[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"branding":3,"analytics":7,"article-fourier-feature-networks-top-extreme-learning-machines-at-pdes":10,"sections":35},{"siteName":4,"siteTagline":5,"publisherName":4,"contactEmail":6},"The Revision","Tech news, decoded.","editor@therevision.news",{"gaMeasurementId":8,"adsenseClientId":9},"G-ZW2MV82GYR","ca-pub-8533917693782264",{"article":11},{"id":12,"slug":13,"title":14,"dek":15,"body_md":16,"tags_json":17,"published_at":18,"created_at":19,"updated_at":20,"status":21,"review_note":22,"review_notes":23,"image_url":22,"persona_id":22,"persona_name":22,"section":24,"tags":25,"sources":30,"feedback":34,"feedback_at":22,"cost_usd":34,"total_tokens":34},5319,"fourier-feature-networks-top-extreme-learning-machines-at-pdes","Fourier Feature Networks Top Extreme Learning Machines at PDEs","A new single-layer neural network using sine and cosine features solves differential equations more accurately than the Extreme Learning Machine approach.","Researchers have built a simple neural network that solves differential equations more accurately than a widely used shortcut method, without extra mathematical machinery.\n\nThe new architecture, called a Fourier Feature Network (FEN), uses a single hidden layer, much like the existing Extreme Learning Machine (ELM) approach. Instead of relying on affine transformations of the input to boost accuracy, as ELMs typically do, FEN builds its basis functions from sine and cosine waves. The coefficients for combining those basis functions are still solved with ordinary least squares. In head-to-head tests against ELMs running sigmoid, tanh, and swish activation functions, the researchers tuned a scaling factor for each method's random weights to keep the comparison fair, and FEN came out more accurate every time.\n\nThat matters because differential equations underpin everything from bridge-stress models to climate simulations, and machine-learning solvers are being pitched as a faster alternative to traditional numerical methods. A network that reaches higher precision without added transformations is simpler to build and tune, which could make these solvers more practical outside research labs.\n\nStill, this is one arXiv paper testing one class of problems, not a benchmark against industrial-grade solvers, and simplicity claims like this tend to get complicated once real-world noise and boundary conditions show up.","[\"ai research\",\"neural networks\",\"differential equations\",\"machine learning\"]","2026-08-18T04:00:00.000Z","2026-08-18T14:55:37.320Z","2026-08-18T14:55:49.140Z","published",null,[],"ai",[26,27,28,29],"ai research","neural networks","differential equations","machine learning",[31],{"name":32,"url":33},"arXiv cs.AI","https:\u002F\u002Farxiv.org\u002Fabs\u002F2608.14733",0,{"sections":36},[37,41,45,50,55,60,65,70,75,79,84,89,94,99],{"name":38,"slug":24,"count":39,"latest_published_at":40},"AI",3293,"2026-08-20T04:00:00.000Z",{"name":42,"slug":43,"count":44,"latest_published_at":40},"Security","security",435,{"name":46,"slug":47,"count":48,"latest_published_at":49},"Policy","policy",210,"2026-08-19T09:32:27.000Z",{"name":51,"slug":52,"count":53,"latest_published_at":54},"Deals","deals",179,"2026-06-29T20:02:07.000Z",{"name":56,"slug":57,"count":58,"latest_published_at":59},"Hardware","hardware",140,"2026-08-19T18:25:42.000Z",{"name":61,"slug":62,"count":63,"latest_published_at":64},"Consumer Tech","consumer-tech",95,"2026-08-18T16:05:00.000Z",{"name":66,"slug":67,"count":68,"latest_published_at":69},"Science","science",90,"2026-08-19T18:41:02.000Z",{"name":71,"slug":72,"count":73,"latest_published_at":74},"Software","software",73,"2026-08-18T07:51:50.000Z",{"name":76,"slug":77,"count":78,"latest_published_at":18},"Dev Tools","dev-tools",69,{"name":80,"slug":81,"count":82,"latest_published_at":83},"Startups","startups",47,"2026-08-19T19:13:46.000Z",{"name":85,"slug":86,"count":87,"latest_published_at":88},"Gaming","gaming",41,"2026-07-09T04:00:00.000Z",{"name":90,"slug":91,"count":92,"latest_published_at":93},"General","general",33,"2026-08-18T22:18:13.000Z",{"name":95,"slug":96,"count":97,"latest_published_at":98},"Reviews","reviews",20,"2026-06-24T12:00:01.000Z",{"name":100,"slug":101,"count":102,"latest_published_at":103},"How-To","how-to",6,"2026-06-16T09:00:00.000Z"]