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Computational inverse problems for biomedical simulators suffer from limited data and relatively high parameter dimensionality. This often requires sensitivity analysis, where parameters of the model are ranked based on their influence on…

Tissues and Organs · Quantitative Biology 2025-06-06 Mitchel J. Colebank

The problem of continuous inverse optimal control (over finite time horizon) is to learn the unknown cost function over the sequence of continuous control variables from expert demonstrations. In this article, we study this fundamental…

Machine Learning · Computer Science 2022-04-20 Yifei Xu , Jianwen Xie , Tianyang Zhao , Chris Baker , Yibiao Zhao , Ying Nian Wu

Determining the mathematical dynamics and associated parameter values that should be used to accurately reflect tumor growth continues to be of interest to mathematical modelers, experimentalists and practitioners. However, while there are…

Cell Behavior · Quantitative Biology 2013-12-18 E. A. Sarapata , L. G. de Pillis

Mechanical effects have mostly been neglected so far in phase field tumour models that are based on a Cahn-Hilliard approach. In this paper we study a macroscopic mechanical model for tumour growth in which cell-cell adhesion effects are…

Analysis of PDEs · Mathematics 2021-01-20 Harald Garcke , Kei Fong Lam , Andrea Signori

We consider a fully practical finite element approximation of a diffuse interface model for tumour growth that takes the form of a degenerate parabolic system. In addition to showing stability bounds for the approximation, we prove…

Numerical Analysis · Mathematics 2022-02-07 Joe Eyles , Robert Nürnberg , Vanessa Styles

We consider a model describing the evolution of a tumor inside a host tissue in terms of the parameters $\varphi_p$, $\varphi_d$ (proliferating and dead cells, respectively), $u$ (cell velocity) and $n$ (nutrient concentration). The…

Analysis of PDEs · Mathematics 2017-09-06 Sergio Frigeri , Kei Fong Lam , Elisabetta Rocca , Giulio Schimperna

In this paper, we study a system of three evolutionary operator equations involving fractional powers of selfadjoint, monotone, unbounded, linear operators having compact resolvents. This system constitutes a generalization of a phase field…

Analysis of PDEs · Mathematics 2019-06-27 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

For parameter identification problems the Fr\'echet-derivative of the parameter-to-state map is of particular interest. In many applications, e.g. in seismic tomography, the unknown quantity is modeled as a coefficient in a linear…

Analysis of PDEs · Mathematics 2019-01-30 Thies Gerken , Simon Grützner

This paper treats a distributed optimal control problem for a tumor growth model of viscous Cahn--Hilliard type. The evolution of the tumor fraction is governed by a thermodynamic force induced by a double-well potential of logarithmic…

Optimization and Control · Mathematics 2023-06-14 Jürgen Sprekels , Fredi Tröltzsch

In this paper, we study a phase field model for a tumor growth model of Cahn--Hilliard type in which the often assumed parabolic relaxation of the chemical potential is replaced by a hyperbolic one. We show that the resulting…

Analysis of PDEs · Mathematics 2026-02-16 Pierluigi Colli , Elisabetta Rocca , Jürgen Sprekels

We investigate a multiphase Cahn-Hilliard model for tumor growth with general source terms. The multiphase approach allows us to consider multiple cell types and multiple chemical species (oxygen and/or nutrients) that are consumed by the…

Analysis of PDEs · Mathematics 2022-06-22 Patrik Knopf , Andrea Signori

The inverse linear-quadratic optimal control problem is a system identification problem whose aim is to recover the quadratic cost function and hence the closed-loop system matrices based on observations of optimal trajectories. In this…

Optimization and Control · Mathematics 2022-09-22 Han Zhang , Axel Ringh

This study is a first step towards using data-informed differential models to predict and control the dynamics of cancer-on-chip experiments. We consider a conceptualized one-dimensional device, containing a cancer and a population of white…

Computational Engineering, Finance, and Science · Computer Science 2026-02-06 Silvia Bertoluzza , Vittoria Bianchi , Gabriella Bretti , Lorenzo Tamellini , Pietro Zanotti

We propose a multi-patient inverse modeling framework for identifying effective calcium and citrate diffusion coefficients in hollow-fiber hemodialysis devices. The approach relies on a coupled forward model combining axisymmetric fluid…

Numerical Analysis · Mathematics 2026-03-03 Geoffrey Lacour , Nicolae Cîndea , Julien Aniort

A novel numerical technique has been proposed to solve a two-phase tumour growth model in one spatial dimension without needing to account for the boundary dynamics explicitly. The equivalence to the standard definition of a weak solution…

Numerical Analysis · Mathematics 2019-02-19 Gopikrishnan C. Remesan

In this contribution, we are concerned with model order reduction in the context of iterative regularization methods for the solution of inverse problems arising from parameter identification in elliptic partial differential equations. Such…

Numerical Analysis · Mathematics 2024-10-14 Michael Kartmann , Tim Keil , Mario Ohlberger , Stefan Volkwein , Barbara Kaltenbacher

We consider numerical approaches for deterministic, finite-dimensional optimal control problems whose dynamics depend on unknown or uncertain parameters. We seek to amortize the solution over a set of relevant parameters in an offline stage…

Optimization and Control · Mathematics 2024-02-16 Deepanshu Verma , Nick Winovich , Lars Ruthotto , Bart van Bloemen Waanders

In this paper, we develop a sharp interface tumor growth model in two dimensions to study the effect of both the intratumoral structure using a controlled necrotic core and the extratumoral nutrient supply from vasculature on tumor…

Numerical Analysis · Mathematics 2022-03-30 Min-Jhe Lu , Wenrui Hao , Chun Liu , John Lowengrub , Shuwang Li

In this paper, we consider the inverse problem of recovering a diffusion and absorption coefficients in steady-state optical tomography problem from the Neumann-to-Dirichlet map. We first prove a Global uniqueness and Lipschitz stability…

Analysis of PDEs · Mathematics 2020-12-21 Houcine Meftahi

We derive a class of Navier--Stokes--Cahn--Hilliard systems that models two-phase flows with mass transfer coupled to the process of chemotaxis. These thermodynamically consistent models can be seen as the natural Navier--Stokes analogues…

Analysis of PDEs · Mathematics 2023-07-28 Kei Fong Lam , Hao Wu