{"id":"https://openalex.org/W7163062585","doi":"https://doi.org/10.48550/arxiv.2605.31276","title":"Learning Parametric Nitrogen Fertilizer Response Curves Using Neuro Symbolic Regression","display_name":"Learning Parametric Nitrogen Fertilizer Response Curves Using Neuro Symbolic Regression","publication_year":2026,"publication_date":"2026-05-29","ids":{"openalex":"https://openalex.org/W7163062585","doi":"https://doi.org/10.48550/arxiv.2605.31276"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.31276","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.31276","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.31276","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135541318","display_name":"Giorgio Morales","orcid":"https://orcid.org/0000-0003-2911-8558"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Morales, Giorgio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137535265","display_name":"John Sheppard","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sheppard, John","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T10616","display_name":"Smart Agriculture and AI","score":0.42890000343322754,"subfield":{"id":"https://openalex.org/subfields/1110","display_name":"Plant Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10616","display_name":"Smart Agriculture and AI","score":0.42890000343322754,"subfield":{"id":"https://openalex.org/subfields/1110","display_name":"Plant Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10184","display_name":"Plant Molecular Biology Research","score":0.050999999046325684,"subfield":{"id":"https://openalex.org/subfields/1110","display_name":"Plant Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12093","display_name":"Greenhouse Technology and Climate Control","score":0.047200001776218414,"subfield":{"id":"https://openalex.org/subfields/1110","display_name":"Plant Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.7251999974250793},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5264999866485596},{"id":"https://openalex.org/keywords/symbolic-regression","display_name":"Symbolic regression","score":0.5149000287055969},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.4812999963760376},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.42309999465942383},{"id":"https://openalex.org/keywords/parametric-model","display_name":"Parametric model","score":0.3869999945163727}],"concepts":[{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.7251999974250793},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5422999858856201},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5264999866485596},{"id":"https://openalex.org/C2776400721","wikidata":"https://www.wikidata.org/wiki/Q18171762","display_name":"Symbolic regression","level":3,"score":0.5149000287055969},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4860000014305115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48399999737739563},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.4812999963760376},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.42309999465942383},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40849998593330383},{"id":"https://openalex.org/C24574437","wikidata":"https://www.wikidata.org/wiki/Q7135228","display_name":"Parametric model","level":3,"score":0.3869999945163727},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.36640000343322754},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.34040001034736633},{"id":"https://openalex.org/C84525736","wikidata":"https://www.wikidata.org/wiki/Q831366","display_name":"Decision tree","level":2,"score":0.33180001378059387},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.326200008392334},{"id":"https://openalex.org/C99636146","wikidata":"https://www.wikidata.org/wiki/Q35889","display_name":"Parametric equation","level":2,"score":0.31859999895095825},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2944999933242798},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27459999918937683},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.259799987077713}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.31276","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.31276","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.31276","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.31276","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"},"sustainable_development_goals":[{"score":0.8254542946815491,"display_name":"Zero hunger","id":"https://metadata.un.org/sdg/2"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Accurately":[0],"modeling":[1],"crop":[2],"response":[3],"to":[4,40,60,115,131,151,170,225],"Nitrogen":[5],"(N)":[6],"fertilization":[7],"is":[8],"a":[9,54,67,74,119,184],"fundamental":[10],"challenge":[11],"in":[12,156,237],"precision":[13,238],"agriculture,":[14],"as":[15,203],"it":[16],"impacts":[17],"both":[18],"economic":[19],"returns":[20],"and":[21,100,205,233],"environmental":[22],"sustainability.":[23],"Existing":[24],"approaches":[25],"either":[26],"rely":[27],"on":[28,127],"predefined":[29,68],"parametric":[30,62,177],"forms":[31],"or":[32,42,91],"opaque":[33],"machine":[34],"learning":[35,175],"models,":[36],"limiting":[37],"their":[38],"ability":[39,145],"interpret":[41],"discover":[43],"site-specific":[44,230],"functional":[45,69,86,212],"relationships":[46,232],"from":[47],"data.":[48],"In":[49,159],"this":[50,160],"work,":[51,161],"we":[52,162],"propose":[53],"neuro":[55,222],"symbolic":[56,109],"regression":[57],"(SR)":[58],"approach":[59,72,150],"learn":[61],"N-response":[63,178],"curves":[64,179],"without":[65],"assuming":[66],"form.":[70],"Our":[71],"integrates":[73],"transformer-based":[75],"Multi-Set":[76],"Symbolic":[77],"Skeleton":[78],"Prediction":[79],"strategy,":[80],"enabling":[81],"the":[82,105,144,147,164,190,219,227],"discovery":[83,228],"of":[84,138,146,166,229],"shared":[85],"structures":[87],"across":[88,103,214],"multiple":[89],"subdomains":[90],"management":[92],"zones":[93],"(MZs).":[94],"By":[95],"constructing":[96],"diverse":[97,211],"input":[98],"subsets":[99],"enforcing":[101],"consistency":[102],"them,":[104],"method":[106,169],"recovers":[107],"robust":[108],"skeletons":[110],"that":[111,189,221],"are":[112],"subsequently":[113],"fitted":[114],"observed":[116],"data":[117],"using":[118],"genetic":[120],"algorithm.":[121],"This":[122,217],"framework":[123],"was":[124],"first":[125],"evaluated":[126],"synthetic":[128],"one-dimensional":[129],"problems":[130],"assess":[132],"its":[133],"robustness":[134],"under":[135],"varying":[136],"levels":[137],"epistemic":[139],"uncertainty.":[140],"The":[141,186],"results":[142,165,187],"demonstrate":[143],"proposed":[148],"SR":[149,223],"recover":[152],"correct":[153],"expressions":[154,192],"even":[155],"data-scarce":[157],"regimes.":[158],"present":[163],"applying":[167],"our":[168],"real-world":[171],"winter":[172],"wheat":[173],"data,":[174],"distinct":[176],"for":[180],"different":[181],"MZs":[182],"within":[183],"field.":[185],"show":[188],"discovered":[191],"not":[193],"only":[194],"achieve":[195],"lower":[196],"fitting":[197],"errors":[198],"than":[199],"traditional":[200],"models":[201],"such":[202],"quadratic-plateau":[204],"exponential":[206],"functions,":[207],"but":[208],"also":[209],"capture":[210],"behaviors":[213],"spatial":[215],"regions.":[216],"demonstrates":[218],"potential":[220],"has":[224],"enable":[226],"agronomic":[231],"support":[234],"informed":[235],"decision-making":[236],"agriculture.":[239]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-02T00:00:00"}
