A Bayesian approach with persistent homology prior for Robin coefficient identification in a parabolic problem

Jiaying Jia; Xiaomei Yang; Zhiliang Deng

arxiv: 2512.24046 · v2 · submitted 2025-12-30 · 📊 stat.CO

A Bayesian approach with persistent homology prior for Robin coefficient identification in a parabolic problem

Xiaomei Yang , Jiaying Jia , Zhiliang Deng This is my paper

Pith reviewed 2026-05-16 19:29 UTC · model grok-4.3

classification 📊 stat.CO

keywords persistent homologyBayesian inferenceinverse problemsRobin coefficientparabolic equationstopological priorsheat transfer

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The pith

A persistent homology prior in hierarchical Bayesian inference recovers time-dependent Robin coefficients while preserving their multiscale temporal profiles.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper proposes using persistent homology to define a prior distribution in a Bayesian framework for solving an inverse problem: identifying the time-dependent Robin coefficient from observations in a parabolic partial differential equation modeling heat transfer. The approach quantifies topological features like the persistence of connected components in the coefficient's evolution to impose a global constraint. This helps maintain complex variations in the coefficient without the blocky artifacts from total variation methods or the smoothing from Gaussian priors. The hierarchical Bayesian structure allows the data to determine the prior's strength automatically. Tests on synthetic data show competitive accuracy with advantages in feature preservation for applications like convective heat transfer analysis.

Core claim

The paper establishes that integrating a persistent homology prior into a hierarchical Bayesian model provides a global topological constraint for the Robin coefficient in parabolic inverse problems, enabling reconstructions that capture intricate temporal dynamics more faithfully than local regularization techniques such as total variation or Gaussian smoothing.

What carries the argument

The persistent homology prior, which encodes the birth and death times of topological features in the time series of the Robin coefficient to act as a structural regularizer transcending local derivative penalties.

If this is right

The hierarchical implementation automates the selection of hyperparameters based on the data.
It preserves complex temporal profiles without staircase distortions typical of total variation priors.
It avoids excessive blurring associated with Gaussian models.
It demonstrates superior performance in maintaining multiscale characteristics of the Robin coefficient.
Provides a robust method for diagnostics in convective heat transfer problems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar topological priors might improve inverse problems in other domains with structured time series data, such as signal processing or medical imaging.
Combining persistent homology with other priors could yield hybrid methods balancing local and global constraints.
Extensions to higher-dimensional or spatially varying coefficients could be explored to broaden applicability.

Load-bearing premise

The persistent homology computed from the Robin coefficient time series provides a meaningful global structural constraint that improves the accuracy of the inverse solution in the parabolic model without introducing undetected artifacts.

What would settle it

Numerical simulations with a true Robin coefficient featuring distinct topological features, such as multiple significant persistence intervals, where the proposed method reconstructs a coefficient lacking those features or performs worse than standard TV regularization.

Figures

Figures reproduced from arXiv: 2512.24046 by Jiaying Jia, Xiaomei Yang, Zhiliang Deng.

**Figure 2.** Figure 2: The posterior density of the scaling parameter [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: The numerical results for Example 1 with (a) 1 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: The numerical results for Example 2 with (a) 1 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: The posterior density of the scaling parameter [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: The numerical results for Example 2 with (a) 1 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

**Figure 7.** Figure 7: The numerical results for Example 3 with (a) 1 [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

**Figure 8.** Figure 8: The posterior density of the scaling parameter [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗

**Figure 9.** Figure 9: The numerical results for Example 3 with (a) 1 [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗

read the original abstract

The reconstruction of time-dependent Robin coefficients is a challenging inverse heat transfer problem due to its inherent ill-posedness. This paper introduces a hierarchical Bayesian approach integrated with a persistent homology (PH) prior for robust coefficient estimation. By quantifying the birth and death of topological features, the PH-based prior provides a global structural constraint that transcends local derivative based penalties. Numerical experiments show that this topological perspective allows for the preservation of complex temporal profiles without the typical staircase distortions of total variation (TV) priors or the excessive blurring of Gaussian models. A key feature of our framework is the hierarchical implementation, which yields an automated, data-driven selection of hyperparameters. The results demonstrate that while PH-based inference yields competitive accuracy compared to TV regularization, it offers superior performance in preserving the multiscale characteristics of the Robin coefficient, providing a robust alternative for convective heat transfer diagnostics

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper offers a hierarchical Bayesian method with a persistent homology prior on the Robin coefficient time series for a parabolic inverse problem, which is a fresh regularization angle but rests on unshown numerical gains.

read the letter

The main contribution is a hierarchical Bayesian setup that treats persistent homology of the coefficient's time series as a structural prior. This is meant to enforce global topological features during recovery of time-dependent Robin coefficients in the parabolic forward model, avoiding the staircase artifacts of total variation or the smoothing of Gaussian priors. The hierarchical layer for data-driven hyperparameter choice is a practical touch that removes some manual tuning. Numerical tests are described as showing competitive accuracy with better multiscale preservation, which aligns with the goal of handling complex temporal profiles in convective heat transfer diagnostics. The integration itself appears new for this specific inverse problem. The approach builds on standard Bayesian updating and existing PH tools, so the advance is mainly in the application and the claim that topology supplies a useful global constraint beyond local penalties. Soft spots include the lack of any error tables, specific metrics, or protocol details in the abstract, which makes it difficult to judge how large or consistent the reported improvements actually are. The central assumption that the PH features provide an unbiased and artifact-free constraint for this parabolic setting needs the full experiments to confirm it holds without hidden distortions. Persistent homology on one-dimensional time series is straightforward, so the performance edge may be modest once the numbers are examined. This work is aimed at researchers in inverse heat transfer problems or Bayesian methods that incorporate topological data analysis. A reader already working on time-dependent coefficient identification would find the comparison to TV and Gaussian baselines useful if the numerics check out. It deserves peer review because the framing is coherent and the problem class is relevant, even though revisions will likely be needed to supply the quantitative evidence and implementation specifics.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a hierarchical Bayesian framework for recovering time-dependent Robin coefficients in a parabolic inverse heat transfer problem. It integrates a persistent homology prior on the coefficient time series to enforce global topological structure, claiming competitive pointwise accuracy alongside superior multiscale feature preservation relative to total-variation and Gaussian priors, with fully data-driven hyperparameter selection.

Significance. The work demonstrates a concrete way to embed persistent-homology summaries as structural priors inside a hierarchical Bayesian model. If the numerical recovery results hold under the reported forward model and noise levels, the approach supplies a new regularization mechanism that can avoid both the staircasing of TV penalties and the over-smoothing of Gaussian priors while remaining computationally tractable. The automated hyperparameter treatment is a clear practical advantage.

major comments (2)

[§4] §4 (Numerical experiments): the abstract asserts 'competitive accuracy' and 'superior multiscale preservation,' yet the reported tables or figures must include explicit L2 or pointwise error norms, together with a precise description of the synthetic coefficient profiles, noise levels, and mesh resolutions used for the parabolic forward solves. Without these quantities the central performance claim cannot be assessed quantitatively.
[§3.2] §3.2 (PH prior construction): the birth-death persistence diagram is computed on the discrete time series of the Robin coefficient; it is unclear whether the filtration is taken with respect to the time index alone or incorporates the coefficient magnitude, and how the resulting persistence measure is turned into a prior density (e.g., via a likelihood on the diagram or a summary statistic). This step is load-bearing for the claimed global structural constraint.

minor comments (2)

[Abstract] The abstract should be expanded by one sentence that states the specific error metrics and the number of test cases on which the superiority over TV and Gaussian priors is observed.
[§3] Notation for the persistence diagram and the associated prior functional should be introduced once in §3 and used consistently thereafter; currently the same symbol appears to denote both the diagram and its summary statistic.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the recommendation for minor revision. We address each major point below and have revised the manuscript to improve quantitative rigor and clarity.

read point-by-point responses

Referee: [§4] §4 (Numerical experiments): the abstract asserts 'competitive accuracy' and 'superior multiscale preservation,' yet the reported tables or figures must include explicit L2 or pointwise error norms, together with a precise description of the synthetic coefficient profiles, noise levels, and mesh resolutions used for the parabolic forward solves. Without these quantities the central performance claim cannot be assessed quantitatively.

Authors: We agree that explicit quantitative error measures are required to support the performance claims. In the revised manuscript we have added a new table in §4 reporting L2 reconstruction errors for the PH, TV, and Gaussian priors at each tested noise level. We have also expanded the experimental description to specify the exact synthetic coefficient profiles (piecewise-linear with two discontinuities and a superimposed low-amplitude sinusoid), the noise model (additive i.i.d. Gaussian noise at 1 %, 5 %, and 10 % of the signal range), and the discretization (100 spatial elements, 200 uniform time steps for the forward parabolic solver). These additions allow direct quantitative evaluation of the reported accuracy and multiscale preservation. revision: yes
Referee: [§3.2] §3.2 (PH prior construction): the birth-death persistence diagram is computed on the discrete time series of the Robin coefficient; it is unclear whether the filtration is taken with respect to the time index alone or incorporates the coefficient magnitude, and how the resulting persistence measure is turned into a prior density (e.g., via a likelihood on the diagram or a summary statistic). This step is load-bearing for the claimed global structural constraint.

Authors: We apologize for the insufficient detail. The filtration is a sublevel-set filtration on the 1-D point cloud whose coordinate is the time index and whose function value is the coefficient magnitude; the resulting persistence diagram enters the prior density through an exponential penalty on the bottleneck distance to a reference diagram that encodes the desired multiscale topology. We have rewritten §3.2 to include the explicit prior density formula, the definition of the bottleneck distance, and a short algorithmic pseudocode for the diagram computation. This revision makes the global structural constraint fully transparent. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's derivation chain consists of a standard hierarchical Bayesian update that incorporates an off-the-shelf persistent-homology construction as the prior on the Robin coefficient time series. No equation reduces a claimed performance gain to a fitted parameter by construction, nor does any load-bearing step rely on a self-citation whose content is itself unverified or defined in terms of the target result. Numerical experiments are presented as independent validation against TV and Gaussian baselines, rendering the framework self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of persistent homology to encode useful global structure for the Robin coefficient and on standard Bayesian modeling assumptions for inverse parabolic problems. No new physical entities are introduced.

free parameters (1)

hyperparameters of the hierarchical model
Even though selected automatically, they remain tunable quantities whose values affect the posterior.

axioms (1)

domain assumption The time series of the Robin coefficient admits a persistent homology representation that encodes structurally relevant features for the inverse problem.
This assumption underpins the construction of the PH prior and is invoked when the prior is stated to provide a global structural constraint.

pith-pipeline@v0.9.0 · 5444 in / 1344 out tokens · 31761 ms · 2026-05-16T19:29:39.503766+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

the PH-Gaussian prior term is based on the concept of persistent distance, defined as ∥γ∥per = ∑(xk,xl)∈P1 |γ(xl)−γ(xk)| + ∑(xk,xl)∈P2 |γ(xl)−γ(xk)|
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

R(γ) = λ ∑(xj,˜xj)∈P(γ) αj(γ)|γ(xj)−γ(˜xj)|

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

22 extracted references · 22 canonical work pages

[1]

Numerical estimation of piecewise constant robin coefficient.SIAM journal on control and optimization, 48(3):1977–2002, 2009

Bangti Jin and Jun Zou. Numerical estimation of piecewise constant robin coefficient.SIAM journal on control and optimization, 48(3):1977–2002, 2009

work page 1977
[2]

An inverse problem in corrosion detection.Inverse problems, 13(4):977, 1997

Gabriele Inglese. An inverse problem in corrosion detection.Inverse problems, 13(4):977, 1997

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Stable determination of corrosion by a single electrostatic boundary measurement.Inverse problems, 19(4):973–984, 2003

Giovanni Alessandrini, L Del Piero, Luca Rondi, et al. Stable determination of corrosion by a single electrostatic boundary measurement.Inverse problems, 19(4):973–984, 2003

work page 2003
[4]

Initialization of ice-sheet forecasts viewed as an inverse robin problem.Journal of Glaciology, 56(197):527–533, 2010

Robert J Arthern and G Hilmar Gudmundsson. Initialization of ice-sheet forecasts viewed as an inverse robin problem.Journal of Glaciology, 56(197):527–533, 2010

work page 2010
[5]

On the determination of an unknown boundary function in a parabolic equation

Mourad Choulli. On the determination of an unknown boundary function in a parabolic equation. Inverse problems, 15(3):659, 1999

work page 1999
[6]

Stability estimate for an inverse boundary coefficient problem in thermal imaging.Journal of mathematical analysis and applications, 343(1):328–336, 2008

Mourad Bellassoued, Jin Cheng, and Mourad Choulli. Stability estimate for an inverse boundary coefficient problem in thermal imaging.Journal of mathematical analysis and applications, 343(1):328–336, 2008

work page 2008
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A numerical method for solving of a nonlinear inverse diffusion problem.Computers & Mathematics with Applications, 52(6-7):1021–1030, 2006

Abdollah Shidfar, R Pourgholi, and M Ebrahimi. A numerical method for solving of a nonlinear inverse diffusion problem.Computers & Mathematics with Applications, 52(6-7):1021–1030, 2006

work page 2006
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Determination of a robin coefficient in semilinear parabolic problems by means ofboundary measurements.Inverse Problems, 18(1):139, 2002

Marián Slodicka and Roger Van Keer. Determination of a robin coefficient in semilinear parabolic problems by means ofboundary measurements.Inverse Problems, 18(1):139, 2002

work page 2002
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Determination of a time-dependent heat transfer coefficient in a nonlinear inverse heat conduction problem.Inverse Problems in Science and Engineering, 18(1):65–81, 2010

M Slodička, D Lesnic, and TTM Onyango. Determination of a time-dependent heat transfer coefficient in a nonlinear inverse heat conduction problem.Inverse Problems in Science and Engineering, 18(1):65–81, 2010

work page 2010
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The heat equation with nonlinear generalized robin boundary conditions.Journal of Differential Equations, 247(7):1949–1979, 2009

Markus Biegert and Mahamadi Warma. The heat equation with nonlinear generalized robin boundary conditions.Journal of Differential Equations, 247(7):1949–1979, 2009

work page 1949
[11]

Numerical identification of a robin coefficient in parabolic problems

Bangti Jin and Xiliang Lu. Numerical identification of a robin coefficient in parabolic problems. Mathematics of Computation, 81(279):1369–1398, 2012

work page 2012
[12]

Inverse reconstruction of boundary condition coefficients in one-dimensional transient heat conduction.Applied mathematics and computation, 207(2):569–575, 2009

TTM Onyango, Derek B Ingham, and Daniel Lesnic. Inverse reconstruction of boundary condition coefficients in one-dimensional transient heat conduction.Applied mathematics and computation, 207(2):569–575, 2009

work page 2009
[13]

The identification of a robin coefficient by a conjugate gradient method.International journal for numerical methods in engineering, 78(7):800–816, 2009

Fenglian Yang, Liang Yan, and Ting Wei. The identification of a robin coefficient by a conjugate gradient method.International journal for numerical methods in engineering, 78(7):800–816, 2009

work page 2009
[14]

A direct solution of the robin inverse problem.The Journal of Integral Equations and Applications, pages 545–557, 2009

Weifu Fang and Suxing Zeng. A direct solution of the robin inverse problem.The Journal of Integral Equations and Applications, pages 545–557, 2009

work page 2009
[15]

WBdaSilva, JCSDutra, CEPKopperschimidt, DLesnic, andRGAykroyd. Sequentialestimationof the time-dependent heat transfer coefficient using the method of fundamental solutions and particle filters.Inverse Problems in Science and Engineering, 29(13):3322–3341, 2021

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Fast bayesian approach for parameter estimation.International Journal for Numerical Methods in Engineering, 76(2):230–252, 2008

Bangti Jin. Fast bayesian approach for parameter estimation.International Journal for Numerical Methods in Engineering, 76(2):230–252, 2008

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Abayesianinferenceapproachtoidentifyarobincoefficient in one-dimensional parabolic problems.Journal of Computational and Applied Mathematics, 231(2):840–850, 2009

LiangYan, FenglianYang, andChuliFu. Abayesianinferenceapproachtoidentifyarobincoefficient in one-dimensional parabolic problems.Journal of Computational and Applied Mathematics, 231(2):840–850, 2009

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[18]

A bayesian inference approach to the ill-posed cauchy problem of steady- state heat conduction.International journal for numerical methods in engineering, 76(4):521–544, 2008

Bangti Jin and Jun Zou. A bayesian inference approach to the ill-posed cauchy problem of steady- state heat conduction.International journal for numerical methods in engineering, 76(4):521–544, 2008

work page 2008
[19]

Identify the robin coefficient in an inhomogeneous time-fractional diffusion-wave equation.Journal of Computational and Applied Mathematics, 434:115337, 2023

Chengxin Shi and Hao Cheng. Identify the robin coefficient in an inhomogeneous time-fractional diffusion-wave equation.Journal of Computational and Applied Mathematics, 434:115337, 2023

work page 2023
[20]

The bayesian approach to inverse robin problems.SIAM/ASA Journal on Uncertainty Quantification, 12(3):1050–1084, 2024

Aksel K Rasmussen, Fanny Seizilles, Mark Girolami, and Ieva Kazlauskaite. The bayesian approach to inverse robin problems.SIAM/ASA Journal on Uncertainty Quantification, 12(3):1050–1084, 2024

work page 2024
[21]

A tv-gaussian prior for infinite-dimensional bayesian inverse problems and its numerical implementations.Inverse Problems, 32(7):075006, 2016

Zhewei Yao, Zixi Hu, and Jinglai Li. A tv-gaussian prior for infinite-dimensional bayesian inverse problems and its numerical implementations.Inverse Problems, 32(7):075006, 2016

work page 2016
[22]

A persistent- homology-based bayesian prior for potential coefficient reconstruction in an elliptic partial differential equation

Zhiliang Deng, Haiyang Liu, Xiaofei Guan, Zhiyuan Wang, and Xiaomei Yang. A persistent- homology-based bayesian prior for potential coefficient reconstruction in an elliptic partial differential equation. 2025

work page 2025

[1] [1]

Numerical estimation of piecewise constant robin coefficient.SIAM journal on control and optimization, 48(3):1977–2002, 2009

Bangti Jin and Jun Zou. Numerical estimation of piecewise constant robin coefficient.SIAM journal on control and optimization, 48(3):1977–2002, 2009

work page 1977

[2] [2]

An inverse problem in corrosion detection.Inverse problems, 13(4):977, 1997

Gabriele Inglese. An inverse problem in corrosion detection.Inverse problems, 13(4):977, 1997

work page 1997

[3] [3]

Stable determination of corrosion by a single electrostatic boundary measurement.Inverse problems, 19(4):973–984, 2003

Giovanni Alessandrini, L Del Piero, Luca Rondi, et al. Stable determination of corrosion by a single electrostatic boundary measurement.Inverse problems, 19(4):973–984, 2003

work page 2003

[4] [4]

Initialization of ice-sheet forecasts viewed as an inverse robin problem.Journal of Glaciology, 56(197):527–533, 2010

Robert J Arthern and G Hilmar Gudmundsson. Initialization of ice-sheet forecasts viewed as an inverse robin problem.Journal of Glaciology, 56(197):527–533, 2010

work page 2010

[5] [5]

On the determination of an unknown boundary function in a parabolic equation

Mourad Choulli. On the determination of an unknown boundary function in a parabolic equation. Inverse problems, 15(3):659, 1999

work page 1999

[6] [6]

Stability estimate for an inverse boundary coefficient problem in thermal imaging.Journal of mathematical analysis and applications, 343(1):328–336, 2008

Mourad Bellassoued, Jin Cheng, and Mourad Choulli. Stability estimate for an inverse boundary coefficient problem in thermal imaging.Journal of mathematical analysis and applications, 343(1):328–336, 2008

work page 2008

[7] [7]

A numerical method for solving of a nonlinear inverse diffusion problem.Computers & Mathematics with Applications, 52(6-7):1021–1030, 2006

Abdollah Shidfar, R Pourgholi, and M Ebrahimi. A numerical method for solving of a nonlinear inverse diffusion problem.Computers & Mathematics with Applications, 52(6-7):1021–1030, 2006

work page 2006

[8] [8]

Determination of a robin coefficient in semilinear parabolic problems by means ofboundary measurements.Inverse Problems, 18(1):139, 2002

Marián Slodicka and Roger Van Keer. Determination of a robin coefficient in semilinear parabolic problems by means ofboundary measurements.Inverse Problems, 18(1):139, 2002

work page 2002

[9] [9]

Determination of a time-dependent heat transfer coefficient in a nonlinear inverse heat conduction problem.Inverse Problems in Science and Engineering, 18(1):65–81, 2010

M Slodička, D Lesnic, and TTM Onyango. Determination of a time-dependent heat transfer coefficient in a nonlinear inverse heat conduction problem.Inverse Problems in Science and Engineering, 18(1):65–81, 2010

work page 2010

[10] [10]

The heat equation with nonlinear generalized robin boundary conditions.Journal of Differential Equations, 247(7):1949–1979, 2009

Markus Biegert and Mahamadi Warma. The heat equation with nonlinear generalized robin boundary conditions.Journal of Differential Equations, 247(7):1949–1979, 2009

work page 1949

[11] [11]

Numerical identification of a robin coefficient in parabolic problems

Bangti Jin and Xiliang Lu. Numerical identification of a robin coefficient in parabolic problems. Mathematics of Computation, 81(279):1369–1398, 2012

work page 2012

[12] [12]

Inverse reconstruction of boundary condition coefficients in one-dimensional transient heat conduction.Applied mathematics and computation, 207(2):569–575, 2009

TTM Onyango, Derek B Ingham, and Daniel Lesnic. Inverse reconstruction of boundary condition coefficients in one-dimensional transient heat conduction.Applied mathematics and computation, 207(2):569–575, 2009

work page 2009

[13] [13]

The identification of a robin coefficient by a conjugate gradient method.International journal for numerical methods in engineering, 78(7):800–816, 2009

Fenglian Yang, Liang Yan, and Ting Wei. The identification of a robin coefficient by a conjugate gradient method.International journal for numerical methods in engineering, 78(7):800–816, 2009

work page 2009

[14] [14]

A direct solution of the robin inverse problem.The Journal of Integral Equations and Applications, pages 545–557, 2009

Weifu Fang and Suxing Zeng. A direct solution of the robin inverse problem.The Journal of Integral Equations and Applications, pages 545–557, 2009

work page 2009

[15] [15]

WBdaSilva, JCSDutra, CEPKopperschimidt, DLesnic, andRGAykroyd. Sequentialestimationof the time-dependent heat transfer coefficient using the method of fundamental solutions and particle filters.Inverse Problems in Science and Engineering, 29(13):3322–3341, 2021

work page 2021

[16] [16]

Fast bayesian approach for parameter estimation.International Journal for Numerical Methods in Engineering, 76(2):230–252, 2008

Bangti Jin. Fast bayesian approach for parameter estimation.International Journal for Numerical Methods in Engineering, 76(2):230–252, 2008

work page 2008

[17] [17]

Abayesianinferenceapproachtoidentifyarobincoefficient in one-dimensional parabolic problems.Journal of Computational and Applied Mathematics, 231(2):840–850, 2009

LiangYan, FenglianYang, andChuliFu. Abayesianinferenceapproachtoidentifyarobincoefficient in one-dimensional parabolic problems.Journal of Computational and Applied Mathematics, 231(2):840–850, 2009

work page 2009

[18] [18]

A bayesian inference approach to the ill-posed cauchy problem of steady- state heat conduction.International journal for numerical methods in engineering, 76(4):521–544, 2008

Bangti Jin and Jun Zou. A bayesian inference approach to the ill-posed cauchy problem of steady- state heat conduction.International journal for numerical methods in engineering, 76(4):521–544, 2008

work page 2008

[19] [19]

Identify the robin coefficient in an inhomogeneous time-fractional diffusion-wave equation.Journal of Computational and Applied Mathematics, 434:115337, 2023

Chengxin Shi and Hao Cheng. Identify the robin coefficient in an inhomogeneous time-fractional diffusion-wave equation.Journal of Computational and Applied Mathematics, 434:115337, 2023

work page 2023

[20] [20]

The bayesian approach to inverse robin problems.SIAM/ASA Journal on Uncertainty Quantification, 12(3):1050–1084, 2024

Aksel K Rasmussen, Fanny Seizilles, Mark Girolami, and Ieva Kazlauskaite. The bayesian approach to inverse robin problems.SIAM/ASA Journal on Uncertainty Quantification, 12(3):1050–1084, 2024

work page 2024

[21] [21]

A tv-gaussian prior for infinite-dimensional bayesian inverse problems and its numerical implementations.Inverse Problems, 32(7):075006, 2016

Zhewei Yao, Zixi Hu, and Jinglai Li. A tv-gaussian prior for infinite-dimensional bayesian inverse problems and its numerical implementations.Inverse Problems, 32(7):075006, 2016

work page 2016

[22] [22]

A persistent- homology-based bayesian prior for potential coefficient reconstruction in an elliptic partial differential equation

Zhiliang Deng, Haiyang Liu, Xiaofei Guan, Zhiyuan Wang, and Xiaomei Yang. A persistent- homology-based bayesian prior for potential coefficient reconstruction in an elliptic partial differential equation. 2025

work page 2025