{"id":"https://openalex.org/W7154223041","doi":"https://doi.org/10.48550/arxiv.2604.11422","title":"Emulating Non-Differentiable Metrics via Knowledge-Guided Learning: Introducing the Minkowski Image Loss","display_name":"Emulating Non-Differentiable Metrics via Knowledge-Guided Learning: Introducing the Minkowski Image Loss","publication_year":2026,"publication_date":"2026-04-13","ids":{"openalex":"https://openalex.org/W7154223041","doi":"https://doi.org/10.48550/arxiv.2604.11422"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.11422","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.11422","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.2604.11422","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5094118621","display_name":"Filippo Quarenghi","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Quarenghi, Filippo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133591559","display_name":"Ryan Cotsakis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cotsakis, Ryan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5045746109","display_name":"Tom Beucler","orcid":"https://orcid.org/0000-0002-5731-1040"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Beucler, Tom","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5094118621"],"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.3377000093460083,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.3377000093460083,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.15230000019073486,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.08630000054836273,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6312999725341797},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5968999862670898},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4505000114440918},{"id":"https://openalex.org/keywords/minkowski-space","display_name":"Minkowski space","score":0.44760000705718994},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.40939998626708984},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.37700000405311584},{"id":"https://openalex.org/keywords/heaviside-step-function","display_name":"Heaviside step function","score":0.3560999929904938}],"concepts":[{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6312999725341797},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5968999862670898},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4505000114440918},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.44760000705718994},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4417000114917755},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.40939998626708984},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39239999651908875},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38359999656677246},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.37700000405311584},{"id":"https://openalex.org/C7980502","wikidata":"https://www.wikidata.org/wiki/Q322339","display_name":"Heaviside step function","level":2,"score":0.3560999929904938},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3361999988555908},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.3248000144958496},{"id":"https://openalex.org/C149810388","wikidata":"https://www.wikidata.org/wiki/Q5374873","display_name":"Emulation","level":2,"score":0.31150001287460327},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.29190000891685486},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.2888999879360199},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2847999930381775},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2761000096797943},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.2705000042915344},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.26339998841285706}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.11422","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.11422","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.2604.11422","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.11422","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"``differentiability":[1],"gap''":[2],"presents":[3],"a":[4,42,68,139,183,188],"primary":[5],"bottleneck":[6],"in":[7,174],"Earth":[8],"system":[9],"deep":[10],"learning:":[11],"since":[12],"models":[13],"cannot":[14],"be":[15],"trained":[16],"directly":[17],"on":[18,25,155],"non-differentiable":[19,55,65],"scientific":[20,80],"metrics":[21],"and":[22,95,120],"must":[23],"rely":[24],"smooth":[26],"proxies":[27],"(e.g.,":[28],"MSE),":[29],"they":[30],"often":[31],"fail":[32],"to":[33,52,60,75,107,115,182,225],"capture":[34],"high-frequency":[35],"details,":[36],"yielding":[37],"``blurry''":[38],"outputs.":[39],"We":[40,82,128],"develop":[41],"framework":[43],"that":[44],"bridges":[45],"this":[46,130],"gap":[47],"using":[48,92],"two":[49],"different":[50],"methods":[51],"deal":[53],"with":[54,221],"functions:":[56],"the":[57,63,72,84,117,135,143,156,170,204,214],"first":[58],"is":[59,74],"analytically":[61],"approximate":[62],"original":[64],"function":[66],"into":[67],"differentiable":[69,77,140,180],"equivalent":[70,141],"one;":[71],"second":[73],"learn":[76],"surrogates":[78,181],"for":[79,142],"functionals.":[81],"formulate":[83],"analytical":[85],"approximation":[86],"by":[87,133],"relaxing":[88],"discrete":[89],"topological":[90,219],"operations":[91],"temperature-controlled":[93],"sigmoids":[94],"continuous":[96],"logical":[97],"operators.":[98],"Conversely,":[99],"our":[100,160],"neural":[101,105,162],"emulator":[102],"uses":[103],"Lipschitz-convolutional":[104],"networks":[106],"stabilize":[108],"gradient":[109,201],"learning":[110],"via:":[111],"(1)":[112],"spectral":[113],"normalization":[114],"bound":[116],"Lipschitz":[118,193],"constant;":[119],"(2)":[121],"hard":[122],"architectural":[123],"constraints":[124,220],"enforcing":[125],"geometric":[126,171],"principles.":[127],"demonstrate":[129],"framework's":[131],"utility":[132],"developing":[134],"Minkowski":[136],"image":[137],"loss,":[138],"integral-geometric":[144],"measures":[145],"of":[146,206,216],"surface":[147],"precipitation":[148],"fields":[149],"(area,":[150],"perimeter,":[151],"connected":[152],"components).":[153],"Validated":[154],"EUMETNET":[157],"OPERA":[158],"dataset,":[159],"constrained":[161],"surrogate":[163],"achieves":[164],"high":[165],"emulation":[166],"accuracy,":[167],"completely":[168],"eliminating":[169],"violations":[172],"observed":[173],"unconstrained":[175],"baselines.":[176],"However,":[177],"applying":[178],"these":[179],"deterministic":[184],"super-resolution":[185],"task":[186],"reveals":[187],"fundamental":[189],"trade-off:":[190],"while":[191],"strict":[192],"regularization":[194],"ensures":[195],"optimization":[196],"stability,":[197],"it":[198],"inherently":[199],"over-smooths":[200],"signals,":[202],"restricting":[203],"recovery":[205],"highly":[207],"localized":[208],"convective":[209],"textures.":[210],"This":[211],"work":[212],"highlights":[213],"necessity":[215],"coupling":[217],"such":[218],"stochastic":[222],"generative":[223],"architectures":[224],"achieve":[226],"full":[227],"morphological":[228],"realism.":[229]},"counts_by_year":[],"updated_date":"2026-05-03T08:25:01.440150","created_date":"2026-04-15T00:00:00"}