{"id":"https://openalex.org/W7162800549","doi":"https://doi.org/10.48550/arxiv.2605.30272","title":"IGA-ODIL: Optimizing DIscretre robust Loss with Isogeometric Analysis to solve forward and inverse problems faster using machine learning tools","display_name":"IGA-ODIL: Optimizing DIscretre robust Loss with Isogeometric Analysis to solve forward and inverse problems faster using machine learning tools","publication_year":2026,"publication_date":"2026-05-28","ids":{"openalex":"https://openalex.org/W7162800549","doi":"https://doi.org/10.48550/arxiv.2605.30272"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.30272","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.30272","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.30272","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126632386","display_name":"Maciej Paszy\u0144ski","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paszy\u0144ski, Maciej","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137347766","display_name":"Tomasz S\u0142u\u017calec","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S\u0142u\u017calec, Tomasz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9502999782562256,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9502999782562256,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.006099999882280827,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.005100000184029341,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/isogeometric-analysis","display_name":"Isogeometric analysis","score":0.5968999862670898},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5911999940872192},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.4932999908924103},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.48570001125335693},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.4611999988555908},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.44510000944137573},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42289999127388},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4122999906539917},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.391400009393692},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.38769999146461487}],"concepts":[{"id":"https://openalex.org/C2780737243","wikidata":"https://www.wikidata.org/wiki/Q17082433","display_name":"Isogeometric analysis","level":3,"score":0.5968999862670898},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5911999940872192},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5282999873161316},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.4932999908924103},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4862000048160553},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.48570001125335693},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.4611999988555908},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.44510000944137573},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4323999881744385},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42289999127388},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4122999906539917},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.391400009393692},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.38769999146461487},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.3871000111103058},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.37619999051094055},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3605000078678131},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3571000099182129},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35359999537467957},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.3481000065803528},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.29339998960494995},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2928999960422516},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.2833999991416931},{"id":"https://openalex.org/C158847443","wikidata":"https://www.wikidata.org/wiki/Q1997812","display_name":"Method of steepest descent","level":2,"score":0.27959999442100525},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.2712000012397766},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.2680000066757202},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.2558000087738037},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.2538999915122986},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.2515999972820282},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.2502000033855438}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.30272","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.30272","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.30272","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.30272","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Physics-informed":[0],"neural":[1,16],"networks":[2],"(PINNs)":[3],"formulate":[4],"the":[5,36,45,60,98,129,134,155],"solution":[6,100],"of":[7,23,28,41,62,93,96,146,158],"partial":[8],"differential":[9],"equations":[10],"as":[11],"residual":[12,74,86,121],"minimization":[13,75],"problems":[14,178],"over":[15],"network":[17],"parameterizations.":[18],"Although":[19],"highly":[20,180],"flexible,":[21],"optimization":[22,64],"PINNs":[24,198],"using":[25,44],"modern":[26],"variants":[27],"Stochastic":[29],"Gradient":[30],"Descent":[31],"algorithms":[32],"is":[33,101,165],"expensive.":[34],"On":[35],"other":[37],"hand,":[38],"iterative":[39],"computation":[40],"PINN":[42],"parameterization":[43],"Gauss-Newton":[46],"method":[47],"suffers":[48],"from":[49,79],"convergence":[50],"difficulties,":[51],"dense":[52],"Jacobian":[53],"structures,":[54],"and":[55,88,113,143,150,186,199,205],"poor":[56],"conditioning":[57],"that":[58],"limit":[59],"effectiveness":[61],"second-order":[63],"methods.":[65],"In":[66],"this":[67],"work,":[68],"we":[69],"introduce":[70],"IGA-ODIL,":[71],"a":[72],"spline-based":[73],"framework":[76],"combining":[77],"ideas":[78],"Optimizing":[80],"DIscrete":[81],"Loss":[82],"(ODIL),":[83],"robust":[84,120],"variational":[85],"minimization,":[87],"Isogeometric":[89],"Analysis":[90],"(IGA).":[91],"Instead":[92],"neural-network":[94],"parameterizations":[95],"PINNs,":[97],"unknown":[99],"represented":[102],"by":[103],"smooth":[104],"B-spline":[105],"basis":[106],"functions,":[107],"leading":[108],"to":[109],"sparse":[110],"structured":[111],"Jacobians":[112],"efficient":[114],"Gauss--Newton":[115],"optimization.":[116],"We":[117],"also":[118],"derive":[119],"formulations":[122],"based":[123],"on":[124,167],"weighted":[125],"Gram":[126],"operators,":[127],"making":[128],"loss":[130],"function":[131],"related":[132],"with":[133,179,197],"true":[135],"error.":[136],"The":[137,162],"resulting":[138],"systems":[139],"inherit":[140],"locality,":[141],"sparsity,":[142],"approximation-theoretic":[144],"properties":[145],"classical":[147],"finite":[148],"element":[149],"isogeometric":[151],"methods":[152],"while":[153,201],"preserving":[154],"residual-learning":[156],"philosophy":[157],"scientific":[159],"machine":[160],"learning.":[161],"proposed":[163],"methodology":[164],"evaluated":[166],"several":[168],"benchmark":[169],"problems,":[170],"including":[171],"Poisson":[172],"equations,":[173,176,185],"convection-dominated":[174],"advection--diffusion":[175],"Helmholtz":[177,188],"oscillatory":[181],"solutions,":[182],"nonlinear":[183],"Allen--Cahn":[184],"inverse":[187],"parameter":[189],"identification.":[190],"Numerical":[191],"experiments":[192],"demonstrate":[193],"orders-of-magnitude":[194],"speedups":[195],"compared":[196],"CRVPINNs":[200],"maintaining":[202],"high":[203],"accuracy":[204],"robustness.":[206]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-30T00:00:00"}