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Paper Citation Record · LEDGER

Inverse design of anisotropic microstructures using physics-augmented neural networks

As of 15 August 2026, this Paper Citation Record lists 92 of 92 outbound references and 1 inbound Pith citation observation for arXiv:2412.13370.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2412.13370 v1

Coverage vector

measured 92 of 92 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T13:17:52.723855Z

measured 93 of 93 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T21:11:55.521745Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-06T21:11:56.081015Z

Reference resolution

92 of 92 outbound references displayed

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External citation measurements

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Outbound references

Observation 3f8b46c2-e897-497e-9b30-ad625f80d5e4 · outbound

This paper cites Modeling the anisotropic finite-deformation viscoelastic behavior of soft fiber-reinforced composites.

Inverse design of anisotropic microstructures using physics-augmented neural networks Modeling the anisotropic finite-deformation viscoelastic behavior of soft fiber-reinforced composites

Reference 1

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Observation 0849ed9b-01ea-46b0-9b3d-a0d04405e7ea · outbound

This paper cites Mechanical properties of anisotropic fiber-reinforced composites.

Inverse design of anisotropic microstructures using physics-augmented neural networks Mechanical properties of anisotropic fiber-reinforced composites

Reference 2

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Observation beb55f4e-7a62-44cf-9aa4-c70f2cf06a20 · outbound

This paper cites Effects of fiber orientation and anisotropy on tensile strength and elastic modulus of short fiber reinforced polymer composites.

Inverse design of anisotropic microstructures using physics-augmented neural networks Effects of fiber orientation and anisotropy on tensile strength and elastic modulus of short fiber reinforced polymer composites

Reference 3

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Observation 8b9aa9c0-0b30-408f-98ef-f67e4f4a8223 · outbound

This paper cites The anisotropic hooke’s law for cancellous bone and wood.

Inverse design of anisotropic microstructures using physics-augmented neural networks The anisotropic hooke’s law for cancellous bone and wood

Reference 4

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Unavailable: canonical work link unavailable.

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Observation e603e585-44e7-4a03-aaff-0dc8a37d841c · outbound

This paper cites Computational modeling of mechanical anisotropy in the cornea and sclera.

Inverse design of anisotropic microstructures using physics-augmented neural networks Computational modeling of mechanical anisotropy in the cornea and sclera

Reference 5

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Unavailable: canonical work link unavailable.

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Observation 6d16e072-a199-4b37-af8d-8f3fe6190746 · outbound

This paper cites Anisotropy properties of tissues: a basis for fabrication of biomimetic anisotropic scaffolds for tissue engineering.

Inverse design of anisotropic microstructures using physics-augmented neural networks Anisotropy properties of tissues: a basis for fabrication of biomimetic anisotropic scaffolds for tissue engineering

Reference 6

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Observation dcfe6615-8a8d-4dce-9f82-575952fbaca5 · outbound

This paper cites Mechanical behavior of materials.

Inverse design of anisotropic microstructures using physics-augmented neural networks Mechanical behavior of materials

Reference 7

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Observation 406a1aac-3c3a-42bb-9774-a9eec53bd0f8 · outbound

This paper cites Aspects of computational homogenization at finite deformations: a unifying review from reuss’ to voigt’s bound.

Inverse design of anisotropic microstructures using physics-augmented neural networks Aspects of computational homogenization at finite deformations: a unifying review from reuss’ to voigt’s bound

Reference 8

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This paper cites Bickel, Jan Rys, Steve Marschner, Chiara Daraio, and Markus H.

Inverse design of anisotropic microstructures using physics-augmented neural networks Bickel, Jan Rys, Steve Marschner, Chiara Daraio, and Markus H

Reference 9

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Observation 6945aa36-71ab-4a9d-a65e-9948f5db8625 · outbound

This paper cites Mechanical metamaterials and their engineering applications.

Inverse design of anisotropic microstructures using physics-augmented neural networks Mechanical metamaterials and their engineering applications

Reference 10

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Observation d9996b32-301b-4166-9ced-2d9de24aa24d · outbound

This paper cites Anisotropy and heterogeneity of microstructure and mechanical properties in metal additive manufacturing: A critical review.

Inverse design of anisotropic microstructures using physics-augmented neural networks Anisotropy and heterogeneity of microstructure and mechanical properties in metal additive manufacturing: A critical review

Reference 11

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Observation 39d03daa-bf5d-4ebf-9d2e-b7eee058615d · outbound

This paper cites Properties of materials: anisotropy, symmetry, structure.

Inverse design of anisotropic microstructures using physics-augmented neural networks Properties of materials: anisotropy, symmetry, structure

Reference 12

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Observation b073f265-c8ab-462f-9172-9b13585b4370 · outbound

This paper cites Microstructural image analysis applied to fibre composite materials: a review.

Inverse design of anisotropic microstructures using physics-augmented neural networks Microstructural image analysis applied to fibre composite materials: a review

Reference 13

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Observation 2483ffce-f0c6-4b30-a3c5-f5051f618056 · outbound

This paper cites Microstructural imaging techniques: a comparison between light and scanning electron microscopy.

Inverse design of anisotropic microstructures using physics-augmented neural networks Microstructural imaging techniques: a comparison between light and scanning electron microscopy

Reference 14

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Observation 303dd65c-c551-4909-97f1-80d032c61c9e · outbound

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Inverse design of anisotropic microstructures using physics-augmented neural networks Multiscale modeling: a review

Reference 15

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Observation 6391376b-669b-4714-accb-c114eab8a7cd · outbound

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Inverse design of anisotropic microstructures using physics-augmented neural networks Principles of multiscale modeling

Reference 16

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Observation c3948827-307e-4ddc-b717-f420ecc86320 · outbound

This paper cites A numerical two-scale homogenization scheme: the fe2-method.

Inverse design of anisotropic microstructures using physics-augmented neural networks A numerical two-scale homogenization scheme: the fe2-method

Reference 17

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Inverse design of anisotropic microstructures using physics-augmented neural networks Unresolved cited work

Reference 18

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Inverse design of anisotropic microstructures using physics-augmented neural networks Unresolved cited work

Reference 19

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Inverse design of anisotropic microstructures using physics-augmented neural networks Unresolved cited work

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Inverse design of anisotropic microstructures using physics-augmented neural networks Unresolved cited work

Reference 21

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Inverse design of anisotropic microstructures using physics-augmented neural networks A variational approach to the theory of the elastic behaviour of multiphase materials

Reference 22

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Inverse design of anisotropic microstructures using physics-augmented neural networks Variational bounds on the effective moduli of anisotropic composites

Reference 23

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Inverse design of anisotropic microstructures using physics-augmented neural networks Homogenization approach in engineering

Reference 24

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Inverse design of anisotropic microstructures using physics-augmented neural networks The determination of the elastic field of an ellipsoidal inclusion, and related problems

Reference 25

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Inverse design of anisotropic microstructures using physics-augmented neural networks Unresolved cited work

Reference 26

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Inverse design of anisotropic microstructures using physics-augmented neural networks Average stress in matrix and average elastic energy of materials with misfitting inclusions

Reference 27

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Inverse design of anisotropic microstructures using physics-augmented neural networks Luo and G.J

Reference 28

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Inverse design of anisotropic microstructures using physics-augmented neural networks On the elastic moduli of some heterogeneous materials

Reference 29

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Inverse design of anisotropic microstructures using physics-augmented neural networks Unresolved cited work

Reference 30

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Inverse design of anisotropic microstructures using physics-augmented neural networks On constitutive macro-variables for heterogeneous solids at finite strain

Reference 31

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Inverse design of anisotropic microstructures using physics-augmented neural networks Unresolved cited work

Reference 32

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Inverse design of anisotropic microstructures using physics-augmented neural networks Geers, V .G

Reference 33

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Inverse design of anisotropic microstructures using physics-augmented neural networks Unresolved cited work

Reference 34

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Inverse design of anisotropic microstructures using physics-augmented neural networks Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and voronoi cell finite element model

Reference 35

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Inverse design of anisotropic microstructures using physics-augmented neural networks Multiscale modeling of microstructure–property relations

Reference 36

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Source-reported events for the cited work

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Observation cbb1c0cc-c60c-4313-8baf-a1cc90f68d4d · outbound

This paper cites Multiscale fe2 elastoviscoplastic analysis of composite structures.

Inverse design of anisotropic microstructures using physics-augmented neural networks Multiscale fe2 elastoviscoplastic analysis of composite structures

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Resolution
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Observation 2519e217-d5d2-4daa-bf81-3c39d92ad613 · outbound

This paper cites A review of the fe 2 method for composites.

Inverse design of anisotropic microstructures using physics-augmented neural networks A review of the fe 2 method for composites

Reference 38

Resolution
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raw_fallback, observed 2026-08-11T13:17:53.168885Z

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Observation 161b2365-7a9f-4da6-a3a7-552a7dfcf16c · outbound

This paper cites Local approximate gaussian process regression for data- driven constitutive models: development and comparison with neural networks.

Inverse design of anisotropic microstructures using physics-augmented neural networks Local approximate gaussian process regression for data- driven constitutive models: development and comparison with neural networks

Reference 39

Resolution
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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 4226b042-cc89-4111-80d0-c87efd4eecb7 · outbound

This paper cites A review on data-driven constitutive laws for solids.

Inverse design of anisotropic microstructures using physics-augmented neural networks A review on data-driven constitutive laws for solids

Reference 40

Resolution
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raw_fallback, observed 2026-08-11T13:17:53.150341Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.581605Z digest=sha256:46939ad6447c7cd93b3f83738aa734ec42b39abd897fb022eee3da5ac1f45868

Observation ff08e3a4-7faf-4a9c-898a-dfc10cad1513 · outbound

This paper cites Representations for isotropic and anisotropic non-polynomial tensor functions.

Inverse design of anisotropic microstructures using physics-augmented neural networks Representations for isotropic and anisotropic non-polynomial tensor functions

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:53.134013Z

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Observation 551dbcb5-3840-4a36-a589-d5776eafb893 · outbound

This paper cites A class of orthotropic and transversely isotropic hyperelastic constitutive models based on a polyconvex strain energy function.

Inverse design of anisotropic microstructures using physics-augmented neural networks A class of orthotropic and transversely isotropic hyperelastic constitutive models based on a polyconvex strain energy function

Reference 42

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 45a661f7-45a8-43ef-a1e9-e94b9531ba10 · outbound

This paper cites Multilayer feedforward networks are universal approx- imators.

Inverse design of anisotropic microstructures using physics-augmented neural networks Multilayer feedforward networks are universal approx- imators

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:53.117806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation a0234aff-bdd4-4968-a253-0269a2b523df · outbound

This paper cites Tensor basis gaussian process models of hyperelastic materials.

Inverse design of anisotropic microstructures using physics-augmented neural networks Tensor basis gaussian process models of hyperelastic materials

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:53.109515Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.592099Z digest=sha256:b10e99d0f2231b7e98f55fe4c4a417cc064e2897e12a8bc49fab70c03bd052f9

Observation c677de18-a0c5-4032-91b5-e59dd6f06bbd · outbound

This paper cites On physics-informed data-driven isotropic and anisotropic constitutive mod- els through probabilistic machine learning and space-filling sampling.

Inverse design of anisotropic microstructures using physics-augmented neural networks On physics-informed data-driven isotropic and anisotropic constitutive mod- els through probabilistic machine learning and space-filling sampling

Reference 45

Resolution
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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:17:52.594690Z digest=sha256:42a0680ecac95e9c564bd72f5c07a89c118763e92a80661e2ca934a1994223c2

Observation 5e476b27-9795-4157-82e4-e3e293a72ce0 · outbound

This paper cites Neural networks meet hyperelasticity: A guide to enforcing physics.

Inverse design of anisotropic microstructures using physics-augmented neural networks Neural networks meet hyperelasticity: A guide to enforcing physics

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:53.096146Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 38d5d9dc-5656-4ecc-a5a9-d0f8fd9a5045 · outbound

This paper cites Polyconvex anisotropic hyperelasticity with neural networks.

Inverse design of anisotropic microstructures using physics-augmented neural networks Polyconvex anisotropic hyperelasticity with neural networks

Reference 47

Resolution
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no resolver link, observed 2026-08-11T13:17:52.600046Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:17:52.600046Z digest=sha256:34546627ff0a5f4a2c2cda8086c0d34087b548e4cf05f3afd3eaab03b8959db7

Observation b69c34df-425e-4e13-9265-359f7afa90f6 · outbound

This paper cites Learning hyperelastic anisotropy from data via a tensor basis neural network.

Inverse design of anisotropic microstructures using physics-augmented neural networks Learning hyperelastic anisotropy from data via a tensor basis neural network

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:53.084121Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.602817Z digest=sha256:110eb8896ddefe90bc0598ac947f50eccb256e164af124d1dfad4447f18272c8

Observation 62b068dd-4155-4d6d-8226-4e520c6d1606 · outbound

This paper cites A new family of constitutive artificial neural networks towards automated model discovery.

Inverse design of anisotropic microstructures using physics-augmented neural networks A new family of constitutive artificial neural networks towards automated model discovery

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:53.075754Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.605584Z digest=sha256:c2d97552028fe52e543882d33b65d463a6b57dd0efbe0c697270bd45d32478f1

Observation 75787a14-917a-4f3a-8589-bc91b7f3ed50 · outbound

This paper cites Klein, Fabian J.

Inverse design of anisotropic microstructures using physics-augmented neural networks Klein, Fabian J

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:53.067050Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 11f7121a-053e-4f79-b0cf-40758670cd23 · outbound

This paper cites Non-linear elastic deformations.

Inverse design of anisotropic microstructures using physics-augmented neural networks Non-linear elastic deformations

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:53.057425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 94e339d0-34f4-4f40-99da-0db8a0e03b73 · outbound

This paper cites Structural tensors for anisotropic solids.

Inverse design of anisotropic microstructures using physics-augmented neural networks Structural tensors for anisotropic solids

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:53.048264Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 26c6335a-2193-453a-986b-f22a5c89bb8c · outbound

This paper cites On the representation of constitutive relations using structure tensors.

Inverse design of anisotropic microstructures using physics-augmented neural networks On the representation of constitutive relations using structure tensors

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:53.040198Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation eed8f818-04bb-4e3a-8db4-5822b923c7d5 · outbound

This paper cites Kalina, J ¨org Brummund, WaiChing Sun, and Markus K¨astner.

Inverse design of anisotropic microstructures using physics-augmented neural networks Kalina, J ¨org Brummund, WaiChing Sun, and Markus K¨astner

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:53.032256Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.618569Z digest=sha256:da77d054c8ae296aa3b8a5b76c5d1cda8d7afd6b60ba06ae64fe28b39da7dc28

Observation fd6b28f4-af77-470b-9afb-a5381dba6fe4 · outbound

This paper cites An introduction to continuum mechanics , volume 158.

Inverse design of anisotropic microstructures using physics-augmented neural networks An introduction to continuum mechanics , volume 158

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:53.024122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation e7e81b5e-e926-48a6-b5fd-df6227c6d87f · outbound

This paper cites Ordinary and strong ellipticity in the equilibrium theory of incompressible hyper- elastic solids.

Inverse design of anisotropic microstructures using physics-augmented neural networks Ordinary and strong ellipticity in the equilibrium theory of incompressible hyper- elastic solids

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:53.015694Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.623693Z digest=sha256:9bdbea9d7c92c741c6c3a1a835d7409d527c76a65fc991fde520acee6ce972af

Observation 4a6db226-805f-4117-b3f9-28cddf55c973 · outbound

This paper cites Convexity conditions and existence theorems in nonlinear elasticity.Archive for rational mechanics and Analysis, 63(4):337–403, 1976.

Inverse design of anisotropic microstructures using physics-augmented neural networks Convexity conditions and existence theorems in nonlinear elasticity.Archive for rational mechanics and Analysis, 63(4):337–403, 1976

Reference 57

Resolution
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no resolver link, observed 2026-08-11T13:17:52.626219Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:17:52.626219Z digest=sha256:070d56a841d1e9f2341777410670489076b5d972489ae4603f09417e374d6b98

Observation 6b14b3a3-4935-458a-958b-061afdef3a4c · outbound

This paper cites An example of a quasiconvex function that is not polyconvex in two dimensions.

Inverse design of anisotropic microstructures using physics-augmented neural networks An example of a quasiconvex function that is not polyconvex in two dimensions

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:53.003156Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 5b093cf2-deec-481c-93ea-7c44d0d21f1c · outbound

This paper cites an unresolved cited work.

Inverse design of anisotropic microstructures using physics-augmented neural networks Unresolved cited work

Reference 59

Resolution
unresolved
raw_fallback, observed 2026-08-11T13:17:52.995120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 0fe39214-89b9-4370-bdad-bb0b1e489e42 · outbound

This paper cites Boyd and Lieven Vandenberghe.

Inverse design of anisotropic microstructures using physics-augmented neural networks Boyd and Lieven Vandenberghe

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.986913Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.633454Z digest=sha256:8c7e2fdfae09bc569367f257e184fde7cbbbd2f58dfb0056d8157c9f48053f21

Observation 89699aa0-8649-4a11-8afb-05e397d3cd41 · outbound

This paper cites Input convex neural networks.

Inverse design of anisotropic microstructures using physics-augmented neural networks Input convex neural networks

Reference 61

Resolution
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no resolver link, observed 2026-08-11T13:17:52.635749Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:17:52.635749Z digest=sha256:f8bdd273e828de9431e176966ddeb30dd875fbf25c323b12199d9b44249c170c

Observation efb1b4ec-2648-4259-8622-b4958976e2b6 · outbound

This paper cites Mathematical methods in continuum mechanics of solids.

Inverse design of anisotropic microstructures using physics-augmented neural networks Mathematical methods in continuum mechanics of solids

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.974092Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.638367Z digest=sha256:28d8300f29fda6dea6cafc302b056510a7fe649ba90e71af55337b2529cc1c04

Observation 85d3b1d6-1521-487e-88f1-9a09e6435cd7 · outbound

This paper cites Nonlinear solid mechanics: a continuum approach for engineering science.

Inverse design of anisotropic microstructures using physics-augmented neural networks Nonlinear solid mechanics: a continuum approach for engineering science

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Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.965876Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation ce72249e-7491-4dbf-a0d5-41c0b4e4c39c · outbound

This paper cites Polyconvexity of generalized polynomial-type hyperelastic strain energy functions for near-incompressibility.

Inverse design of anisotropic microstructures using physics-augmented neural networks Polyconvexity of generalized polynomial-type hyperelastic strain energy functions for near-incompressibility

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.957570Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.644103Z digest=sha256:6ba9defae684d8d053b5bf8e76f070587c406b185bee44c166082195834175d2

Observation e81501fd-15e8-459d-b5a2-afdd624558bd · outbound

This paper cites Unsupervised discovery of interpretable hyperelastic constitutive laws.

Inverse design of anisotropic microstructures using physics-augmented neural networks Unsupervised discovery of interpretable hyperelastic constitutive laws

Reference 65

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.948238Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.647249Z digest=sha256:c018638d4ce2f88fcc831e936ea627df9d00ec871b950eb30e724edcb0985c5d

Observation 136f65c1-6a2e-40c5-904c-71e3d9ff03a2 · outbound

This paper cites Pytorch: An imperative style, high-performance deep learning library.

Inverse design of anisotropic microstructures using physics-augmented neural networks Pytorch: An imperative style, high-performance deep learning library

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Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.939910Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.650014Z digest=sha256:80c8587e1e85d3c02ec89f8daa87e105c60eeb9507fb913805a54c655298329a

Observation 4966d406-a4f9-4e19-bd27-b1aadb0d2571 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Inverse design of anisotropic microstructures using physics-augmented neural networks Adam: A Method for Stochastic Optimization

Reference 67

Resolution
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no resolver link, observed 2026-08-11T13:17:52.652954Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:17:52.652954Z digest=sha256:ebd14498d7ff59d7ce30220f863cdb2d7cb3616e0957f0edd8c76ed12d2fc436

Observation c04ccc0a-9a0e-4fbc-be7f-27fe67efad30 · outbound

This paper cites A simplex method for function minimization.

Inverse design of anisotropic microstructures using physics-augmented neural networks A simplex method for function minimization

Reference 68

Resolution
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no resolver link, observed 2026-08-11T13:17:52.656659Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:17:52.656659Z digest=sha256:fccc1f73cdd42dc8a8c1b38d2eb57d47c2c192aa91519ddc321774815917ca4a

Observation 45e4ebcf-46cf-49ed-bb49-ba2fa525f437 · outbound

This paper cites Implementing the nelder-mead simplex algorithm with adaptive parameters.

Inverse design of anisotropic microstructures using physics-augmented neural networks Implementing the nelder-mead simplex algorithm with adaptive parameters

Reference 69

Resolution
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no resolver link, observed 2026-08-11T13:17:52.659489Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:17:52.659489Z digest=sha256:2ac9763c084f579b0d96889aaf8efc657d4414d8f116ab7ddc18a913ad3ed33d

Observation f63bae96-9d6f-4503-ba2e-42c0b1db29c4 · outbound

This paper cites M ¨uller, and Petros Koumoutsakos.

Inverse design of anisotropic microstructures using physics-augmented neural networks M ¨uller, and Petros Koumoutsakos

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Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.923353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.662980Z digest=sha256:d82e32a89b0470ba5f059cac73577a1772844dddf814b0fffa597de3120e7552

Observation acbbfa41-8a51-4307-84f7-b82fe935fd1d · outbound

This paper cites The CMA Evolution Strategy: A Tutorial.

Inverse design of anisotropic microstructures using physics-augmented neural networks The CMA Evolution Strategy: A Tutorial

Reference 71

Resolution
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no resolver link, observed 2026-08-11T13:17:52.665669Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:17:52.665669Z digest=sha256:683da29c640efdf47433eff9097f58d1f79eb6959459f81069532ebc91c2f7cf

Observation e33dce28-aa92-4dae-b423-6a44144745af · outbound

This paper cites Large sample properties of simulations using latin hypercube sampling.

Inverse design of anisotropic microstructures using physics-augmented neural networks Large sample properties of simulations using latin hypercube sampling

Reference 72

Resolution
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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:17:52.668599Z digest=sha256:373e00f2daa10f1414d1bfabac64afaade26f689b7846b278793bbccc3a73ca8

Observation 4a7c1ebf-3e69-42b3-8906-d0f223fb60c8 · outbound

This paper cites Mathematical elasticity: Three-dimensional elasticity.

Inverse design of anisotropic microstructures using physics-augmented neural networks Mathematical elasticity: Three-dimensional elasticity

Reference 73

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.911236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.671277Z digest=sha256:630dfd4066d566d1712ee7cff56e43ae04b18cbd3fe1e2dcabcde60f172d2299

Observation f175724d-c1bf-4899-95c4-d82ef721d094 · outbound

This paper cites A simple orthotropic, transversely isotropic hyperelastic constitutive equation for large strain computations.

Inverse design of anisotropic microstructures using physics-augmented neural networks A simple orthotropic, transversely isotropic hyperelastic constitutive equation for large strain computations

Reference 74

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.903390Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.673921Z digest=sha256:47037eca65fd44c21c7c88f3a6482b71b21d1828f7916cb1a8c5a4de2c55232c

Observation 071ec043-77fb-4949-8128-26bfcdb8bd95 · outbound

This paper cites A new constitutive framework for arterial wall mechanics and a comparative study of material models.

Inverse design of anisotropic microstructures using physics-augmented neural networks A new constitutive framework for arterial wall mechanics and a comparative study of material models

Reference 75

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.895918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.678644Z digest=sha256:05eef2b3a8f647c9ed3bc3cef8147fef70f323fe69f3ce378373eef54c13bcbe

Observation 4433db73-b560-45eb-9405-b2f71f3ac6a5 · outbound

This paper cites Model- data-driven constitutive responses: application to a multiscale computational framework.

Inverse design of anisotropic microstructures using physics-augmented neural networks Model- data-driven constitutive responses: application to a multiscale computational framework

Reference 76

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.888187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.681242Z digest=sha256:474ef4979626bd11806f475f9bd8053433e08384b59b1db0bfed7d0e6a64b2cd

Observation c365bb22-d86d-4a4d-ae94-679d6bf625cc · outbound

This paper cites Neural network-based multiscale modeling of finite strain magneto-elasticity with relaxed convexity criteria.

Inverse design of anisotropic microstructures using physics-augmented neural networks Neural network-based multiscale modeling of finite strain magneto-elasticity with relaxed convexity criteria

Reference 77

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.879929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.684125Z digest=sha256:95305f16f02d2e535bcde97cc660a266eae138eded7f792de76ab67dac385f83

Observation f52c2b83-b054-47ed-83ed-427bcb24dfd8 · outbound

This paper cites an unresolved cited work.

Inverse design of anisotropic microstructures using physics-augmented neural networks Unresolved cited work

Reference 78

Resolution
unresolved
raw_fallback, observed 2026-08-11T13:17:52.871625Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.686879Z digest=sha256:8196ba496d289f1626d5353f0800c2f26c1b57646e83448525ca3a08d32fb138

Observation 6823ab87-60c9-4dfa-86d5-4364e0bd7527 · outbound

This paper cites Ranganathan and Martin Ostoja-Starzewski.

Inverse design of anisotropic microstructures using physics-augmented neural networks Ranganathan and Martin Ostoja-Starzewski

Reference 79

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.864001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.689468Z digest=sha256:185896e40aff5547e7dfa59f76f958046caa3f1625c6ec1e4878de3381f39067

Observation 6aa88ae0-0a41-4561-bfd0-f2fe0d10b40e · outbound

This paper cites Homogenization of carbon/polymer composites with anisotropic distribution of particles and stochastic interface defects.

Inverse design of anisotropic microstructures using physics-augmented neural networks Homogenization of carbon/polymer composites with anisotropic distribution of particles and stochastic interface defects

Reference 80

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.855735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.692166Z digest=sha256:968c9e0b3c57dc566ad9aa1ffb0cf6b556daa6142ddba6191093b29cb2943479

Observation cfced910-c418-4851-be0a-c5ba0e834b28 · outbound

This paper cites Vlassis, Puhan Zhao, Ran Ma, Tommy Sewell, and WaiChing Sun.

Inverse design of anisotropic microstructures using physics-augmented neural networks Vlassis, Puhan Zhao, Ran Ma, Tommy Sewell, and WaiChing Sun

Reference 81

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.847230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.694642Z digest=sha256:72ee386243b7271e3a03b2a2d7e9d59db099739e51aa6d8f9b3279ea09eb9d59

Observation 55993317-c47c-4297-a376-54347848bebd · outbound

This paper cites Hyperelastic behaviors of closed-cell porous materials at a wide porosity range.

Inverse design of anisotropic microstructures using physics-augmented neural networks Hyperelastic behaviors of closed-cell porous materials at a wide porosity range

Reference 82

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.839057Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.697402Z digest=sha256:78528073411a5797d213b56817dcda58f3cccc325c0a808638d7709baacf938d

Observation 2b7111b2-b3d2-46ec-bc5e-b77369c584ed · outbound

This paper cites Mechanical analysis of heterogeneous materials with higher-order parameters.

Inverse design of anisotropic microstructures using physics-augmented neural networks Mechanical analysis of heterogeneous materials with higher-order parameters

Reference 83

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.831017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.699998Z digest=sha256:a2e11c15811f0aeefae8efaca2942fbd2f8c13bf9c2a2e33ef53e426ef9d7a19

Observation c2c09d58-85bf-4a84-880b-f950fef073dc · outbound

This paper cites Fe ann: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining.

Inverse design of anisotropic microstructures using physics-augmented neural networks Fe ann: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

Reference 84

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.823190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.702664Z digest=sha256:aea644f775972475cdb4961a28e747a448b0f60f7d4107471a603c692849a1d6

Observation 22cfccc0-4f25-44b8-a5b4-8e8e89042f57 · outbound

This paper cites Loss of polyconvexity by homogenization: a new example.

Inverse design of anisotropic microstructures using physics-augmented neural networks Loss of polyconvexity by homogenization: a new example

Reference 85

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.814658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.705399Z digest=sha256:994ca178059731ec73430d6848072a375ce2ed9cf285f0a75421086dfcf594d0

Observation a3715512-1664-43e9-8000-e43bb371e475 · outbound

This paper cites Loss of polyconvexity by homogenization.

Inverse design of anisotropic microstructures using physics-augmented neural networks Loss of polyconvexity by homogenization

Reference 86

Resolution
unresolved
no resolver link, observed 2026-08-11T13:17:52.707933Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:17:52.707933Z digest=sha256:af924485bdf5c69e2d9d20eb5db6c5eed2b58017e3fd92dd89657be26ef9e94b

Observation 47fd40a3-d0e4-46e5-a29e-57d1965b419a · outbound

This paper cites Parameter identification for viscoplastic models based on analytical derivatives of a least-squares functional and stability investigations.

Inverse design of anisotropic microstructures using physics-augmented neural networks Parameter identification for viscoplastic models based on analytical derivatives of a least-squares functional and stability investigations

Reference 87

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.801824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.710559Z digest=sha256:5bd96c4332e8e0fa9a4a2c4b55514bc1dc16c47dab0b492d61ca6a566184b403

Observation 4fb2a1ea-0d01-4102-84db-cea5b27195ed · outbound

This paper cites Identification of material parameters for constitutive equations.

Inverse design of anisotropic microstructures using physics-augmented neural networks Identification of material parameters for constitutive equations

Reference 88

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.793702Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.713126Z digest=sha256:d0fe62b63c6f2f3b0a340ef1151669e50f120b2ab01fd7ad7cd38de983c1084e

Observation a50b0a3f-7079-4e31-84c3-43f22efa8466 · outbound

This paper cites Viscoelasticty with physics-augmented neural networks: Model formulation and training methods without prescribed internal vari- ables.

Inverse design of anisotropic microstructures using physics-augmented neural networks Viscoelasticty with physics-augmented neural networks: Model formulation and training methods without prescribed internal vari- ables

Reference 89

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.785473Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.715717Z digest=sha256:cbefbb4fd3612e434ebab50e0af44f7172009bf0af543a62d806d85fec296a70

Observation e372aca2-319f-4788-b816-ed23c7aef222 · outbound

This paper cites Automated model discovery of finite strain elastoplasticity from uniaxial experiments.

Inverse design of anisotropic microstructures using physics-augmented neural networks Automated model discovery of finite strain elastoplasticity from uniaxial experiments

Reference 90

Resolution
unresolved
no resolver link, observed 2026-08-11T13:17:52.718308Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:17:52.718308Z digest=sha256:95843d3eb87bf3894a40fcc82738b698c82904521e5c8e0c3905d6bcbee51095

Observation c0a31151-c780-4795-b671-f4ce8021b0a3 · outbound

This paper cites Fuhg, Asghar Jadoon, Oliver Weeger, D.

Inverse design of anisotropic microstructures using physics-augmented neural networks Fuhg, Asghar Jadoon, Oliver Weeger, D

Reference 91

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.776426Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.721286Z digest=sha256:ccbf728536a974e8808f3561b272e8f97b8081c69b13ae684db5b8a624c30a73

Observation 27ff4b21-133c-40c7-b37d-dcd11b82bd8d · outbound

This paper cites Russ, Glaucio H.

Inverse design of anisotropic microstructures using physics-augmented neural networks Russ, Glaucio H

Reference 92

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:17:52.767307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T13:17:52.723855Z digest=sha256:bcc03f04b5d70b273e965a7b46e790c88436a4f0d15a102841610439866c4775

Pith citing papers

Observation 83e9d771-4d69-48e5-887a-82af60630c98 · inbound

Physics Augmented Machine Learning Discovery of Composition-Dependent Constitutive Laws for 3D Printed Digital Materials cites this paper.

Physics Augmented Machine Learning Discovery of Composition-Dependent Constitutive Laws for 3D Printed Digital Materials Inverse design of anisotropic microstructures using physics-augmented neural networks

Reference 52

Resolution
verified exact
local_arxiv, observed 2026-08-06T21:11:56.179122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T21:11:55.521745Z digest=sha256:a130ea3cbe1f84fa98ff6068208f78df87af75d07e03ba88e99fd5911f451bdd