,</mo><msub><mrow><mi>δ</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>999</mn></mrow></math></span>. The autonomous system produces a globally Lipschitz hidden memory chaotic attractor when system orders become <span><math><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>997</mn></mrow></math></span>, <span><math><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>998</mn></mrow></math></span>, <span><math><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>999</mn></mrow></math></span> as well as <span><math><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>997</mn></mrow></math></span>, <span><math><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>997</mn></mrow></math></span>, <span><math><mrow><msub><mrow><mi>δ</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>997</mn></mrow></math></span>. In many applications of interest, it is often needed to have globally Lipschitz hidden memory chaotic attractors and reference control goal dynamics that seem crucial to widen the use of important nonlinear systems. We introduce a novel control strategy to address controlling hidden memory chaotic attractors found in such systems that seem impossible to control in many control design problems. Numerical simulations, including theoretical analysis, illustrate the effective","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"88 ","pages":"Article 102603"},"PeriodicalIF":3.1,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143899650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alvaro Magdaleno , José María García-Terán , César Peláez-Rodríguez , Guillermo Fernández , Antolin Lorenzana
{"title":"Generating vertical ground reaction forces using a stochastic data-driven model for pedestrian walking","authors":"Alvaro Magdaleno , José María García-Terán , César Peláez-Rodríguez , Guillermo Fernández , Antolin Lorenzana","doi":"10.1016/j.jocs.2025.102602","DOIUrl":"10.1016/j.jocs.2025.102602","url":null,"abstract":"<div><div>A novel time-domain approach to the characterization of the forces induced by a pedestrian is proposed. It focuses on the vertical component while walking, but thanks to how it is conceived, the algorithm can be easily adapted to other activities or any other force component. The work has been developed from the statistical point of view, so a stochastic data-driven model is finally obtained after the algorithm is applied to a set of experimentally measured steps. The model is composed of two mean vectors and their corresponding covariance matrices to represent the steps, as well as some more means and standard deviations to account for the step scaling and double support phase, under the assumption that the random variables follow normal distributions. Velocity and step length are also provided, so the model and the latter data enable the realistic generation of virtual gaits. Some application examples at different walking paces are shown, in which comparisons between the original steps and a set of virtual ones are performed to show the similarities between both. For reproducibility purposes, the data and the developed algorithm have been made available.</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"88 ","pages":"Article 102602"},"PeriodicalIF":3.1,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chongjiexin Jia , Tuanjie Li , Hangjia Dong , Chao Xie , Wenxuan Peng , Yuming Ning
{"title":"A leading adaptive activation function for deep reinforcement learning","authors":"Chongjiexin Jia , Tuanjie Li , Hangjia Dong , Chao Xie , Wenxuan Peng , Yuming Ning","doi":"10.1016/j.jocs.2025.102608","DOIUrl":"10.1016/j.jocs.2025.102608","url":null,"abstract":"<div><div>The activation function provides deep reinforcement learning with the capability to solve nonlinear problems. However, traditional activation functions have fixed parameter settings and cannot be adjusted adaptively based on constantly changing environmental conditions. This limitation frequently leads to slow convergence speed and inadequate performance of trained agents when confronted with highly complex nonlinear problems. This paper proposes a new method to enhance the ability of reinforcement learning to handle nonlinear problems. This method is mainly divided into two parts. Firstly, an activation function parameter initialization strategy based on environmental characteristics is adopted. Secondly, the Adam algorithm is used to dynamically update the activation function parameters. The activation function proposed in this paper is compared with both traditional activation functions and state-of-the-art activation functions through two experiments. Experimental data show that compared to ReLu, TanH, APA, and EReLu, its convergence speed in DQN tasks is improved by 3.89, 1.29, 0.981, and 2.173 times, respectively, and in SAC tasks, it is improved by 1.504, 1.013, 1.017, and 1.131 times, respectively. The results demonstrate that when the agent utilizes LaTanH as the activation function, it exhibits significant advantages in terms of convergence speed and performance and alleviates the problems of bilateral saturation and gradient vanishing.</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"88 ","pages":"Article 102608"},"PeriodicalIF":3.1,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jeremy J. Williams , Felix Liu , Jordy Trilaksono , David Tskhakaya , Stefan Costea , Leon Kos , Ales Podolnik , Jakub Hromadka , Pratibha Hegde , Marta Garcia-Gasulla , Valentin Seitz , Frank Jenko , Erwin Laure , Stefano Markidis
{"title":"Accelerating Particle-in-Cell Monte Carlo simulations with MPI, OpenMP/OpenACC and Asynchronous Multi-GPU Programming","authors":"Jeremy J. Williams , Felix Liu , Jordy Trilaksono , David Tskhakaya , Stefan Costea , Leon Kos , Ales Podolnik , Jakub Hromadka , Pratibha Hegde , Marta Garcia-Gasulla , Valentin Seitz , Frank Jenko , Erwin Laure , Stefano Markidis","doi":"10.1016/j.jocs.2025.102590","DOIUrl":"10.1016/j.jocs.2025.102590","url":null,"abstract":"<div><div>As fusion energy devices advance, plasma simulations play a critical role in fusion reactor design. Particle-in-Cell Monte Carlo simulations are essential for modeling plasma-material interactions and analyzing power load distributions on tokamak divertors. Previous work (Williams, 2024) introduced hybrid parallelization in BIT1 using MPI and OpenMP/OpenACC for shared-memory and multicore CPU processing. In this extended work, we integrate MPI with OpenMP and OpenACC, focusing on asynchronous multi-GPU programming with OpenMP Target Tasks using the “nowait” and “depend” clauses, and OpenACC Parallel with the “async(n)” clause. Our results show significant performance improvements: 16 MPI ranks plus OpenMP threads reduced simulation runtime by 53% on a petascale EuroHPC supercomputer, while the OpenACC multicore implementation achieved a 58% reduction compared to the MPI-only version. Scaling to 64 MPI ranks, OpenACC outperformed OpenMP, achieving a 24% improvement in the particle mover function. On the HPE Cray EX supercomputer, OpenMP and OpenACC consistently reduced simulation times, with a 37% reduction at 100 nodes. Results from MareNostrum 5, a pre-exascale EuroHPC supercomputer, highlight OpenACC’s effectiveness, with the “async(n)” configuration delivering notable performance gains. However, OpenMP asynchronous configurations outperform OpenACC at larger node counts, particularly for extreme scaling runs. As BIT1 scales asynchronously to 128 GPUs, OpenMP asynchronous multi-GPU configurations outperformed OpenACC in runtime, demonstrating superior scalability, which continues up to 400 GPUs, further improving runtime. Speedup and parallel efficiency (PE) studies reveal OpenMP asynchronous multi-GPU achieving an 8.77<span><math><mo>×</mo></math></span> speedup (54.81% PE) and OpenACC achieving an 8.14<span><math><mo>×</mo></math></span> speedup (50.87% PE) on MareNostrum 5, surpassing the CPU-only version. At higher node counts, PE declined across all implementations due to communication and synchronization costs. However, the asynchronous multi-GPU versions maintained better PE, demonstrating the benefits of asynchronous multi-GPU execution in reducing scalability bottlenecks. While the CPU-only implementation is faster in some cases, OpenMP’s asynchronous multi-GPU approach delivers better GPU performance through asynchronous data transfer and task dependencies, ensuring data consistency and avoiding race conditions. Using NVIDIA Nsight tools, we confirmed BIT1’s overall efficiency for large-scale plasma simulations, leveraging current and future exascale supercomputing infrastructures. Asynchronous data transfers and dedicated GPU assignments to MPI ranks enhance performance, with OpenMP’s asynchronous multi-GPU implementation utilizing OpenMP Target Tasks with “nowait” and “depend” clauses outperforming other configurations. This makes OpenMP the preferred application programming interface when performance portability, high thr","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"88 ","pages":"Article 102590"},"PeriodicalIF":3.1,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Spline tie-decay temporal networks","authors":"Chanon Thongprayoon , Naoki Masuda","doi":"10.1016/j.jocs.2025.102591","DOIUrl":"10.1016/j.jocs.2025.102591","url":null,"abstract":"<div><div>Increasing amounts of data are available on temporal, or time-varying, networks. There have been various representations of temporal network data each of which has different advantages for downstream tasks such as mathematical analysis, visualizations, agent-based and other dynamical simulations on the temporal network, and discovery of useful structure. The tie-decay network is a representation of temporal networks whose advantages include the capability of generating continuous-time networks from discrete time-stamped contact event data with mathematical tractability and a low computational cost. However, the current framework of tie-decay networks is limited in terms of how each discrete contact event can affect the time-dependent tie strength (which we call the kernel). Here we extend the tie-decay network model in terms of the kernel. Specifically, we use a cubic spline function for modeling short-term behavior of the kernel and an exponential decay function for long-term behavior, and graft them together. This spline version of tie-decay network enables delayed and <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-continuous interaction rates between two nodes while it only marginally increases the computational and memory burden relative to the conventional tie-decay network. We show mathematical properties of the spline tie-decay network and numerically showcase it with three tasks: network embedding, a deterministic opinion dynamics model, and a stochastic epidemic spreading model.</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"88 ","pages":"Article 102591"},"PeriodicalIF":3.1,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143912810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An embedding-based method for inferring novel interlayers in multilayer networks","authors":"Pietro Cinaglia","doi":"10.1016/j.jocs.2025.102592","DOIUrl":"10.1016/j.jocs.2025.102592","url":null,"abstract":"<div><div>In biology, networks are applied for modelling heterogeneous entities (e.g., gene, disease, drugs) and their own interactions. In this context, the multilayer networks allow modelling multiple types of interactions on independent layers, which are in turn interconnected by interlayer edges. Link prediction is a crucial task, e.g., which allows discovering of novel relationships between biological entities (e.g., proteins and genes). The state-of-the-art reports several methods focused on link prediction. However, no one is specifically designed for inferring entire interlayers between the unconnected layers of a multilayer network. In this paper, we presented an in-house method for the inference of entire interlayers from pairs of unconnected layers of interest. The proposed method exploits two main approaches: the first constructs a set of primitive links between unconnected layers of interest, based on properties intrinsic to graph network models; the second refines these based on more complex features denoted from node embeddings to infer the candidate interlayer edges, which ultimately constitute the resulting interlayer. In our experimentation, the proposed method has exhibited an effective capability in inferring novel interlayers, even when the number of nodes within the layers of interest increase. Performance was evaluated by using several well-known Key Performance Indicators. Briefly, results showed an improvement by +15.73% and +116.38% in terms of F1-Score and MCC, respectively. Furthermore, the accuracy improved on average by +46.30%, as can also be seen from ROC-AUC and PR-AUC, which showed +44.48% and +38.45%, respectively.</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"88 ","pages":"Article 102592"},"PeriodicalIF":3.1,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143859557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A three-stage framework combining neural networks and Monte Carlo tree search for approximating analytical solutions to the Thomas–Fermi equation","authors":"Hassan Dana Mazraeh , Kourosh Parand","doi":"10.1016/j.jocs.2025.102582","DOIUrl":"10.1016/j.jocs.2025.102582","url":null,"abstract":"<div><div>This study presents an innovative framework that integrates physics-informed neural networks with Monte Carlo tree search to develop an approximate analytical solution for the Thomas–Fermi equation. The framework operates in three stages. Initially, a physics-informed neural network is used to generate a numerical approximation of the Thomas–Fermi equation. Subsequently, the Monte Carlo tree search algorithm identifies an analytical expression that closely approximates the numerical solution from the first stage, resulting in an initial analytical solution. In the final stage, the physics-informed neural network is employed once more to optimize the coefficients of the expression found by Monte Carlo tree search, further refining the accuracy of the solution. Experimental results validate the effectiveness of this approach, demonstrating its capability to solve the challenging and nonlinear Thomas–Fermi equation, for which an exact analytical solution is not available.</div></div>","PeriodicalId":48907,"journal":{"name":"Journal of Computational Science","volume":"87 ","pages":"Article 102582"},"PeriodicalIF":3.1,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143816994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}