Paper Citation Record · LEDGER

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems

As of 14 August 2026, this Paper Citation Record lists 61 of 61 outbound references and 1 inbound Pith citation observation for arXiv:2507.11130.

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

pith.paper-citation-record.v1
2507.11130 v1

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measured 61 of 61 reference resolution

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Reference resolution

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Outbound references

Observation 8c42b8c6-7d33-4e7a-9fd9-159d085bb915 · outbound

This paper cites all-at-once formulations.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems all-at-once formulations

Reference 1

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This paper cites PhD thesis, Technische Universit¨ at M¨ unchen (2014).

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems PhD thesis, Technische Universit¨ at M¨ unchen (2014)

Reference 2

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This paper cites Springer, Heidelberg (2021).

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Springer, Heidelberg (2021)

Reference 4

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This paper cites Inverse Problems 31(2), 025006 (2015) https://doi.org/10.1088/0266-5611/31/2/ 025006.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Inverse Problems 31(2), 025006 (2015) https://doi.org/10.1088/0266-5611/31/2/ 025006

Reference 5

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This paper cites Time-dependent problems in imaging and parameter identification, 165–190 (2021) https://doi.org/10.1007/978-3-030-57784-1 6.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Time-dependent problems in imaging and parameter identification, 165–190 (2021) https://doi.org/10.1007/978-3-030-57784-1 6

Reference 6

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This paper cites Mathematical Methods in the Applied Sciences 40(1), 183–204 (2017) https:// doi.org/10.1002/mma.3979.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Mathematical Methods in the Applied Sciences 40(1), 183–204 (2017) https:// doi.org/10.1002/mma.3979

Reference 7

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This paper cites Inverse Problems 33(12), 124004 (2017) https://doi.org/10.1088/1361-6420/aa8d91.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Inverse Problems 33(12), 124004 (2017) https://doi.org/10.1088/1361-6420/aa8d91

Reference 8

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This paper cites Inverse Problems in Science and Engineering 25(1), 2–26 (2017) https://doi.org/10.1080/17415977.2015.1132713.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Inverse Problems in Science and Engineering 25(1), 2–26 (2017) https://doi.org/10.1080/17415977.2015.1132713

Reference 9

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This paper cites Applied Mathe- matical Sciences.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Applied Mathe- matical Sciences

Reference 10

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This paper cites In: Sonnendr¨ ucker, E.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems In: Sonnendr¨ ucker, E

Reference 11

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This paper cites Mathematics and Its Applications, vol.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Mathematics and Its Applications, vol

Reference 12

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Reference 13

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This paper cites De Gruyter, Berlin, New York (2008).

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems De Gruyter, Berlin, New York (2008)

Reference 14

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This paper cites Springer, New York (1996).

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Springer, New York (1996)

Reference 15

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This paper cites Inverse Problems 40(8), 085008 (2024) https://doi.org/10.1088/1361-6420/ad5a35.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Inverse Problems 40(8), 085008 (2024) https://doi.org/10.1088/1361-6420/ad5a35

Reference 16

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This paper cites John Wiley & Sons, Washington, D.C.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems John Wiley & Sons, Washington, D.C

Reference 17

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This paper cites Pitman, Boston (1984).

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Pitman, Boston (1984)

Reference 18

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This paper cites Inverse Problems 17(6), 1743–1763 (2001) https://doi.org/ 10.1088/0266-5611/17/6/314.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Inverse Problems 17(6), 1743–1763 (2001) https://doi.org/ 10.1088/0266-5611/17/6/314

Reference 20

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Reference 21

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This paper cites Inverse Problems 28(1), 015012 (2012) https://doi.org/10.1088/0266-5611/28/1/015012.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Inverse Problems 28(1), 015012 (2012) https://doi.org/10.1088/0266-5611/28/1/015012

Reference 22

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This paper cites Numerische Mathematik 140, 449–478 (2018) https: //doi.org/10.1007/s00211-018-0971-5.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Numerische Mathematik 140, 449–478 (2018) https: //doi.org/10.1007/s00211-018-0971-5

Reference 23

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Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems reduced formulation

Reference 24

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Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems POD Suboptimal Control of Evolution Problems: Theory and Applications

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Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Acta Numer

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This paper cites Inverse Problems 34(8), 085008–27 (2018) https://doi.org/10.1088/1361-6420/aac8f3.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Inverse Problems 34(8), 085008–27 (2018) https://doi.org/10.1088/1361-6420/aac8f3

Reference 32

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Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Inverse Problems 32(3), 035001 (2016) https:// doi.org/10.1088/0266-5611/32/3/035001

Reference 33

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This paper cites Society for Industrial and Applied Mathematics, Philadelphia, PA (2017).

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Society for Industrial and Applied Mathematics, Philadelphia, PA (2017)

Reference 34

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Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems (eds.): Model Reduction of Parametrized Systems

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Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems In: Model Order Reduction and Applications

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Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Inverse Problems 41(5), 055015–24 (2025) https://doi.org/10.1088/1361-6420/add17d

Reference 40

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This paper cites Mathematical Modelling and Numerical Analysis 42(2), 277–302 (2008) https://doi.org/10.1051/m2an: 2008001.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Mathematical Modelling and Numerical Analysis 42(2), 277–302 (2008) https://doi.org/10.1051/m2an: 2008001

Reference 41

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Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems ESAIM Math

Reference 42

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This paper cites SIAM Journal on Scientific Computing 40(5), 3267–3292 (2018) https://doi.org/10.1137/16M1085413.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems SIAM Journal on Scientific Computing 40(5), 3267–3292 (2018) https://doi.org/10.1137/16M1085413

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Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Computational Science and Engineering 1(3) (2024) https://doi.org/10.1007/ s44207-024-00002-z

Reference 44

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Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Mathematical Problems in Engineering, 843869–13 (2014) https://doi.org/10.1155/2014/843869

Reference 46

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Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Technical report, Technical Report 2000-25, ICASE (2000)

Reference 48

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This paper cites Journal of Com- putational Physics 227, 7813–7840 (2008) https://doi.org/10.1016/j.jcp.2008.04.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Journal of Com- putational Physics 227, 7813–7840 (2008) https://doi.org/10.1016/j.jcp.2008.04

Reference 49

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This paper cites Optimization and Engineering 14, 3–35 (2013) https://doi.org/10.1007/s11081-011-9164-0.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Optimization and Engineering 14, 3–35 (2013) https://doi.org/10.1007/s11081-011-9164-0

Reference 50

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Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems PAMM 18(1), 201800453 (2018) https://doi.org/ 10.1002/pamm.201800453

Reference 51

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Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Konstanzer Schriften in Mathematik No

Reference 52

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Observation 5a260de1-0c1f-41e1-b1b4-2008195a6f53 · outbound

This paper cites A trust-region framework for optimization using Hermite kernel surrogate models.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems A trust-region framework for optimization using Hermite kernel surrogate models

Reference 54

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This paper cites https://doi.org/10.5281/zenodo.15834305.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems https://doi.org/10.5281/zenodo.15834305

Reference 55

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This paper cites SIAM Journal on Scientific Computing 38, 194–216 (2016) https://doi.org/10.1137/15M1026614.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems SIAM Journal on Scientific Computing 38, 194–216 (2016) https://doi.org/10.1137/15M1026614

Reference 56

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This paper cites Springer Series in Operations Research and Financial Engineering.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Springer Series in Operations Research and Financial Engineering

Reference 57

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Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Unresolved cited work

Reference 58

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This paper cites On the nonmonotone linesearch for a class of infinite-dimensional nonsmooth problems.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems On the nonmonotone linesearch for a class of infinite-dimensional nonsmooth problems

Reference 59

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This paper cites Mathematical and Computational Applications 27(3), 39 (2022) https://doi.org/ 38 10.3390/mca27030039.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Mathematical and Computational Applications 27(3), 39 (2022) https://doi.org/ 38 10.3390/mca27030039

Reference 60

Resolution: verified exact; doi, observed 2026-08-06T17:24:27.564333Z

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This paper cites Multi-fidelity Learning of Reduced Order Models for Parabolic PDE Constrained Optimization.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Multi-fidelity Learning of Reduced Order Models for Parabolic PDE Constrained Optimization

Reference 61

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This paper cites Adaptive Reduced Basis Methods for Multiscale Problems and Large-scale PDE-constrained Optimization.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Adaptive Reduced Basis Methods for Multiscale Problems and Large-scale PDE-constrained Optimization

Reference 62

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Observation 0a811a30-ec22-4d11-9bb8-78265c5e4f50 · outbound

This paper cites Pure and Applied Functional Analysis 7, 1561–1596 (2022).

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems Pure and Applied Functional Analysis 7, 1561–1596 (2022)

Reference 63

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Observation e7193de8-94e7-4f7f-85f9-6436b02e336e · outbound

This paper cites (eds.) Model Reduction via Proper Orthogonal Decomposition, pp.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems (eds.) Model Reduction via Proper Orthogonal Decomposition, pp

Reference 64

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Observation a9ae490a-f81d-45d7-8fd7-89e35ec5fd71 · outbound

This paper cites A numerically stable a posteriori error estimator for reduced basis approximations of elliptic equations.

Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems A numerically stable a posteriori error estimator for reduced basis approximations of elliptic equations

Reference 65

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Pith citing papers

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Optimality-Based Control Space Reduction for Infinite-Dimensional Control Spaces cites this paper.

Optimality-Based Control Space Reduction for Infinite-Dimensional Control Spaces Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems

Reference 4

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