[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117747-en":3,"doc-seo-117747-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},117747,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","PDEBENCH - An Extensive Benchmark for Scientific Machine Learning","Machine learning-based modeling of physical systems has accelerated in recent years, yet benchmarks for Scientific ML remain limited in usability, breadth, and representativeness. PDEBENCH introduces a benchmark suite of time-dependent PDE simulation tasks, delivering both code and data to compare new ML models with classical numerical solvers and ML baselines. It expands PDE coverage, provides larger ready-to-use datasets over varied initial/boundary conditions and parameters, and includes extensible implementations with user-friendly APIs and standardized baselines. The work also adds holistic evaluation metrics to expose hard tasks for modern methods and defines them as future community challenges.","PDEBENCH: An Extensive Benchmark for Scientific  \nMachine Learning  \nMakoto Takamoto􀀃 NEC Labs Europe  \nTimothy Praditiay University of Stuttgart  \nRaphael Leiteritz  \nUniversity of Stuttgart  \narXiv :2210 .07 182v 3 [ cs .LG] 9 Dec 2022  \nDan MacKinlay Francesco Alesiani  \nCSIRO's Data61 NEC Labs Europe  \nDirk Pflüger Mathias Niepert  \nUniversity of Stuttgart University of Stuttgart  \nAbstract  \nMachine learning-based modeling of physical systems has experienced increased interest in recent years. Despite some impressive progress, there is still a lack of benchmarks for Scientific ML that are easy to use but still challenging and representative of a wide range of problems. We introduce PDEBENCH, a benchmark suite of time-dependent simulation tasks based on Partial Differential Equations (PDEs) . PDEBENCH comprises both code and data to benchmark the performance of novel machine learning models against both classical numerical simulationsand machine learning baselines. Our proposed set of benchmark problems contribute the following unique features: (1) A much wider range of PDEs compared to existing benchmarks, ranging from relatively common examples to more realistic and difficult problems; (2) much larger ready-to-use datasets compared to prior work, comprising multiple simulation runs across a larger number of initial and boundary conditions and PDE parameters; (3) more extensible source codes with user-friendly APIs for data generation and baseline results with popular machine learning models (FNO, U-Net, PINN, Gradient-Based Inverse Method) .  \nPDEBENCH allows researchers to extend the benchmark freely for their own purposes using a standardized API and to compare the performance of new models to existing baseline methods. We also propose new evaluation metrics with the aim to provide a more holistic understanding of learning methods in the context of Scientific ML. With those metrics we identify tasks which are challenging for recent ML methods and propose these tasks as future challenges for the community.  \nThe code is available at [https://github.com/pdebench/PDEBench](https://github.com/pdebench/PDEBench).  \n1 Motivation  \nIn the emergent area of Scientific Machine Learning (or machine learning for physical sciences or data-driven science), recent progress has broadened the scope of traditional machine learning (ML) methods to include the time-evolution of physical systems. Within this field, rapid progress has been made in the use of neural networks to make predictions using functional observations over continuous domains [8, 46] or with challenging constraints and with physically-motivated conservation laws [34, 61, 47] . These neural networks provide an approach to solving PDEs complementing traditional  \n􀀃 E-mail:Makoto .Takamoto@neclab .eu yE-mail:timothy.praditia@iws .uni-stuttgart.de  \n36th Conference on Neural Information Processing Systems (NeurIPS 2022) Track on Datasets and Benchmarks.  \nFigure 1: PDEBENCH provides multiple non-trivial challenges from the Sciences to benchmark current and future ML methods, including wave propagation and turbulent flow in 2D and 3D  \nnumerical solvers. For instance, data-driven ML methods are useful when observations are noisy orthe underlying physical model is not fully known or defined [11] . Moreover, neural models have the advantage of being continuously differentiable in their inputs, a useful property in several applications. In physical system design [1], for instance, the models are themselves physical objects and thus not analytically differentiable. Similarly, in many fields such as hydrology [14], benchmark physical simulation models exist but the forward simulation models non-differentiable black boxes. This complicates optimisation, control, sensitivity analysis, and solving inverse inference problems. While complex methods such as Bayesian optimisation [38, 50, 42] or reduced order modelling [16] are in part an attempt to circumvent this lack of differentiability, grad","cbCaincma8GDmFb3","https://ap.wps.com/l/cbCaincma8GDmFb3","pdf",4051710,1,50,"English","en",105,"# Motivation\n## Benchmark need and scope\n## PDEBENCH contributions and API\n## Data generation and evaluation metrics","[{\"question\":\"What is PDEBENCH and what does it benchmark?\",\"answer\":\"PDEBENCH benchmarks time-dependent simulation tasks based on partial differential equations (PDEs). It compares machine learning models against classical numerical simulations and ML baselines.\"},{\"question\":\"What unique features does PDEBENCH provide?\",\"answer\":\"It covers a wider range of PDEs, offers larger ready-to-use datasets spanning many initial/boundary conditions and PDE parameters, and provides extensible code with user-friendly APIs plus standard baselines.\"},{\"question\":\"How can researchers use PDEBENCH to evaluate new models?\",\"answer\":\"Researchers can extend the benchmark via a standardized API, generate data through the provided interface, and evaluate models using the proposed metrics against baseline simulators that supply ground truth.\"}]","PDEBENCH - An Extensive Benchmark for Scientific Machine Learning | PDF",1785679332,126,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"pdebench-an-extensive-benchmark-for-scientific-machine-learning","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/pdebench-an-extensive-benchmark-for-scientific-machine-learning/117747/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is PDEBENCH and what does it benchmark?","Question",{"text":75,"@type":76},"PDEBENCH benchmarks time-dependent simulation tasks based on partial differential equations (PDEs). It compares machine learning models against classical numerical simulations and ML baselines.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What unique features does PDEBENCH provide?",{"text":80,"@type":76},"It covers a wider range of PDEs, offers larger ready-to-use datasets spanning many initial/boundary conditions and PDE parameters, and provides extensible code with user-friendly APIs plus standard baselines.",{"name":82,"@type":73,"acceptedAnswer":83},"How can researchers use PDEBENCH to evaluate new models?",{"text":84,"@type":76},"Researchers can extend the benchmark via a standardized API, generate data through the provided interface, and evaluate models using the proposed metrics against baseline simulators that supply ground truth.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,114,119,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":21,"slug":113},6,"Technology","technology",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]