Lipschitz stability for Bayesian inference in porous medium tissue growth models
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arXiv
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| Format: | Preprint |
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2025
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| author | Dębiec, Tomasz Gwiazda, Piotr Miasojedow, Błażej Ryszewska, Katarzyna Szymańska, Zuzanna Wróblewska-Kamińska, Aneta |
| author_facet | Dębiec, Tomasz Gwiazda, Piotr Miasojedow, Błażej Ryszewska, Katarzyna Szymańska, Zuzanna Wróblewska-Kamińska, Aneta |
| contents | We consider a macroscopic model for the dynamics of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Given a power-law constitutive relation between the pressure and cell density, the model can be written as a porous medium equation with a growth term. We prove Lipschitz continuity of the mild solutions of the model with respect to the diffusion parameter (the exponent $γ$ in the pressure-density law) in the $L_1$ norm. While of independent analytical interest, our motivation for this result is to provide a vital step towards using Bayesian inverse problem methodology for parameter estimation based on experimental data -- such stability estimates are indispensable for applying sampling algorithms which rely on the gradient of the likelihood function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04769 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lipschitz stability for Bayesian inference in porous medium tissue growth models Dębiec, Tomasz Gwiazda, Piotr Miasojedow, Błażej Ryszewska, Katarzyna Szymańska, Zuzanna Wróblewska-Kamińska, Aneta Analysis of PDEs 35B30, 35B35, 35B45, 35K57, 35K65, 35Q92 We consider a macroscopic model for the dynamics of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Given a power-law constitutive relation between the pressure and cell density, the model can be written as a porous medium equation with a growth term. We prove Lipschitz continuity of the mild solutions of the model with respect to the diffusion parameter (the exponent $γ$ in the pressure-density law) in the $L_1$ norm. While of independent analytical interest, our motivation for this result is to provide a vital step towards using Bayesian inverse problem methodology for parameter estimation based on experimental data -- such stability estimates are indispensable for applying sampling algorithms which rely on the gradient of the likelihood function. |
| title | Lipschitz stability for Bayesian inference in porous medium tissue growth models |
| topic | Analysis of PDEs 35B30, 35B35, 35B45, 35K57, 35K65, 35Q92 |
| url | https://arxiv.org/abs/2506.04769 |