{"id":"https://openalex.org/W7153977705","doi":"https://doi.org/10.48550/arxiv.2604.08863","title":"Hidden in Plain Sight: Visual-to-Symbolic Analytical Solution Inference from Field Visualizations","display_name":"Hidden in Plain Sight: Visual-to-Symbolic Analytical Solution Inference from Field Visualizations","publication_year":2026,"publication_date":"2026-04-10","ids":{"openalex":"https://openalex.org/W7153977705","doi":"https://doi.org/10.48550/arxiv.2604.08863"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.08863","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.08863","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.2604.08863","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133507068","display_name":"Pengze Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Li, Pengze","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133550789","display_name":"Jiaquan Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Jiaquan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130714483","display_name":"Yunbo Long","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Long, Yunbo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133547088","display_name":"Xinping Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Xinping","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133502671","display_name":"Zhou wenjie","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"wenjie, Zhou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5116867627","display_name":"Encheng Su","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Su, Encheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128121411","display_name":"Zihang Zeng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zeng, Zihang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133532692","display_name":"Jiaqi Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Jiaqi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133532590","display_name":"Jiyao Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Jiyao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060684352","display_name":"Junchi Yu","orcid":"https://orcid.org/0000-0003-4118-3248"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu, Junchi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133506701","display_name":"Lihao Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Lihao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133534006","display_name":"Philip Torr","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Torr, Philip","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133494934","display_name":"Shixiang Tang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tang, Shixiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133550516","display_name":"Aoran Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Aoran","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100330062","display_name":"Xi Chen","orcid":"https://orcid.org/0000-0003-4612-4044"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Xi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":15,"corresponding_author_ids":["https://openalex.org/A5133507068"],"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/T11948","display_name":"Machine Learning in Materials Science","score":0.5943999886512756,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.5943999886512756,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11986","display_name":"Scientific Computing and Data Management","score":0.07490000128746033,"subfield":{"id":"https://openalex.org/subfields/1802","display_name":"Information Systems and Management"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.07440000027418137,"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/inference","display_name":"Inference","score":0.7138000130653381},{"id":"https://openalex.org/keywords/pipeline","display_name":"Pipeline (software)","score":0.6672999858856201},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.6559000015258789},{"id":"https://openalex.org/keywords/executable","display_name":"Executable","score":0.6448000073432922},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5978000164031982},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5759000182151794},{"id":"https://openalex.org/keywords/visualization","display_name":"Visualization","score":0.4959999918937683},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.4392000138759613}],"concepts":[{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.7138000130653381},{"id":"https://openalex.org/C43521106","wikidata":"https://www.wikidata.org/wiki/Q2165493","display_name":"Pipeline (software)","level":2,"score":0.6672999858856201},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.6559000015258789},{"id":"https://openalex.org/C160145156","wikidata":"https://www.wikidata.org/wiki/Q778586","display_name":"Executable","level":2,"score":0.6448000073432922},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6104000210762024},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5978000164031982},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5759000182151794},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.4959999918937683},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4641999900341034},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.4392000138759613},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.4316999912261963},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.41499999165534973},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35019999742507935},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3447999954223633},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.3398999869823456},{"id":"https://openalex.org/C95167961","wikidata":"https://www.wikidata.org/wiki/Q4483495","display_name":"Fiducial inference","level":5,"score":0.336899995803833},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C172367668","wikidata":"https://www.wikidata.org/wiki/Q6504956","display_name":"Data visualization","level":3,"score":0.26820001006126404},{"id":"https://openalex.org/C917703","wikidata":"https://www.wikidata.org/wiki/Q7239668","display_name":"Predictive inference","level":5,"score":0.2669999897480011},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C2777055276","wikidata":"https://www.wikidata.org/wiki/Q7936580","display_name":"Visual approach","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C115901376","wikidata":"https://www.wikidata.org/wiki/Q184199","display_name":"Automation","level":2,"score":0.26460000872612},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.25940001010894775}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.08863","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.08863","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.2604.08863","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.08863","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":{"Recovering":[0],"analytical":[1,22],"solutions":[2],"of":[3],"physical":[4],"fields":[5],"from":[6],"visual":[7],"observations":[8],"is":[9],"a":[10,45,62,69,86,128],"fundamental":[11],"yet":[12],"underexplored":[13],"capability":[14],"for":[15,26],"AI-assisted":[16],"scientific":[17],"reasoning.":[18],"We":[19,55,82],"study":[20],"visual-to-symbolic":[21],"solution":[23],"inference":[24],"(ViSA)":[25],"two-dimensional":[27],"linear":[28,92],"steady-state":[29,93],"fields:":[30],"given":[31],"field":[32],"visualizations":[33],"(and":[34],"first-order":[35],"derivatives)":[36],"plus":[37],"minimal":[38],"auxiliary":[39],"metadata,":[40],"the":[41,122],"model":[42],"must":[43],"output":[44],"single":[46],"executable":[47],"SymPy":[48],"expression":[49],"with":[50,61,95],"fully":[51],"instantiated":[52],"numeric":[53],"constants.":[54],"introduce":[56],"ViSA-R2":[57,116],"and":[58,99,107,121],"align":[59],"it":[60],"self-verifying,":[63],"solution-centric":[64],"chain-of-thought":[65],"pipeline":[66],"that":[67],"follows":[68],"physicist-like":[70],"pathway:":[71],"structural":[72],"pattern":[73],"recognition":[74],"solution-family":[75],"(ansatz)":[76],"hypothesis":[77],"parameter":[78],"derivation":[79],"consistency":[80],"verification.":[81],"also":[83],"release":[84],"ViSA-Bench,":[85],"VLM-ready":[87],"synthetic":[88],"benchmark":[89],"covering":[90],"30":[91],"scenarios":[94],"verifiable":[96],"analytical/symbolic":[97],"annotations,":[98],"evaluate":[100],"predictions":[101],"by":[102],"numerical":[103],"accuracy,":[104],"expression-structure":[105],"similarity,":[106],"character-level":[108],"accuracy.":[109],"Using":[110],"an":[111],"8B":[112],"open-weight":[113],"Qwen3-VL":[114],"backbone,":[115],"outperforms":[117],"strong":[118],"open-source":[119],"baselines":[120],"evaluated":[123],"closed-source":[124],"frontier":[125],"VLMs":[126],"under":[127],"standardized":[129],"protocol.":[130]},"counts_by_year":[],"updated_date":"2026-04-29T09:16:38.111599","created_date":"2026-04-14T00:00:00"}