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background-size:cover!important;background-position:center!important; color:#193645; }\/* nd-shared-components:end *\/\n<\/style>\n<div class=\"ndb\">\n<div class=\"ndb-wrap\">\n<section class=\"ndb-executive\">\n<h2>Modelling yacht residuary resistance<\/h2>\n<p>A hydrodynamic surrogate can help compare hull configurations within an experimental domain. This example estimates residuary resistance from six hull and flow descriptors and examines the response to Froude number.<\/p>\n<div class=\"ndb-kpis\">\n<div class=\"ndb-kpi\"><strong>308<\/strong><span>Source records<\/span><\/div>\n<div class=\"ndb-kpi\"><strong>6<\/strong><span>Final input features<\/span><\/div>\n<div class=\"ndb-kpi\"><strong>61<\/strong><span>Test observations<\/span><\/div>\n<div class=\"ndb-kpi\"><strong>0.981<\/strong><span>Test prediction R\u00b2<\/span><\/div>\n<\/div>\n<div class=\"ndb-actions\"><a class=\"aui aui-button\" href=\"#7-model-deployment\">Explore the model<\/a><a class=\"aui aui-button aui-button--secondary\" href=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/09\/yacht-data-20260921.csv\">Download the data<\/a><\/div>\n<\/section>\n<ul class=\"ndb-toc\">\n<li><a href=\"#1-industrial-challenge\">Industrial challenge<\/a><\/li><li><a href=\"#2-data-set\">Data set<\/a><\/li><li><a href=\"#3-model\">Model<\/a><\/li><li><a href=\"#4-training\">Training<\/a><\/li><li><a href=\"#5-selection\">Model selection<\/a><\/li><li><a href=\"#6-testing\">Testing<\/a><\/li><li><a href=\"#7-model-deployment\">Deployment<\/a><\/li><li><a href=\"#8-limitations\">Limitations<\/a><\/li>\n<\/ul>\n<section id=\"1-industrial-challenge\" class=\"ndb-card\"><h2>1. Industrial challenge<\/h2><p>Early hull studies compare resistance across geometric proportions and operating conditions. This surrogate reproduces a prepared experimental dataset and should be checked on separate hull designs before broader use.<\/p><div class=\"ndb-value-grid\"><div class=\"ndb-value\"><h3>Hull geometry<\/h3><p>Describe the design with the retained dimensionless inputs.<\/p><\/div><div class=\"ndb-value\"><h3>Resistance response<\/h3><p>Inspect the predicted residuary resistance and its directional curve.<\/p><\/div><div class=\"ndb-value\"><h3>Design comparison<\/h3><p>Assess transfer to new hull families with a grouped evaluation.<\/p><\/div><\/div><div class=\"ndb-audience\"><span>Naval architecture<\/span><span>Hydrodynamics<\/span><span>Surrogate modelling<\/span><\/div><div class=\"ndb-note\">The model is not a substitute for a towing-tank campaign or a validated hydrodynamic calculation. Predictions may be negative because the exported model does not clamp resistance. Restrict exploratory use to represented configurations, preserve coupled geometric constraints and review physical plausibility.<\/div><\/section>\n<section id=\"2-data-set\" class=\"ndb-card\"><h2>2. Data set<\/h2><p>The UCI Delft Yacht Hydrodynamics dataset contains 308 records. The supplied project uses 186 training, 61 validation and 61 testing records. Repeated operating conditions for related hulls make hull-level validation important when claiming transfer to a new design.<\/p><p>The downloadable project, saved report and supplied source CSV define the exact version used here. Repository: <a href=\"https:\/\/archive.ics.uci.edu\/dataset\/243\/yacht+hydrodynamics\">original dataset\/source record<\/a>. <\/p><div class=\"nd-table-scroll\" tabindex=\"0\"><table><thead><tr><th scope=\"col\">Subset<\/th><th scope=\"col\">Records<\/th><\/tr><\/thead><tbody><tr><th scope=\"row\">Training<\/th><td>186<\/td><\/tr><tr><th scope=\"row\">Validation \/ selection<\/th><td>61<\/td><\/tr><tr><th scope=\"row\">Testing<\/th><td>61<\/td><\/tr><tr><th scope=\"row\">Unused<\/th><td>0<\/td><\/tr><\/tbody><\/table><\/div><div class=\"nd-table-scroll\" tabindex=\"0\"><table><thead><tr><th scope=\"col\">Variable<\/th><th scope=\"col\">Role<\/th><th scope=\"col\">Type<\/th><th scope=\"col\">Encoding<\/th><th scope=\"col\">Unit<\/th><\/tr><\/thead><tbody><tr><th scope=\"row\">center_of_buoyancy<\/th><td>Input<\/td><td>Numeric<\/td><td><\/td><td>As supplied<\/td><\/tr><tr><th scope=\"row\">prismatic_coefficient<\/th><td>Input<\/td><td>Numeric<\/td><td><\/td><td>As supplied<\/td><\/tr><tr><th scope=\"row\">length_displacement<\/th><td>Input<\/td><td>Numeric<\/td><td><\/td><td>As supplied<\/td><\/tr><tr><th scope=\"row\">beam_draught_ratio<\/th><td>Input<\/td><td>Numeric<\/td><td><\/td><td>As supplied<\/td><\/tr><tr><th scope=\"row\">length_beam_ratio<\/th><td>Input<\/td><td>Numeric<\/td><td><\/td><td>As supplied<\/td><\/tr><tr><th scope=\"row\">froude_number<\/th><td>Input<\/td><td>Numeric<\/td><td><\/td><td>As supplied<\/td><\/tr><tr><th scope=\"row\">resistance<\/th><td>Target<\/td><td>Numeric<\/td><td><\/td><td>source resistance units<\/td><\/tr><\/tbody><\/table><\/div><figure class=\"nd-native-figure\"><div class=\"nd-chart-bundle\" tabindex=\"0\" role=\"group\" aria-label=\"Interactive chart; scroll horizontally on narrow screens\" data-native-chart=\"nd-yacht-t0-s7-20260921\"><div class=\"nd-chart-host\" id=\"nd-yacht-t0-s7-20260921\" role=\"img\" aria-label=\"resistance distribution\"><\/div><p class=\"nd-chart-fallback\">Interactive chart: resistance distribution. Enable JavaScript to explore it.<\/p><script type=\"application\/json\">{\"config\":{\"displayModeBar\":true,\"displaylogo\":false,\"editable\":false,\"responsive\":true,\"scrollZoom\":true,\"toImageButtonOptions\":{\"filename\":\"neural-designer-chart\",\"format\":\"svg\"}},\"data\":[{\"marker\":{\"color\":\"#209fdf\"},\"name\":\"\",\"opacity\":1,\"showlegend\":false,\"type\":\"bar\",\"x\":[\"3.13\",\"9.37\",\"15.6\",\"21.9\",\"28.1\",\"34.3\",\"40.6\",\"46.8\",\"53.1\",\"59.3\"],\"y\":[63.599998474121094,10.399999618530273,4.5,6.5,1.2999999523162842,5.199999809265137,1.2999999523162842,1.899999976158142,4.199999809265137,1]}],\"layout\":{\"autosize\":true,\"font\":{\"color\":\"#30343b\",\"family\":\"Arial, sans-serif\",\"size\":14},\"hovermode\":\"closest\",\"margin\":{\"b\":68,\"l\":72,\"pad\":4,\"r\":36,\"t\":112},\"paper_bgcolor\":\"#ffffff\",\"plot_bgcolor\":\"#ffffff\",\"title\":{\"automargin\":true,\"pad\":{\"t\":48},\"text\":\"resistance histogram\",\"x\":0.5,\"xanchor\":\"center\",\"y\":1,\"yanchor\":\"top\",\"yref\":\"container\"},\"xaxis\":{\"automargin\":true,\"categoryarray\":[\"3.13\",\"9.37\",\"15.6\",\"21.9\",\"28.1\",\"34.3\",\"40.6\",\"46.8\",\"53.1\",\"59.3\"],\"categoryorder\":\"array\",\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"title\":{\"text\":\"Bin center\"},\"type\":\"category\",\"zerolinecolor\":\"#aeb6c2\"},\"yaxis\":{\"automargin\":true,\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"range\":[0,80.02],\"title\":{\"text\":\"% frequency\"},\"zerolinecolor\":\"#aeb6c2\"}}}<\/script><\/div><figcaption>resistance distribution. Exported with Neural Designer from the saved task report.<\/figcaption><\/figure><figure class=\"nd-native-figure\"><div class=\"nd-chart-bundle\" tabindex=\"0\" role=\"group\" aria-label=\"Interactive chart; scroll horizontally on narrow screens\" data-native-chart=\"nd-yacht-t1-s11-20260921\"><div class=\"nd-chart-host\" id=\"nd-yacht-t1-s11-20260921\" role=\"img\" aria-label=\"resistance vs. froude_number scatter chart\"><\/div><p class=\"nd-chart-fallback\">Interactive chart: resistance vs. froude_number scatter chart. Enable JavaScript to explore it.<\/p><script 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sans-serif\",\"size\":14},\"hovermode\":\"closest\",\"margin\":{\"b\":68,\"l\":72,\"pad\":4,\"r\":36,\"t\":112},\"paper_bgcolor\":\"#ffffff\",\"plot_bgcolor\":\"#ffffff\",\"title\":{\"automargin\":true,\"pad\":{\"t\":48},\"text\":\"resistance vs. froude_number scatter chart\",\"x\":0.5,\"xanchor\":\"center\",\"y\":1,\"yanchor\":\"top\",\"yref\":\"container\"},\"xaxis\":{\"automargin\":true,\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"range\":[0.1,0.45005],\"title\":{\"text\":\"froude_number\"},\"zerolinecolor\":\"#aeb6c2\"},\"yaxis\":{\"automargin\":true,\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"range\":[0,70.01],\"title\":{\"text\":\"resistance\"},\"zerolinecolor\":\"#aeb6c2\"}}}<\/script><\/div><figcaption>resistance vs. froude_number scatter chart. Exported with Neural Designer from the saved task report.<\/figcaption><\/figure><figure class=\"nd-native-figure\"><div class=\"nd-chart-bundle\" tabindex=\"0\" role=\"group\" aria-label=\"Interactive chart; scroll horizontally on narrow screens\" data-native-chart=\"nd-yacht-t2-s1-20260921\"><div class=\"nd-chart-host\" id=\"nd-yacht-t2-s1-20260921\" role=\"img\" aria-label=\"resistance Pearson correlations chart\"><\/div><p class=\"nd-chart-fallback\">Interactive chart: resistance Pearson correlations chart. Enable JavaScript to explore it.<\/p><script type=\"application\/json\">{\"config\":{\"displayModeBar\":true,\"displaylogo\":false,\"editable\":false,\"responsive\":true,\"scrollZoom\":true,\"toImageButtonOptions\":{\"filename\":\"neural-designer-chart\",\"format\":\"svg\"}},\"data\":[{\"marker\":{\"color\":\"#209fdf\"},\"name\":\"\",\"opacity\":1,\"orientation\":\"h\",\"showlegend\":false,\"type\":\"bar\",\"x\":[-0.02889999933540821,-0.011099999770522118,0.014600000344216824,0.019300000742077827,0.02630000002682209,0.9850000143051147],\"y\":[\"prismatic_coefficient\",\"length_beam_ratio\",\"length_displacement\",\"center_of_buoyancy\",\"beam_draught_ratio\",\"froude_number\"]}],\"layout\":{\"autosize\":true,\"font\":{\"color\":\"#30343b\",\"family\":\"Arial, sans-serif\",\"size\":14},\"hovermode\":\"closest\",\"margin\":{\"b\":68,\"l\":72,\"pad\":4,\"r\":36,\"t\":112},\"paper_bgcolor\":\"#ffffff\",\"plot_bgcolor\":\"#ffffff\",\"title\":{\"automargin\":true,\"pad\":{\"t\":48},\"text\":\"resistance Pearson correlations chart\",\"x\":0.5,\"xanchor\":\"center\",\"y\":1,\"yanchor\":\"top\",\"yref\":\"container\"},\"xaxis\":{\"automargin\":true,\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"range\":[-1,1],\"title\":{\"text\":\"Correlation\"},\"zerolinecolor\":\"#aeb6c2\"},\"yaxis\":{\"automargin\":true,\"autorange\":\"reversed\",\"categoryarray\":[\"prismatic_coefficient\",\"length_beam_ratio\",\"length_displacement\",\"center_of_buoyancy\",\"beam_draught_ratio\",\"froude_number\"],\"categoryorder\":\"array\",\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"type\":\"category\",\"zerolinecolor\":\"#aeb6c2\"}}}<\/script><\/div><figcaption>resistance Pearson correlations chart. Exported with Neural Designer from the saved task report.<\/figcaption><\/figure><div class=\"ndb-note\">This is internal validation using the saved record-level split. Grouped or temporal independence has not been established.<\/div><\/section>\n<section id=\"3-model\" class=\"ndb-card\"><h2>3. Model<\/h2><p>The final model has <strong>6 encoded input features<\/strong> and <strong>1 outputs<\/strong>. The following dimensions describe the final saved network.<\/p><div class=\"nd-table-scroll\" tabindex=\"0\"><table><thead><tr><th scope=\"col\">Layer<\/th><th scope=\"col\">Input shape<\/th><th scope=\"col\">Output shape<\/th><th scope=\"col\">Activation<\/th><\/tr><\/thead><tbody><tr><th scope=\"row\">Scaling<\/th><td>6<\/td><td>6<\/td><td>\u2014<\/td><\/tr><tr><th scope=\"row\">Dense<\/th><td>6<\/td><td>3<\/td><td>Tanh<\/td><\/tr><tr><th scope=\"row\">Dense<\/th><td>3<\/td><td>1<\/td><td>Identity<\/td><\/tr><tr><th scope=\"row\">Unscaling<\/th><td>1<\/td><td>1<\/td><td>\u2014<\/td><\/tr><tr><th scope=\"row\">Clamping<\/th><td>1<\/td><td>1<\/td><td>\u2014<\/td><\/tr><\/tbody><\/table><\/div><p>The final output is a continuous estimate. Scaling, unscaling and any bounds follow the saved implementation; the calculator does not silently impose physical constraints.<\/p><figure class=\"ndb-architecture-figure\" data-model-stage=\"initial\"><a href=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/09\/nd-yacht-t3-s1-20260921.png\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" class=\"ndb-architecture\" src=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/09\/nd-yacht-t3-s1-20260921.png\" alt=\"Modelling yacht residuary resistance: initial Neural Designer architecture\"><\/a><figcaption>Architecture used for this model; no architecture-selection experiment is recorded. Diagram labels show original variables; categorical expansion and the numeric layer dimensions are documented in the model table.<\/figcaption><\/figure><\/section>\n<section id=\"4-training\" class=\"ndb-card\"><h2>4. Training strategy<\/h2><p>The saved training configuration uses NormalizedSquaredError with QuasiNewton. Training minimizes the recorded objective; the validation subset monitors generalization during fitting. The testing subset is used for the evaluation below.<\/p><figure class=\"nd-native-figure\"><div class=\"nd-chart-bundle\" tabindex=\"0\" role=\"group\" aria-label=\"Interactive chart; scroll horizontally on narrow screens\" data-native-chart=\"nd-yacht-t4-s2-20260921\"><div class=\"nd-chart-host\" id=\"nd-yacht-t4-s2-20260921\" role=\"img\" aria-label=\"Quasi-Newton method error history\"><\/div><p class=\"nd-chart-fallback\">Interactive chart: Quasi-Newton method error history. Enable JavaScript to explore it.<\/p><script type=\"application\/json\">{\"config\":{\"displayModeBar\":true,\"displaylogo\":false,\"editable\":false,\"responsive\":true,\"scrollZoom\":true,\"toImageButtonOptions\":{\"filename\":\"neural-designer-chart\",\"format\":\"svg\"}},\"data\":[{\"connectgaps\":false,\"line\":{\"color\":\"#529cc2\",\"dash\":\"solid\",\"width\":2},\"mode\":\"lines\",\"name\":\"Training error\",\"opacity\":1,\"showlegend\":true,\"type\":\"scatter\",\"x\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],\"y\":[0.9959999918937683,0.9670000076293945,0.8100000023841858,0.45100000500679016,0.43299999833106995,0.3269999921321869,0.26899999380111694,0.19300000369548798,0.1459999978542328,0.045099999755620956,0.021700000390410423,0.00773000018671155,0.006500000134110451,0.005750000011175871,0.0053400001488626,0.004900000058114529,0.004540000110864639,0.00430000014603138,0.0040699997916817665,0.003969999961555004,0.0038999998942017555,0.0038499999791383743,0.0037499999161809683,0.0035600000992417336,0.0033400000538676977,0.0031799999997019768,0.003109999932348728,0.0030900000128895044,0.0030700000934302807,0.0030700000934302807,0.003060000017285347,0.0030499999411404133,0.0030499999411404133,0.0030300000216811895,0.003019999945536256,0.003000000026077032,0.0029800001066178083,0.0029700000304728746,0.002950000111013651,0.002940000034868717,0.002940000034868717,0.002940000034868717]},{\"connectgaps\":false,\"line\":{\"color\":\"#ed982a\",\"dash\":\"solid\",\"width\":2},\"mode\":\"lines\",\"name\":\"Validation error\",\"opacity\":1,\"showlegend\":true,\"type\":\"scatter\",\"x\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],\"y\":[0.9700000286102295,0.7979999780654907,0.3959999978542328,0.4269999861717224,0.3009999990463257,0.2370000034570694,0.18199999630451202,0.13500000536441803,0.03200000151991844,0.02879999950528145,0.008329999633133411,0.007939999923110008,0.006089999806135893,0.005570000037550926,0.004980000201612711,0.004670000169426203,0.004290000069886446,0.00406000018119812,0.00394000019878149,0.003819999983534217,0.0036800000816583633,0.003379999892786145,0.0029299999587237835,0.0024399999529123306,0.0022499999031424522,0.002259999979287386,0.002360000042244792,0.0023900000378489494,0.0023900000378489494,0.002360000042244792,0.0023300000466406345,0.002309999894350767,0.002300000051036477,0.002309999894350767,0.0023499999660998583,0.002400000113993883,0.0024300001095980406,0.0024399999529123306,0.002420000033453107,0.0023900000378489494,0.002369999885559082,0.002360000042244792]}],\"layout\":{\"autosize\":true,\"font\":{\"color\":\"#30343b\",\"family\":\"Arial, sans-serif\",\"size\":14},\"hovermode\":\"closest\",\"legend\":{\"orientation\":\"h\",\"x\":0.5,\"xanchor\":\"center\",\"y\":-0.24,\"yanchor\":\"top\"},\"margin\":{\"b\":120,\"l\":72,\"pad\":4,\"r\":36,\"t\":112},\"paper_bgcolor\":\"#ffffff\",\"plot_bgcolor\":\"#ffffff\",\"title\":{\"automargin\":true,\"pad\":{\"t\":48},\"text\":\"Quasi-Newton method error history\",\"x\":0.5,\"xanchor\":\"center\",\"y\":1,\"yanchor\":\"top\",\"yref\":\"container\"},\"xaxis\":{\"automargin\":true,\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"range\":[0,41],\"title\":{\"text\":\"Epoch\"},\"zerolinecolor\":\"#aeb6c2\"},\"yaxis\":{\"automargin\":true,\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"range\":[0,1.0002],\"title\":{\"text\":\"Normalized squared error\"},\"zerolinecolor\":\"#aeb6c2\"}}}<\/script><\/div><figcaption>Quasi-Newton method error history. Exported with Neural Designer from the saved task report.<\/figcaption><\/figure><h3>Quasi-Newton method results<\/h3><div class=\"nd-table-scroll\" tabindex=\"0\"><table><thead><tr><th scope=\"col\">Measure<\/th><th scope=\"col\">Value<\/th><\/tr><\/thead><tbody><tr><th scope=\"row\">Epochs number<\/th><td>42<\/td><\/tr><tr><th scope=\"row\">Elapsed time<\/th><td>00:00:00<\/td><\/tr><tr><th scope=\"row\">Stopping criterion<\/th><td>Minimum loss decrease<\/td><\/tr><tr><th scope=\"row\">Training error<\/th><td>0.003<\/td><\/tr><tr><th scope=\"row\">Validation error<\/th><td>0.002<\/td><\/tr><\/tbody><\/table><\/div><\/section>\n<section id=\"5-selection\" class=\"ndb-card\"><h2>5. Model selection<\/h2><p>No model selection experiment is recorded in this supplied project. The displayed architecture is the trained model used for testing; earlier article claims about a different selected architecture do not apply to this version.<\/p><\/section>\n<section id=\"6-testing\" class=\"ndb-card\"><h2>6. Testing analysis<\/h2><p>The final model is evaluated on <strong>61 testing observations<\/strong>. MAE, RMSE and prediction R\u00b2 below are computed from the exact testing pairs stored by Neural Designer. Errors retain each target\u2019s original units.<\/p><div class=\"nd-table-scroll\" tabindex=\"0\"><table><thead><tr><th scope=\"col\">Target<\/th><th scope=\"col\">Unit<\/th><th scope=\"col\">MAE<\/th><th scope=\"col\">RMSE<\/th><th scope=\"col\">Prediction R\u00b2<\/th><th scope=\"col\">Pearson r\u00b2<\/th><\/tr><\/thead><tbody><tr><th scope=\"row\">resistance<\/th><td>source resistance units<\/td><td>1.352<\/td><td>2.314<\/td><td>0.981<\/td><td>0.996<\/td><\/tr><\/tbody><\/table><\/div><p>The native goodness-of-fit task reports squared Pearson correlation (r\u00b2). Prediction R\u00b2 here is 1 \u2212 squared prediction error \/ squared deviation from the test mean. They measure different properties: a strongly correlated prediction can still have a bias or an incorrect scale.<\/p><div class=\"nd-native-test-figures\"><figure class=\"nd-native-figure\"><div class=\"nd-chart-bundle\" tabindex=\"0\" role=\"group\" aria-label=\"Interactive chart; scroll horizontally on narrow screens\" data-native-chart=\"nd-yacht-t5-s2-20260921\"><div class=\"nd-chart-host\" id=\"nd-yacht-t5-s2-20260921\" role=\"img\" aria-label=\"resistance goodness-of-fit chart\"><\/div><p class=\"nd-chart-fallback\">Interactive chart: resistance goodness-of-fit chart. Enable JavaScript to explore it.<\/p><script type=\"application\/json\">{\"config\":{\"displayModeBar\":true,\"displaylogo\":false,\"editable\":false,\"responsive\":true,\"scrollZoom\":true,\"toImageButtonOptions\":{\"filename\":\"neural-designer-chart\",\"format\":\"svg\"}},\"data\":[{\"connectgaps\":false,\"marker\":{\"color\":\"#209fdf\",\"size\":8,\"symbol\":\"circle\"},\"mode\":\"markers\",\"name\":\"Predicted resistance\",\"opacity\":1,\"showlegend\":false,\"type\":\"scatter\",\"x\":[0.27000001072883606,2.609999895095825,7.159999847412109,49.4900016784668,0.03999999910593033,11.989999771118164,0.09000000357627869,0.28999999165534973,13.079999923706055,21.399999618530273,50.13999938964844,0.20000000298023224,1.3700000047683716,33.970001220703125,0.6499999761581421,1.3700000047683716,21.510000228881836,50.36000061035156,0.4300000071525574,1.090000033378601,6.860000133514404,11.5600004196167,12.800000190734863,1.9800000190734863,5.789999961853027,44.380001068115234,1.2400000095367432,3.450000047683716,0.7900000214576721,1.2799999713897705,4.139999866485596,38.119998931884766,0.18000000715255737,0.4000000059604645,1.1399999856948853,4.119999885559082,0.8299999833106995,0.07999999821186066,0.23999999463558197,49.13999938964844,2.9800000190734863,4.420000076293945,55.16999816894531,0.7599999904632568,1.149999976158142,2.2799999713897705,0.17000000178813934,2.049999952316284,2.1600000858306885,0.05999999865889549,0.9200000166893005,2.619999885559082,0.4699999988079071,0.7799999713897705,1.850000023841858,3.690000057220459,4.460000038146973,31.770000457763672,47.130001068115234,12.270000457763672,46.65999984741211],\"y\":[-0.17675304412841797,2.6777381896972656,9.239336013793945,56.035064697265625,-0.3876218795776367,13.69192123413086,-0.31986331939697266,-0.15644264221191406,13.017661094665527,20.343156814575195,50.322750091552734,-0.3228778839111328,0.9598217010498047,36.95805740356445,0.011716842651367188,0.8267812728881836,23.440807342529297,56.63451385498047,-0.08683013916015625,0.6338052749633789,8.702269554138184,14.244324684143066,14.001697540283203,1.7056608200073242,6.1795973777771,53.51184844970703,0.7903032302856445,3.8482933044433594,0.5605812072753906,1.1377878189086914,4.657130241394043,39.42923355102539,-0.2525138854980469,-0.057415008544921875,0.6569013595581055,3.455880641937256,0.6380338668823242,-0.3601398468017578,-0.2216053009033203,54.166961669921875,3.78359317779541,5.884491920471191,59.81807327270508,0.21630001068115234,0.6476268768310547,2.205866813659668,-0.363616943359375,1.7557945251464844,2.4099950790405273,-0.32074928283691406,0.3675832748413086,2.638437271118164,-0.15674591064453125,0.09032249450683594,1.0038728713989258,3.040931224822998,4.882815361022949,34.20555114746094,51.66792297363281,13.778298377990723,52.942047119140625]},{\"connectgaps\":false,\"line\":{\"color\":\"#3c3c3c\",\"dash\":\"solid\",\"width\":2},\"mode\":\"lines\",\"name\":\"Predicted resistance\",\"opacity\":1,\"showlegend\":false,\"type\":\"scatter\",\"x\":[0,70.01],\"y\":[0,70.01]}],\"layout\":{\"autosize\":true,\"font\":{\"color\":\"#30343b\",\"family\":\"Arial, sans-serif\",\"size\":14},\"hovermode\":\"closest\",\"margin\":{\"b\":68,\"l\":72,\"pad\":4,\"r\":36,\"t\":112},\"paper_bgcolor\":\"#ffffff\",\"plot_bgcolor\":\"#ffffff\",\"title\":{\"automargin\":true,\"pad\":{\"t\":48},\"text\":\"resistance goodness-of-fit chart\",\"x\":0.5,\"xanchor\":\"center\",\"y\":1,\"yanchor\":\"top\",\"yref\":\"container\"},\"xaxis\":{\"automargin\":true,\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"range\":[-1.4002000000000001,71.4102],\"title\":{\"text\":\"Actual resistance\"},\"zerolinecolor\":\"#aeb6c2\"},\"yaxis\":{\"automargin\":true,\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"range\":[-1.4002000000000001,71.4102],\"title\":{\"text\":\"Predicted resistance\"},\"zerolinecolor\":\"#aeb6c2\"}}}<\/script><\/div><figcaption>resistance goodness-of-fit chart. Exported with Neural Designer from the saved task report.<\/figcaption><\/figure><\/div><\/section>\n<section id=\"7-model-deployment\" class=\"ndb-card\"><h2>7. Model deployment<\/h2><p>Validated inputs \u2192 saved preprocessing \u2192 neural network \u2192 score or estimate \u2192 domain review. The ZIP contains the original project, source CSV, schema, test metrics and standalone interactive chart exports. The project hash in the schema identifies this exact version.<\/p><h3>Directional response at a fixed reference point<\/h3><details><summary>Inspect the saved reference point<\/summary><div class=\"nd-table-scroll\" tabindex=\"0\"><table><thead><tr><th scope=\"col\">Measure<\/th><th scope=\"col\">Variable<\/th><th scope=\"col\">Value<\/th><\/tr><\/thead><tbody><tr><th scope=\"row\">1<\/th><td>center_of_buoyancy<\/td><td>-2.3<\/td><\/tr><tr><th scope=\"row\">2<\/th><td>prismatic_coefficient<\/td><td>0.53<\/td><\/tr><tr><th scope=\"row\">3<\/th><td>length_displacement<\/td><td>4.34<\/td><\/tr><tr><th scope=\"row\">4<\/th><td>beam_draught_ratio<\/td><td>2.81<\/td><\/tr><tr><th scope=\"row\">5<\/th><td>length_beam_ratio<\/td><td>3.15<\/td><\/tr><tr><th scope=\"row\">6<\/th><td>froude_number<\/td><td>0.175<\/td><\/tr><\/tbody><\/table><\/div><\/details><figure class=\"nd-native-figure\"><div class=\"nd-chart-bundle\" tabindex=\"0\" role=\"group\" aria-label=\"Interactive chart; scroll horizontally on narrow screens\" data-native-chart=\"nd-yacht-t6-s7-20260921\"><div class=\"nd-chart-host\" id=\"nd-yacht-t6-s7-20260921\" role=\"img\" aria-label=\"resistance - froude_number directional output\"><\/div><p class=\"nd-chart-fallback\">Interactive chart: resistance &#8211; froude_number directional output. Enable JavaScript to explore it.<\/p><script type=\"application\/json\">{\"config\":{\"displayModeBar\":true,\"displaylogo\":false,\"editable\":false,\"responsive\":true,\"scrollZoom\":true,\"toImageButtonOptions\":{\"filename\":\"neural-designer-chart\",\"format\":\"svg\"}},\"data\":[{\"connectgaps\":false,\"line\":{\"color\":\"#529cc2\",\"dash\":\"solid\",\"shape\":\"spline\",\"width\":2},\"mode\":\"lines\",\"name\":\"resistance\",\"opacity\":1,\"showlegend\":false,\"type\":\"scatter\",\"x\":[0.10000000149011612,0.10700000077486038,0.11400000005960464,0.12099999934434891,0.12800000607967377,0.13500000536441803,0.1420000046491623,0.14900000393390656,0.15600000321865082,0.16300000250339508,0.17000000178813934,0.1770000010728836,0.18400000035762787,0.19099999964237213,0.1979999989271164,0.20499999821186066,0.21199999749660492,0.21899999678134918,0.22599999606609344,0.2329999953508377,0.23999999463558197,0.24699999392032623,0.2540000081062317,0.26100000739097595,0.2680000066757202,0.2750000059604645,0.28200000524520874,0.289000004529953,0.29600000381469727,0.30300000309944153,0.3100000023841858,0.31700000166893005,0.3240000009536743,0.3310000002384186,0.33799999952316284,0.3449999988079071,0.35199999809265137,0.35899999737739563,0.3659999966621399,0.37299999594688416,0.3799999952316284,0.3869999945163727,0.39399999380111694,0.4009999930858612,0.40799999237060547,0.41499999165534973,0.421999990940094,0.42899999022483826,0.4359999895095825,0.4429999887943268,0.44999998807907104],\"y\":[-0.5249999761581421,-0.5080000162124634,-0.4880000054836273,-0.46700000762939453,-0.4429999887943268,-0.41600000858306885,-0.38499999046325684,-0.35100001096725464,-0.31299999356269836,-0.27000001072883606,-0.22200000286102295,-0.16899999976158142,-0.10899999737739563,-0.04129999876022339,0.03400000184774399,0.11800000071525574,0.21299999952316284,0.3179999887943268,0.4359999895095825,0.5680000185966492,0.7160000205039978,0.8809999823570251,1.0700000524520874,1.2699999809265137,1.5099999904632568,1.7699999809265137,2.069999933242798,2.4000000953674316,2.7799999713897705,3.2100000381469727,3.700000047683716,4.260000228881836,4.909999847412109,5.670000076293945,6.550000190734863,7.590000152587891,8.819999694824219,10.300000190734863,12,14.100000381469727,16.5,19.299999237060547,22.700000762939453,26.5,30.799999237060547,35.5,40.599998474121094,45.79999923706055,51.099998474121094,56.29999923706055,61.099998474121094]},{\"connectgaps\":false,\"marker\":{\"color\":\"#3c3c3c\",\"size\":8,\"symbol\":\"circle\"},\"mode\":\"markers\",\"name\":\"resistance\",\"opacity\":1,\"showlegend\":false,\"type\":\"scatter\",\"x\":[0.17499999701976776],\"y\":[-0.1845950037240982]}],\"layout\":{\"autosize\":true,\"font\":{\"color\":\"#30343b\",\"family\":\"Arial, sans-serif\",\"size\":14},\"hovermode\":\"closest\",\"margin\":{\"b\":68,\"l\":72,\"pad\":4,\"r\":36,\"t\":112},\"paper_bgcolor\":\"#ffffff\",\"plot_bgcolor\":\"#ffffff\",\"title\":{\"automargin\":true,\"pad\":{\"t\":48},\"text\":\"resistance - froude_number directional output\",\"x\":0.5,\"xanchor\":\"center\",\"y\":1,\"yanchor\":\"top\",\"yref\":\"container\"},\"xaxis\":{\"automargin\":true,\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"range\":[0.1,0.45005],\"title\":{\"text\":\"froude_number\"},\"zerolinecolor\":\"#aeb6c2\"},\"yaxis\":{\"automargin\":true,\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"range\":[0,70.01],\"title\":{\"text\":\"resistance\"},\"zerolinecolor\":\"#aeb6c2\"}}}<\/script><\/div><figcaption>resistance &#8211; froude_number directional output. Exported with Neural Designer from the saved task report. Other inputs are held at the saved reference point. This is a model response, not a causal effect.<\/figcaption><\/figure><div class=\"nd-model-calculator\" id=\"nd-model-yacht\"><h3>Explore the exported model<\/h3><p>This research demonstration runs locally in your browser. Values outside the training range are outside the validated domain and are rejected. A valid input range does not guarantee that a combination is physically or operationally plausible.<\/p><p>This is not a certified control or protection system.<\/p><div class=\"nd-model-fields\"><\/div><div class=\"nd-model-actions\"><button class=\"aui aui-button nd-model-calculate\" type=\"button\">Calculate<\/button><button class=\"aui aui-button aui-button--secondary nd-model-reset\" type=\"button\">Reset example<\/button><\/div><div class=\"nd-model-result\" role=\"status\" aria-live=\"polite\"><\/div><\/div><script data-noptimize=\"1\">(()=>{function Identity(x) {\n\treturn x;\n}\nfunction Tanh(x) {\n\treturn Math.tanh(x);\n}\nfunction calculate_outputs(inputs)\n{\n\tvar center_of_buoyancy = +inputs[0];\n\tvar prismatic_coefficient = +inputs[1];\n\tvar length_displacement = +inputs[2];\n\tvar beam_draught_ratio = +inputs[3];\n\tvar length_beam_ratio = +inputs[4];\n\tvar froude_number = +inputs[5];\n\n\tvar scaled_center_of_buoyancy = center_of_buoyancy*0.6619185209+1.576570749;\n\tvar scaled_prismatic_coefficient = prismatic_coefficient*43.00668335-24.26170349;\n\tvar scaled_length_displacement = length_displacement*3.958107471-18.95395279;\n\tvar scaled_beam_draught_ratio = beam_draught_ratio*1.827141404-7.193126678;\n\tvar scaled_length_beam_ratio = length_beam_ratio*4.038837433-12.95182514;\n\tvar scaled_froude_number = froude_number*9.922801018-2.852805138;\n\tvar dense_layer_1_output_0 = Tanh( -0.1245721057 + (-0.08780998737*scaled_center_of_buoyancy) + (0.04961294681*scaled_prismatic_coefficient) + (0.113354668*scaled_length_displacement) + (0.01366257761*scaled_beam_draught_ratio) + (-0.04701381549*scaled_length_beam_ratio) + (-0.03418398649*scaled_froude_number) );\n\tvar dense_layer_1_output_1 = Tanh( 0.6821155548 + (-0.0546666868*scaled_center_of_buoyancy) + (-0.07460874319*scaled_prismatic_coefficient) + (-0.1063270792*scaled_length_displacement) + (0.0430896394*scaled_beam_draught_ratio) + (0.07744757831*scaled_length_beam_ratio) + (-0.8329852819*scaled_froude_number) );\n\tvar dense_layer_1_output_2 = Tanh( -2.92633605 + (0.01422290504*scaled_center_of_buoyancy) + (-0.03628637269*scaled_prismatic_coefficient) + (0.1375647038*scaled_length_displacement) + (-0.1684535295*scaled_beam_draught_ratio) + (-0.152376622*scaled_length_beam_ratio) + (1.92284286*scaled_froude_number) );\n\tvar approximation_layer_output_0 = Identity( 2.248732328 + (0.006055852398*dense_layer_1_output_0) + (-0.5967329144*dense_layer_1_output_1) + (2.387358665*dense_layer_1_output_2) );\n\tvar unscaling_layer_output_0=approximation_layer_output_0*15.13589954+10.49540043;\n\tvar resistance = unscaling_layer_output_0;\n\tvar out = [];\n\tout.push(resistance);\n\n\treturn out;\n}\nconst cfg={\"fields\":[{\"name\":\"center_of_buoyancy\",\"n\":1,\"type\":\"Numeric\",\"categories\":[],\"min\":-5.0,\"max\":0.0,\"value\":-2.299999952316284,\"unit\":\"\"},{\"name\":\"prismatic_coefficient\",\"n\":1,\"type\":\"Numeric\",\"categories\":[],\"min\":0.53,\"max\":0.6,\"value\":0.5680000185966492,\"unit\":\"\"},{\"name\":\"length_displacement\",\"n\":1,\"type\":\"Numeric\",\"categories\":[],\"min\":4.34,\"max\":5.14,\"value\":4.78000020980835,\"unit\":\"\"},{\"name\":\"beam_draught_ratio\",\"n\":1,\"type\":\"Numeric\",\"categories\":[],\"min\":2.81,\"max\":5.35,\"value\":3.990000009536743,\"unit\":\"\"},{\"name\":\"length_beam_ratio\",\"n\":1,\"type\":\"Numeric\",\"categories\":[],\"min\":2.73,\"max\":3.64,\"value\":3.1700000762939453,\"unit\":\"\"},{\"name\":\"froude_number\",\"n\":1,\"type\":\"Numeric\",\"categories\":[],\"min\":0.125,\"max\":0.45,\"value\":0.15000000596046448,\"unit\":\"\"}],\"output_names\":[\"resistance\"],\"reference\":[-0.15940041465090538]},root=document.getElementById(\"nd-model-yacht\");if(!root)return;const grid=root.querySelector(\".nd-model-fields\"),result=root.querySelector(\".nd-model-result\"),controls=[];cfg.fields.forEach((f,i)=>{const wrap=document.createElement(\"div\");wrap.className=\"nd-model-field\";const label=document.createElement(\"label\"),id=root.id+\"-\"+i;label.htmlFor=id;label.textContent=f.name.replaceAll(\"_\",\" \")+(f.unit?\" (\"+f.unit+\")\":\"\");let input;if(f.categories?.length){input=document.createElement(\"select\");f.categories.forEach((name,k)=>{const option=document.createElement(\"option\");option.value=String(k);option.textContent=name;input.appendChild(option);});}else{input=document.createElement(\"input\");input.type=\"number\";input.step=\"any\";input.min=String(f.min);input.max=String(f.max);}input.id=id;input.value=String(f.value);wrap.append(label,input);grid.appendChild(wrap);controls.push(input);});const calculate=()=>{const inputs=[];let valid=true;cfg.fields.forEach((f,i)=>{const el=controls[i],v=Number(el.value);let bad=el.value.trim()===\"\"||!Number.isFinite(v);if(!f.categories?.length)bad=bad||v<f.min||v>f.max;el.setAttribute(\"aria-invalid\",bad?\"true\":\"false\");if(bad)valid=false;if(f.n>1){for(let k=0;k<f.n;k++)inputs.push(k===v?1:0);}else inputs.push(v);});if(!valid){result.textContent=\"Enter a valid value within every displayed input range.\";return;}let outputs=calculate_outputs(inputs);if(outputs.some(v=>!Number.isFinite(v))){result.textContent=\"The model could not evaluate these inputs.\";return;}result.textContent=outputs.map((v,i)=>cfg.output_names[i]+\": \"+Number(v.toPrecision(7))).join(\"\\n\");root.dataset.outputs=JSON.stringify(outputs);};root.querySelector(\".nd-model-calculate\").addEventListener(\"click\",calculate);root.querySelector(\".nd-model-reset\").addEventListener(\"click\",()=>{controls.forEach((el,i)=>el.value=String(cfg.fields[i].value));calculate();});calculate();})();<\/script><div class=\"ndb-downloads\"><a class=\"aui aui-button\" href=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/09\/yacht-neural-designer-20260921.zip\">Download project and exports (ZIP)<\/a><a class=\"aui aui-button aui-button--secondary\" href=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/09\/yacht-data-20260921.csv\">Download source data (CSV)<\/a><a class=\"aui aui-button aui-button--secondary\" href=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/09\/yacht-schema-20260921.zip\">Download input schema (ZIP)<\/a><a class=\"aui aui-button aui-button--secondary\" href=\"https:\/\/www.neuraldesigner.com\/downloads\/\">Reproduce with Neural Designer<\/a><\/div><\/section>\n<section id=\"8-limitations\" class=\"ndb-card\"><h2>8. Scope and limitations<\/h2><p>The model is not a substitute for a towing-tank campaign or a validated hydrodynamic calculation. Predictions may be negative because the exported model does not clamp resistance. Restrict exploratory use to represented configurations, preserve coupled geometric constraints and review physical plausibility.<\/p><p>No external validation or independent calibration study is included. Preprocessing statistics and model choices should be refitted within a prospective or grouped validation design. Correlations and directional responses describe associations, not causes. Human review is required before an operational decision.<\/p><\/section>\n<section id=\"references\" class=\"ndb-card\"><h2>References<\/h2><ul><li><a href=\"https:\/\/archive.ics.uci.edu\/dataset\/243\/yacht+hydrodynamics\">Dataset source and provenance<\/a>.<\/li><li><a href=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/09\/yacht-neural-designer-20260921.zip\">Neural Designer project and saved task evidence, 21 September 2026<\/a>.<\/li><li><a href=\"https:\/\/www.neuraldesigner.com\/learning\/tutorials\/testing-analysis\/\">Neural Designer testing-analysis documentation<\/a>.<\/li><\/ul><\/section>\n<\/div>\n<\/div>\n<script data-noptimize=\"1\" data-cfasync=\"false\" src=\"https:\/\/cdn.plot.ly\/plotly-basic-4.0.0.min.js\"><\/script><script data-noptimize=\"1\">(()=>{const start=()=>{if(!window.Plotly)return;document.querySelectorAll('.nd-chart-bundle').forEach(bundle=>{if(bundle.dataset.started)return;bundle.dataset.started='1';const 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ready();})();<\/script>","protected":false},"author":13,"featured_media":1275,"template":"","categories":[29],"tags":[43],"class_list":["post-3530","learning","type-learning","status-publish","has-post-thumbnail","hentry","category-examples","tag-industry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Yacht hydrodynamics modeling using machine learning<\/title>\n<meta name=\"description\" content=\"Build a machine learning model to predict the hydrodynamics performance of sailing yachts from dimensions and velocity.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.neuraldesigner.com\/learning\/examples\/yacht-hydrodynamics-modeling\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" 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