Characterization and Inverse Design of Stochastic Mechanical Metamaterials Using Neural Operators Article Swipe
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1002/adma.202420063
Machine learning (ML) is emerging as a transformative tool for the design of mechanical metamaterials, offering properties that far surpass those achievable through lab‐based trial‐and‐error methods. However, a major challenge in current inverse design strategies is their reliance on extensive computational and/or experimental datasets, which becomes particularly problematic for designing micro‐scale stochastic architected materials that exhibit nonlinear mechanical behaviors. Here, a comprehensive end‐to‐end scientific ML framework, leveraging deep neural operators (including DeepONet and its variants) is introduced, to directly learn the relationship between the complete microstructure and mechanical response of architected metamaterials from sparse but high‐quality in situ experimental data. Various neural operators and standard neural networks are systematically compared to identify the model that offers better interpretability and accuracy. The approach facilitates the efficient inverse design of structures tailored to specific nonlinear mechanical behaviors. Results obtained from stochastic spinodal microstructures, printed using two‐photon lithography, reveal that the prediction error for mechanical responses is within a range of 5 ‐ 10%. This work underscores that by employing neural operators with advanced nano‐ and micro‐mechanical experiments, the design of complex micro‐architected materials with desired properties becomes feasible, even in scenarios constrained by data scarcity. This work marks a significant advancement in the field of materials‐by‐design, potentially heralding a new era in the discovery and development of next‐generation metamaterials with unparalleled mechanical characteristics derived directly from experimental insights.
Related Topics
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1002/adma.202420063
- https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/adma.202420063
- OA Status
- hybrid
- Cited By
- 9
- References
- 49
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4409649139
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4409649139Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1002/adma.202420063Digital Object Identifier
- Title
-
Characterization and Inverse Design of Stochastic Mechanical Metamaterials Using Neural OperatorsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2025Year of publication
- Publication date
-
2025-04-21Full publication date if available
- Authors
-
Hanxun Jin, Boyu Zhang, Qianying Cao, Enrui Zhang, Aniruddha Bora, Sridhar Krishnaswamy, George Em Karniadakis, Horacio D. EspinosaList of authors in order
- Landing page
-
https://doi.org/10.1002/adma.202420063Publisher landing page
- PDF URL
-
https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/adma.202420063Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
hybridOpen access status per OpenAlex
- OA URL
-
https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/adma.202420063Direct OA link when available
- Concepts
-
Metamaterial, Interpretability, Artificial neural network, Inverse, Materials science, Computer science, Nonlinear system, Artificial intelligence, Machine learning, Mechanical engineering, Physics, Engineering, Mathematics, Quantum mechanics, Optoelectronics, GeometryTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
9Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 9Per-year citation counts (last 5 years)
- References (count)
-
49Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4409649139 |
|---|---|
| doi | https://doi.org/10.1002/adma.202420063 |
| ids.doi | https://doi.org/10.1002/adma.202420063 |
| ids.pmid | https://pubmed.ncbi.nlm.nih.gov/40255086 |
| ids.openalex | https://openalex.org/W4409649139 |
| fwci | 14.26911432 |
| type | article |
| title | Characterization and Inverse Design of Stochastic Mechanical Metamaterials Using Neural Operators |
| awards[0].id | https://openalex.org/G4005068700 |
| awards[0].funder_id | https://openalex.org/F4320337345 |
| awards[0].display_name | |
| awards[0].funder_award_id | N00014‐22‐1‐2795 |
| awards[0].funder_display_name | Office of Naval Research |
| awards[1].id | https://openalex.org/G3799177075 |
| awards[1].funder_id | https://openalex.org/F4320338279 |
| awards[1].display_name | |
| awards[1].funder_award_id | FA9550‐20‐1‐0258 |
| awards[1].funder_display_name | Air Force Office of Scientific Research |
| awards[2].id | https://openalex.org/G2072716033 |
| awards[2].funder_id | https://openalex.org/F4320338279 |
| awards[2].display_name | |
| awards[2].funder_award_id | FA9550‐20‐1‐0358 |
| awards[2].funder_display_name | Air Force Office of Scientific Research |
| awards[3].id | https://openalex.org/G5839883168 |
| awards[3].funder_id | https://openalex.org/F4320337345 |
| awards[3].display_name | |
| awards[3].funder_award_id | N00014‐22‐1‐2133 |
| awards[3].funder_display_name | Office of Naval Research |
| awards[4].id | https://openalex.org/G3206746880 |
| awards[4].funder_id | https://openalex.org/F4320337345 |
| awards[4].display_name | |
| awards[4].funder_award_id | N00014‐15‐1‐2935 |
| awards[4].funder_display_name | Office of Naval Research |
| awards[5].id | https://openalex.org/G4294102737 |
| awards[5].funder_id | https://openalex.org/F4320337345 |
| awards[5].display_name | |
| awards[5].funder_award_id | N00014‐23‐1‐2529 |
| awards[5].funder_display_name | Office of Naval Research |
| awards[6].id | https://openalex.org/G1447203121 |
| awards[6].funder_id | https://openalex.org/F4320332170 |
| awards[6].display_name | |
| awards[6].funder_award_id | CMMI‐1953806 |
| awards[6].funder_display_name | Directorate for Engineering |
| biblio.issue | 29 |
| biblio.volume | 37 |
| biblio.last_page | e2420063 |
| biblio.first_page | e2420063 |
| topics[0].id | https://openalex.org/T11277 |
| topics[0].field.id | https://openalex.org/fields/25 |
| topics[0].field.display_name | Materials Science |
| topics[0].score | 0.9976999759674072 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2505 |
| topics[0].subfield.display_name | Materials Chemistry |
| topics[0].display_name | Thermal properties of materials |
| topics[1].id | https://openalex.org/T11948 |
| topics[1].field.id | https://openalex.org/fields/25 |
| topics[1].field.display_name | Materials Science |
| topics[1].score | 0.9944999814033508 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2505 |
| topics[1].subfield.display_name | Materials Chemistry |
| topics[1].display_name | Machine Learning in Materials Science |
| topics[2].id | https://openalex.org/T11471 |
| topics[2].field.id | https://openalex.org/fields/25 |
| topics[2].field.display_name | Materials Science |
| topics[2].score | 0.9916999936103821 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2505 |
| topics[2].subfield.display_name | Materials Chemistry |
| topics[2].display_name | Block Copolymer Self-Assembly |
| funders[0].id | https://openalex.org/F4320332170 |
| funders[0].ror | https://ror.org/00b6sbb32 |
| funders[0].display_name | Directorate for Engineering |
| funders[1].id | https://openalex.org/F4320337345 |
| funders[1].ror | https://ror.org/00rk2pe57 |
| funders[1].display_name | Office of Naval Research |
| funders[2].id | https://openalex.org/F4320338279 |
| funders[2].ror | https://ror.org/011e9bt93 |
| funders[2].display_name | Air Force Office of Scientific Research |
| is_xpac | False |
| apc_list.value | 5250 |
| apc_list.currency | USD |
| apc_list.value_usd | 5250 |
| apc_paid.value | 5250 |
| apc_paid.currency | USD |
| apc_paid.value_usd | 5250 |
| concepts[0].id | https://openalex.org/C110367647 |
| concepts[0].level | 2 |
| concepts[0].score | 0.6641407012939453 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q497166 |
| concepts[0].display_name | Metamaterial |
| concepts[1].id | https://openalex.org/C2781067378 |
| concepts[1].level | 2 |
| concepts[1].score | 0.6239385008811951 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q17027399 |
| concepts[1].display_name | Interpretability |
| concepts[2].id | https://openalex.org/C50644808 |
| concepts[2].level | 2 |
| concepts[2].score | 0.5467090606689453 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q192776 |
| concepts[2].display_name | Artificial neural network |
| concepts[3].id | https://openalex.org/C207467116 |
| concepts[3].level | 2 |
| concepts[3].score | 0.5194665789604187 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q4385666 |
| concepts[3].display_name | Inverse |
| concepts[4].id | https://openalex.org/C192562407 |
| concepts[4].level | 0 |
| concepts[4].score | 0.5156627893447876 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q228736 |
| concepts[4].display_name | Materials science |
| concepts[5].id | https://openalex.org/C41008148 |
| concepts[5].level | 0 |
| concepts[5].score | 0.5012557506561279 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[5].display_name | Computer science |
| concepts[6].id | https://openalex.org/C158622935 |
| concepts[6].level | 2 |
| concepts[6].score | 0.42881959676742554 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q660848 |
| concepts[6].display_name | Nonlinear system |
| concepts[7].id | https://openalex.org/C154945302 |
| concepts[7].level | 1 |
| concepts[7].score | 0.38962841033935547 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q11660 |
| concepts[7].display_name | Artificial intelligence |
| concepts[8].id | https://openalex.org/C119857082 |
| concepts[8].level | 1 |
| concepts[8].score | 0.3430689573287964 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q2539 |
| concepts[8].display_name | Machine learning |
| concepts[9].id | https://openalex.org/C78519656 |
| concepts[9].level | 1 |
| concepts[9].score | 0.3347064256668091 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q101333 |
| concepts[9].display_name | Mechanical engineering |
| concepts[10].id | https://openalex.org/C121332964 |
| concepts[10].level | 0 |
| concepts[10].score | 0.15071353316307068 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[10].display_name | Physics |
| concepts[11].id | https://openalex.org/C127413603 |
| concepts[11].level | 0 |
| concepts[11].score | 0.13151291012763977 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q11023 |
| concepts[11].display_name | Engineering |
| concepts[12].id | https://openalex.org/C33923547 |
| concepts[12].level | 0 |
| concepts[12].score | 0.12317296862602234 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[12].display_name | Mathematics |
| concepts[13].id | https://openalex.org/C62520636 |
| concepts[13].level | 1 |
| concepts[13].score | 0.0 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q944 |
| concepts[13].display_name | Quantum mechanics |
| concepts[14].id | https://openalex.org/C49040817 |
| concepts[14].level | 1 |
| concepts[14].score | 0.0 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q193091 |
| concepts[14].display_name | Optoelectronics |
| concepts[15].id | https://openalex.org/C2524010 |
| concepts[15].level | 1 |
| concepts[15].score | 0.0 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q8087 |
| concepts[15].display_name | Geometry |
| keywords[0].id | https://openalex.org/keywords/metamaterial |
| keywords[0].score | 0.6641407012939453 |
| keywords[0].display_name | Metamaterial |
| keywords[1].id | https://openalex.org/keywords/interpretability |
| keywords[1].score | 0.6239385008811951 |
| keywords[1].display_name | Interpretability |
| keywords[2].id | https://openalex.org/keywords/artificial-neural-network |
| keywords[2].score | 0.5467090606689453 |
| keywords[2].display_name | Artificial neural network |
| keywords[3].id | https://openalex.org/keywords/inverse |
| keywords[3].score | 0.5194665789604187 |
| keywords[3].display_name | Inverse |
| keywords[4].id | https://openalex.org/keywords/materials-science |
| keywords[4].score | 0.5156627893447876 |
| keywords[4].display_name | Materials science |
| keywords[5].id | https://openalex.org/keywords/computer-science |
| keywords[5].score | 0.5012557506561279 |
| keywords[5].display_name | Computer science |
| keywords[6].id | https://openalex.org/keywords/nonlinear-system |
| keywords[6].score | 0.42881959676742554 |
| keywords[6].display_name | Nonlinear system |
| keywords[7].id | https://openalex.org/keywords/artificial-intelligence |
| keywords[7].score | 0.38962841033935547 |
| keywords[7].display_name | Artificial intelligence |
| keywords[8].id | https://openalex.org/keywords/machine-learning |
| keywords[8].score | 0.3430689573287964 |
| keywords[8].display_name | Machine learning |
| keywords[9].id | https://openalex.org/keywords/mechanical-engineering |
| keywords[9].score | 0.3347064256668091 |
| keywords[9].display_name | Mechanical engineering |
| keywords[10].id | https://openalex.org/keywords/physics |
| keywords[10].score | 0.15071353316307068 |
| keywords[10].display_name | Physics |
| keywords[11].id | https://openalex.org/keywords/engineering |
| keywords[11].score | 0.13151291012763977 |
| keywords[11].display_name | Engineering |
| keywords[12].id | https://openalex.org/keywords/mathematics |
| keywords[12].score | 0.12317296862602234 |
| keywords[12].display_name | Mathematics |
| language | en |
| locations[0].id | doi:10.1002/adma.202420063 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S99352657 |
| locations[0].source.issn | 0935-9648, 1521-4095 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | False |
| locations[0].source.issn_l | 0935-9648 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | Advanced Materials |
| locations[0].source.host_organization | |
| locations[0].source.host_organization_name | |
| locations[0].license | cc-by-nc-nd |
| locations[0].pdf_url | https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/adma.202420063 |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by-nc-nd |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | Advanced Materials |
| locations[0].landing_page_url | https://doi.org/10.1002/adma.202420063 |
| locations[1].id | pmid:40255086 |
| locations[1].is_oa | False |
| locations[1].source.id | https://openalex.org/S4306525036 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | PubMed |
| locations[1].source.host_organization | https://openalex.org/I1299303238 |
| locations[1].source.host_organization_name | National Institutes of Health |
| locations[1].source.host_organization_lineage | https://openalex.org/I1299303238 |
| locations[1].license | |
| locations[1].pdf_url | |
| locations[1].version | publishedVersion |
| locations[1].raw_type | |
| locations[1].license_id | |
| locations[1].is_accepted | True |
| locations[1].is_published | True |
| locations[1].raw_source_name | Advanced materials (Deerfield Beach, Fla.) |
| locations[1].landing_page_url | https://pubmed.ncbi.nlm.nih.gov/40255086 |
| locations[2].id | pmh:oai:europepmc.org:11099721 |
| locations[2].is_oa | True |
| locations[2].source.id | https://openalex.org/S4306400806 |
| locations[2].source.issn | |
| locations[2].source.type | repository |
| locations[2].source.is_oa | False |
| locations[2].source.issn_l | |
| locations[2].source.is_core | False |
| locations[2].source.is_in_doaj | False |
| locations[2].source.display_name | Europe PMC (PubMed Central) |
| locations[2].source.host_organization | https://openalex.org/I1303153112 |
| locations[2].source.host_organization_name | European Bioinformatics Institute |
| locations[2].source.host_organization_lineage | https://openalex.org/I1303153112 |
| locations[2].license | other-oa |
| locations[2].pdf_url | |
| locations[2].version | submittedVersion |
| locations[2].raw_type | Text |
| locations[2].license_id | https://openalex.org/licenses/other-oa |
| locations[2].is_accepted | False |
| locations[2].is_published | False |
| locations[2].raw_source_name | |
| locations[2].landing_page_url | https://www.ncbi.nlm.nih.gov/pmc/articles/12288774 |
| indexed_in | crossref, pubmed |
| authorships[0].author.id | https://openalex.org/A5047301386 |
| authorships[0].author.orcid | https://orcid.org/0000-0001-7226-533X |
| authorships[0].author.display_name | Hanxun Jin |
| authorships[0].countries | US |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I111979921 |
| authorships[0].affiliations[0].raw_affiliation_string | Department of Mechanical Engineering Northwestern University Evanston IL 60208 USA |
| authorships[0].institutions[0].id | https://openalex.org/I111979921 |
| authorships[0].institutions[0].ror | https://ror.org/000e0be47 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I111979921 |
| authorships[0].institutions[0].country_code | US |
| authorships[0].institutions[0].display_name | Northwestern University |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Hanxun Jin |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | Department of Mechanical Engineering Northwestern University Evanston IL 60208 USA |
| authorships[1].author.id | https://openalex.org/A5100714039 |
| authorships[1].author.orcid | https://orcid.org/0000-0003-0972-3240 |
| authorships[1].author.display_name | Boyu Zhang |
| authorships[1].countries | US |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I111979921 |
| authorships[1].affiliations[0].raw_affiliation_string | Department of Mechanical Engineering Northwestern University Evanston IL 60208 USA |
| authorships[1].institutions[0].id | https://openalex.org/I111979921 |
| authorships[1].institutions[0].ror | https://ror.org/000e0be47 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I111979921 |
| authorships[1].institutions[0].country_code | US |
| authorships[1].institutions[0].display_name | Northwestern University |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Boyu Zhang |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | Department of Mechanical Engineering Northwestern University Evanston IL 60208 USA |
| authorships[2].author.id | https://openalex.org/A5070769758 |
| authorships[2].author.orcid | https://orcid.org/0000-0002-7570-012X |
| authorships[2].author.display_name | Qianying Cao |
| authorships[2].countries | US |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I27804330 |
| authorships[2].affiliations[0].raw_affiliation_string | Division of Applied Mathematics Brown University Providence RI 02912 USA |
| authorships[2].institutions[0].id | https://openalex.org/I27804330 |
| authorships[2].institutions[0].ror | https://ror.org/05gq02987 |
| authorships[2].institutions[0].type | education |
| authorships[2].institutions[0].lineage | https://openalex.org/I27804330 |
| authorships[2].institutions[0].country_code | US |
| authorships[2].institutions[0].display_name | Brown University |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Qianying Cao |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | Division of Applied Mathematics Brown University Providence RI 02912 USA |
| authorships[3].author.id | https://openalex.org/A5061668124 |
| authorships[3].author.orcid | https://orcid.org/0000-0001-6955-1124 |
| authorships[3].author.display_name | Enrui Zhang |
| authorships[3].countries | US |
| authorships[3].affiliations[0].institution_ids | https://openalex.org/I27804330 |
| authorships[3].affiliations[0].raw_affiliation_string | Division of Applied Mathematics Brown University Providence RI 02912 USA |
| authorships[3].institutions[0].id | https://openalex.org/I27804330 |
| authorships[3].institutions[0].ror | https://ror.org/05gq02987 |
| authorships[3].institutions[0].type | education |
| authorships[3].institutions[0].lineage | https://openalex.org/I27804330 |
| authorships[3].institutions[0].country_code | US |
| authorships[3].institutions[0].display_name | Brown University |
| authorships[3].author_position | middle |
| authorships[3].raw_author_name | Enrui Zhang |
| authorships[3].is_corresponding | False |
| authorships[3].raw_affiliation_strings | Division of Applied Mathematics Brown University Providence RI 02912 USA |
| authorships[4].author.id | https://openalex.org/A5024150482 |
| authorships[4].author.orcid | https://orcid.org/0000-0001-8015-9924 |
| authorships[4].author.display_name | Aniruddha Bora |
| authorships[4].countries | US |
| authorships[4].affiliations[0].institution_ids | https://openalex.org/I27804330 |
| authorships[4].affiliations[0].raw_affiliation_string | Division of Applied Mathematics Brown University Providence RI 02912 USA |
| authorships[4].institutions[0].id | https://openalex.org/I27804330 |
| authorships[4].institutions[0].ror | https://ror.org/05gq02987 |
| authorships[4].institutions[0].type | education |
| authorships[4].institutions[0].lineage | https://openalex.org/I27804330 |
| authorships[4].institutions[0].country_code | US |
| authorships[4].institutions[0].display_name | Brown University |
| authorships[4].author_position | middle |
| authorships[4].raw_author_name | Aniruddha Bora |
| authorships[4].is_corresponding | False |
| authorships[4].raw_affiliation_strings | Division of Applied Mathematics Brown University Providence RI 02912 USA |
| authorships[5].author.id | https://openalex.org/A5076269020 |
| authorships[5].author.orcid | https://orcid.org/0000-0002-3015-9149 |
| authorships[5].author.display_name | Sridhar Krishnaswamy |
| authorships[5].countries | US |
| authorships[5].affiliations[0].institution_ids | https://openalex.org/I111979921 |
| authorships[5].affiliations[0].raw_affiliation_string | Department of Mechanical Engineering Northwestern University Evanston IL 60208 USA |
| authorships[5].institutions[0].id | https://openalex.org/I111979921 |
| authorships[5].institutions[0].ror | https://ror.org/000e0be47 |
| authorships[5].institutions[0].type | education |
| authorships[5].institutions[0].lineage | https://openalex.org/I111979921 |
| authorships[5].institutions[0].country_code | US |
| authorships[5].institutions[0].display_name | Northwestern University |
| authorships[5].author_position | middle |
| authorships[5].raw_author_name | Sridhar Krishnaswamy |
| authorships[5].is_corresponding | False |
| authorships[5].raw_affiliation_strings | Department of Mechanical Engineering Northwestern University Evanston IL 60208 USA |
| authorships[6].author.id | https://openalex.org/A5055763595 |
| authorships[6].author.orcid | |
| authorships[6].author.display_name | George Em Karniadakis |
| authorships[6].countries | US |
| authorships[6].affiliations[0].institution_ids | https://openalex.org/I27804330 |
| authorships[6].affiliations[0].raw_affiliation_string | School of Engineering Brown University Providence RI 02912 USA |
| authorships[6].affiliations[1].institution_ids | https://openalex.org/I27804330 |
| authorships[6].affiliations[1].raw_affiliation_string | Division of Applied Mathematics Brown University Providence RI 02912 USA |
| authorships[6].institutions[0].id | https://openalex.org/I27804330 |
| authorships[6].institutions[0].ror | https://ror.org/05gq02987 |
| authorships[6].institutions[0].type | education |
| authorships[6].institutions[0].lineage | https://openalex.org/I27804330 |
| authorships[6].institutions[0].country_code | US |
| authorships[6].institutions[0].display_name | Brown University |
| authorships[6].author_position | middle |
| authorships[6].raw_author_name | George Em Karniadakis |
| authorships[6].is_corresponding | False |
| authorships[6].raw_affiliation_strings | Division of Applied Mathematics Brown University Providence RI 02912 USA, School of Engineering Brown University Providence RI 02912 USA |
| authorships[7].author.id | https://openalex.org/A5078407077 |
| authorships[7].author.orcid | https://orcid.org/0000-0002-1907-3213 |
| authorships[7].author.display_name | Horacio D. Espinosa |
| authorships[7].countries | US |
| authorships[7].affiliations[0].institution_ids | https://openalex.org/I111979921 |
| authorships[7].affiliations[0].raw_affiliation_string | Department of Mechanical Engineering Northwestern University Evanston IL 60208 USA |
| authorships[7].institutions[0].id | https://openalex.org/I111979921 |
| authorships[7].institutions[0].ror | https://ror.org/000e0be47 |
| authorships[7].institutions[0].type | education |
| authorships[7].institutions[0].lineage | https://openalex.org/I111979921 |
| authorships[7].institutions[0].country_code | US |
| authorships[7].institutions[0].display_name | Northwestern University |
| authorships[7].author_position | last |
| authorships[7].raw_author_name | Horacio D. Espinosa |
| authorships[7].is_corresponding | False |
| authorships[7].raw_affiliation_strings | Department of Mechanical Engineering Northwestern University Evanston IL 60208 USA |
| has_content.pdf | True |
| has_content.grobid_xml | True |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/adma.202420063 |
| open_access.oa_status | hybrid |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Characterization and Inverse Design of Stochastic Mechanical Metamaterials Using Neural Operators |
| has_fulltext | True |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T11277 |
| primary_topic.field.id | https://openalex.org/fields/25 |
| primary_topic.field.display_name | Materials Science |
| primary_topic.score | 0.9976999759674072 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2505 |
| primary_topic.subfield.display_name | Materials Chemistry |
| primary_topic.display_name | Thermal properties of materials |
| related_works | https://openalex.org/W2905433371, https://openalex.org/W2888392564, https://openalex.org/W4310278675, https://openalex.org/W4388422664, https://openalex.org/W4390569940, https://openalex.org/W4361193272, https://openalex.org/W2963326959, https://openalex.org/W4388685194, https://openalex.org/W4312407344, https://openalex.org/W2894289927 |
| cited_by_count | 9 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 9 |
| locations_count | 3 |
| best_oa_location.id | doi:10.1002/adma.202420063 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S99352657 |
| best_oa_location.source.issn | 0935-9648, 1521-4095 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | False |
| best_oa_location.source.issn_l | 0935-9648 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | Advanced Materials |
| best_oa_location.source.host_organization | |
| best_oa_location.source.host_organization_name | |
| best_oa_location.license | cc-by-nc-nd |
| best_oa_location.pdf_url | https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/adma.202420063 |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by-nc-nd |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | Advanced Materials |
| best_oa_location.landing_page_url | https://doi.org/10.1002/adma.202420063 |
| primary_location.id | doi:10.1002/adma.202420063 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S99352657 |
| primary_location.source.issn | 0935-9648, 1521-4095 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | False |
| primary_location.source.issn_l | 0935-9648 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | Advanced Materials |
| primary_location.source.host_organization | |
| primary_location.source.host_organization_name | |
| primary_location.license | cc-by-nc-nd |
| primary_location.pdf_url | https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/adma.202420063 |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by-nc-nd |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | Advanced Materials |
| primary_location.landing_page_url | https://doi.org/10.1002/adma.202420063 |
| publication_date | 2025-04-21 |
| publication_year | 2025 |
| referenced_works | https://openalex.org/W2627046073, https://openalex.org/W2908367391, https://openalex.org/W4389160880, https://openalex.org/W2273419141, https://openalex.org/W4387164829, https://openalex.org/W2346040907, https://openalex.org/W4292262780, https://openalex.org/W3173789974, https://openalex.org/W3044416448, https://openalex.org/W1870918401, https://openalex.org/W2765802355, https://openalex.org/W2023813086, https://openalex.org/W2146849757, https://openalex.org/W3010487032, https://openalex.org/W2906727620, https://openalex.org/W2094443469, https://openalex.org/W4200633382, https://openalex.org/W4384525023, https://openalex.org/W4381158297, https://openalex.org/W4295786248, https://openalex.org/W3033937423, https://openalex.org/W4294755044, https://openalex.org/W4386818352, https://openalex.org/W3000404031, https://openalex.org/W3095388982, https://openalex.org/W3049618663, https://openalex.org/W3126876084, https://openalex.org/W4221119194, https://openalex.org/W3183861986, https://openalex.org/W3015947126, https://openalex.org/W3163993681, https://openalex.org/W2979786244, https://openalex.org/W4400199650, https://openalex.org/W4210423197, https://openalex.org/W4294170298, https://openalex.org/W4388718660, https://openalex.org/W4307744072, https://openalex.org/W1901129140, https://openalex.org/W2742127985, https://openalex.org/W2923444658, https://openalex.org/W2973666136, https://openalex.org/W2334053963, https://openalex.org/W3010849941, https://openalex.org/W4315628777, https://openalex.org/W2919958648, https://openalex.org/W3012417314, https://openalex.org/W4386366778, https://openalex.org/W3162087380, https://openalex.org/W214899926 |
| referenced_works_count | 49 |
| abstract_inverted_index.5 | 159 |
| abstract_inverted_index.a | 7, 28, 61, 156, 197, 207 |
| abstract_inverted_index.ML | 65 |
| abstract_inverted_index.as | 6 |
| abstract_inverted_index.by | 166, 191 |
| abstract_inverted_index.in | 31, 97, 188, 200, 210 |
| abstract_inverted_index.is | 4, 36, 76, 154 |
| abstract_inverted_index.of | 13, 90, 128, 158, 178, 203, 215 |
| abstract_inverted_index.on | 39 |
| abstract_inverted_index.to | 78, 111, 131 |
| abstract_inverted_index.The | 121 |
| abstract_inverted_index.and | 73, 87, 104, 119, 173, 213 |
| abstract_inverted_index.are | 108 |
| abstract_inverted_index.but | 95 |
| abstract_inverted_index.era | 209 |
| abstract_inverted_index.far | 19 |
| abstract_inverted_index.for | 10, 49, 151 |
| abstract_inverted_index.its | 74 |
| abstract_inverted_index.new | 208 |
| abstract_inverted_index.the | 11, 81, 84, 113, 124, 148, 176, 201, 211 |
| abstract_inverted_index.‐ | 160 |
| abstract_inverted_index.(ML) | 3 |
| abstract_inverted_index.10%. | 161 |
| abstract_inverted_index.This | 162, 194 |
| abstract_inverted_index.data | 192 |
| abstract_inverted_index.deep | 68 |
| abstract_inverted_index.even | 187 |
| abstract_inverted_index.from | 93, 138, 224 |
| abstract_inverted_index.situ | 98 |
| abstract_inverted_index.that | 18, 55, 115, 147, 165 |
| abstract_inverted_index.tool | 9 |
| abstract_inverted_index.with | 170, 182, 218 |
| abstract_inverted_index.work | 163, 195 |
| abstract_inverted_index.Here, | 60 |
| abstract_inverted_index.data. | 100 |
| abstract_inverted_index.error | 150 |
| abstract_inverted_index.field | 202 |
| abstract_inverted_index.learn | 80 |
| abstract_inverted_index.major | 29 |
| abstract_inverted_index.marks | 196 |
| abstract_inverted_index.model | 114 |
| abstract_inverted_index.range | 157 |
| abstract_inverted_index.their | 37 |
| abstract_inverted_index.those | 21 |
| abstract_inverted_index.using | 143 |
| abstract_inverted_index.which | 45 |
| abstract_inverted_index.and/or | 42 |
| abstract_inverted_index.better | 117 |
| abstract_inverted_index.design | 12, 34, 127, 177 |
| abstract_inverted_index.neural | 69, 102, 106, 168 |
| abstract_inverted_index.offers | 116 |
| abstract_inverted_index.reveal | 146 |
| abstract_inverted_index.sparse | 94 |
| abstract_inverted_index.within | 155 |
| abstract_inverted_index.Machine | 1 |
| abstract_inverted_index.Results | 136 |
| abstract_inverted_index.Various | 101 |
| abstract_inverted_index.becomes | 46, 185 |
| abstract_inverted_index.between | 83 |
| abstract_inverted_index.complex | 179 |
| abstract_inverted_index.current | 32 |
| abstract_inverted_index.derived | 222 |
| abstract_inverted_index.desired | 183 |
| abstract_inverted_index.exhibit | 56 |
| abstract_inverted_index.inverse | 33, 126 |
| abstract_inverted_index.nano‐ | 172 |
| abstract_inverted_index.printed | 142 |
| abstract_inverted_index.surpass | 20 |
| abstract_inverted_index.through | 23 |
| abstract_inverted_index.Abstract | 0 |
| abstract_inverted_index.DeepONet | 72 |
| abstract_inverted_index.However, | 27 |
| abstract_inverted_index.advanced | 171 |
| abstract_inverted_index.approach | 122 |
| abstract_inverted_index.compared | 110 |
| abstract_inverted_index.complete | 85 |
| abstract_inverted_index.directly | 79, 223 |
| abstract_inverted_index.emerging | 5 |
| abstract_inverted_index.identify | 112 |
| abstract_inverted_index.learning | 2 |
| abstract_inverted_index.methods. | 26 |
| abstract_inverted_index.networks | 107 |
| abstract_inverted_index.obtained | 137 |
| abstract_inverted_index.offering | 16 |
| abstract_inverted_index.reliance | 38 |
| abstract_inverted_index.response | 89 |
| abstract_inverted_index.specific | 132 |
| abstract_inverted_index.spinodal | 140 |
| abstract_inverted_index.standard | 105 |
| abstract_inverted_index.tailored | 130 |
| abstract_inverted_index.accuracy. | 120 |
| abstract_inverted_index.challenge | 30 |
| abstract_inverted_index.datasets, | 44 |
| abstract_inverted_index.designing | 50 |
| abstract_inverted_index.discovery | 212 |
| abstract_inverted_index.efficient | 125 |
| abstract_inverted_index.employing | 167 |
| abstract_inverted_index.extensive | 40 |
| abstract_inverted_index.feasible, | 186 |
| abstract_inverted_index.heralding | 206 |
| abstract_inverted_index.insights. | 226 |
| abstract_inverted_index.materials | 54, 181 |
| abstract_inverted_index.nonlinear | 57, 133 |
| abstract_inverted_index.operators | 70, 103, 169 |
| abstract_inverted_index.responses | 153 |
| abstract_inverted_index.scarcity. | 193 |
| abstract_inverted_index.scenarios | 189 |
| abstract_inverted_index.variants) | 75 |
| abstract_inverted_index.(including | 71 |
| abstract_inverted_index.achievable | 22 |
| abstract_inverted_index.behaviors. | 59, 135 |
| abstract_inverted_index.framework, | 66 |
| abstract_inverted_index.leveraging | 67 |
| abstract_inverted_index.mechanical | 14, 58, 88, 134, 152, 220 |
| abstract_inverted_index.prediction | 149 |
| abstract_inverted_index.properties | 17, 184 |
| abstract_inverted_index.scientific | 64 |
| abstract_inverted_index.stochastic | 52, 139 |
| abstract_inverted_index.strategies | 35 |
| abstract_inverted_index.structures | 129 |
| abstract_inverted_index.advancement | 199 |
| abstract_inverted_index.architected | 53, 91 |
| abstract_inverted_index.constrained | 190 |
| abstract_inverted_index.development | 214 |
| abstract_inverted_index.facilitates | 123 |
| abstract_inverted_index.introduced, | 77 |
| abstract_inverted_index.lab‐based | 24 |
| abstract_inverted_index.potentially | 205 |
| abstract_inverted_index.problematic | 48 |
| abstract_inverted_index.significant | 198 |
| abstract_inverted_index.underscores | 164 |
| abstract_inverted_index.experimental | 43, 99, 225 |
| abstract_inverted_index.experiments, | 175 |
| abstract_inverted_index.lithography, | 145 |
| abstract_inverted_index.particularly | 47 |
| abstract_inverted_index.relationship | 82 |
| abstract_inverted_index.two‐photon | 144 |
| abstract_inverted_index.unparalleled | 219 |
| abstract_inverted_index.comprehensive | 62 |
| abstract_inverted_index.computational | 41 |
| abstract_inverted_index.metamaterials | 92, 217 |
| abstract_inverted_index.micro‐scale | 51 |
| abstract_inverted_index.end‐to‐end | 63 |
| abstract_inverted_index.high‐quality | 96 |
| abstract_inverted_index.metamaterials, | 15 |
| abstract_inverted_index.microstructure | 86 |
| abstract_inverted_index.systematically | 109 |
| abstract_inverted_index.transformative | 8 |
| abstract_inverted_index.characteristics | 221 |
| abstract_inverted_index.interpretability | 118 |
| abstract_inverted_index.microstructures, | 141 |
| abstract_inverted_index.next‐generation | 216 |
| abstract_inverted_index.micro‐mechanical | 174 |
| abstract_inverted_index.micro‐architected | 180 |
| abstract_inverted_index.trial‐and‐error | 25 |
| abstract_inverted_index.materials‐by‐design, | 204 |
| cited_by_percentile_year.max | 99 |
| cited_by_percentile_year.min | 98 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 8 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/9 |
| sustainable_development_goals[0].score | 0.4699999988079071 |
| sustainable_development_goals[0].display_name | Industry, innovation and infrastructure |
| citation_normalized_percentile.value | 0.97582224 |
| citation_normalized_percentile.is_in_top_1_percent | True |
| citation_normalized_percentile.is_in_top_10_percent | True |