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Researcher profile

George Biros

George Biros contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Quantitative Methodseess.IVmath.NANumerical Analysisphysics.med-phComputational Engineering, Finance, and Sciencecond-mat.softphysics.flu-dynTissues and OrgansComputer VisionDistributed, Parallel, and Cluster Computingmath.DSmath.OC

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Published work

13 published item(s)

preprint2026arXiv

Inverse problems for history-enriched linear model reduction

Standard projection-based model reduction for dynamical systems incurs closure error because it only accounts for instantaneous dependence on the resolved state. From the Mori-Zwanzig (MZ) perspective, projecting the full dynamics onto a low-dimensional resolved subspace induces additional noise and memory terms arising from the dynamics of the unresolved component in the orthogonal complement. The memory term makes the resolved dynamics explicitly history dependent. In this work, based on the MZ identity, we derive exact, history-enriched models for the resolved dynamics of linear driven dynamical systems and formulate inverse problems to learn model operators from discrete snapshot data via least-squares regression. We propose a greedy time-marching scheme to solve the inverse problems efficiently and analyze operator identifiability under full and partial observation data availability. For full observation data, we show that, under mild assumptions, the operators are identifiable even when the full-state dynamics are governed by a general time-varying linear operator, whereas with partial observation data the inverse problem has a unique solution only when the full-state operator is time-invariant. To address the resulting non-uniqueness in the time-varying case, we introduce a time-smoothing Tikhonov regularization. Numerical results demonstrate that the operators can be faithfully reconstructed from both full and partial observation data and that the learned history-enriched MZ models yield accurate trajectories of the resolved state.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

LNODE: latent dynamics reveal the shared spatiotemporal structure of amyloid-$β$ progression

We introduce LNODE, a mechanism-based phenomenological model for amyloid beta (A$β$) dynamics, calibrated using positron emission tomography (PET) imaging. A$β$ is a key biomarker of Alzheimer's disease. LNODE is designed to support the fusion, harmonization, quantitative analysis, and interpretation of Abeta PET scans. We evaluate LNODE on 1461 subjects in the ADNI cohort and 1070 subjects in the A4 Study, using MUSE and DKT anatomical atlases. LNODE is formulated as a regional neural ordinary differential equation (ODE) model that is jointly calibrated on all available scans within a cohort. The model captures the spatial propagation, proliferation, and clearance of A$β$ and incorporates a latent-state representation that modulates A$β$ dynamics. The temporal evolution of these latent states is governed by cohort-shared parameters, enabling LNODE to represent both population-level trajectories and subject-specific deviations. The proposed model demonstrates strong parameter identifiability and stability properties, supported by synthetic experiments and analytical analysis of the Hessian condition number. To mitigate overfitting and reduce spurious correlations, LNODE is intentionally underparameterized, employing approximately five to ten parameters per subject. Despite this parsimonious parameterization, LNODE achieves $R^2 > 0.99$ in both the ADNI and A4 datasets. LNODE exhibits strong predictive performance: in the A4 cohort, it accurately forecasts the A$β$ PET signal in previously unseen follow-up scans, including cases with inter-scan intervals exceeding four years. Clustering in the learned latent-state space reveals distinct subgroups, consistent with the existence of different subtypes of Alzheimer's disease progression.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Overlapping Domain Decomposition Preconditioner for Integral Equations

The discretization of certain integral equations, e.g., the first-kind Fredholm equation of Laplace's equation, leads to symmetric positive-definite linear systems, where the coefficient matrix is dense and often ill-conditioned. We introduce a new preconditioner based on a novel overlapping domain decomposition that can be combined efficiently with fast direct solvers. Empirically, we observe that the condition number of the preconditioned system is $O(1)$, independent of the problem size. Our domain decomposition is designed so that we can construct approximate factorizations of the subproblems efficiently. In particular, we apply the recursive skeletonization algorithm to subproblems associated with every subdomain. We present numerical results on problem sizes up to $16\,384^2$ in 2D and $256^3$ in 3D, which were solved in less than 16 hours and three hours, respectively, on an Intel Xeon Platinum 8280M.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Shape dynamics of a red blood cell in Poiseuille flow

We use numerical simulations to study the dynamics of red blood cells (RBCs) in unconfined and confined Poiseuille flow. Previous numerical studies with 3D vesicles have indicated that the slipper shape observed in experiments at high capillary number can be attributed to the bistability due to the interplay of wall push and outward migration tendency at higher viscosity contrasts. In this paper, we study this outward migration and bistability using numerical simulations for 3D capsules and provide phase diagrams of RBC dynamics with and without viscosity contrast. We observe a bistability of slipper and croissants in confined Poiseuille flow with viscosity contrast as observed in experiments.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Quantitative in vivo imaging to enable tumor forecasting and treatment optimization

Current clinical decision-making in oncology relies on averages of large patient populations to both assess tumor status and treatment outcomes. However, cancers exhibit an inherent evolving heterogeneity that requires an individual approach based on rigorous and precise predictions of cancer growth and treatment response. To this end, we advocate the use of quantitative in vivo imaging data to calibrate mathematical models for the personalized forecasting of tumor development. In this chapter, we summarize the main data types available from both common and emerging in vivo medical imaging technologies, and how these data can be used to obtain patient-specific parameters for common mathematical models of cancer. We then outline computational methods designed to solve these models, thereby enabling their use for producing personalized tumor forecasts in silico, which, ultimately, can be used to not only predict response, but also optimize treatment. Finally, we discuss the main barriers to making the above paradigm a clinical reality.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

An efficient method for modeling flow in porous media with immersed faults

Modeling flow in geosystems with natural fault is a challenging problem due to low permeability of fault compared to its surrounding porous media. One way to predict the behavior of the flow while taking the effects of fault into account is to use the mixed finite element method. However, the mixed method could be time consuming due to large number of degree of freedom since both pressure and velocity are considered in the system. A new modeling method is presented in this paper. First, we introduce approximations of pressure based on the relation of pressure and velocity. We furthure decouple the approximated pressure from velocity so that it can be solved independently by continuous Galerkin finite element method. The new problem involves less degree of freedom than the mixed method for a given mesh . Moreover, local problem associated with a small subdomain around the fault is additionally solved to increase the accuracy of approximations around fault. Numerical experiments are conducted to examine the accuracy and efficiency of the new method. Results of three-dimensional tests show that our new method is up to 30$\times$ faster than the the mixed method at given $L^2$ pressure error.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Automatic MRI-Driven Model Calibration for Advanced Brain Tumor Progression Analysis

Our objective is the calibration of mathematical tumor growth models from a single multiparametric scan. The target problem is the analysis of preoperative Glioblastoma (GBM) scans. To this end, we present a fully automatic tumor-growth calibration methodology that integrates a single-species reaction-diffusion partial differential equation (PDE) model for tumor progression with multiparametric Magnetic Resonance Imaging (mpMRI) scans to robustly extract patient specific biomarkers i.e., estimates for (i) the tumor cell proliferation rate, (ii) the tumor cell migration rate, and (iii) the original, localized site(s) of tumor initiation. Our method is based on a sparse reconstruction algorithm for the tumor initial location (TIL). This problem is particularly challenging due to nonlinearity, ill-posedeness, and ill conditioning. We propose a coarse-to-fine multi-resolution continuation scheme with parameter decomposition to stabilize the inversion. We demonstrate robustness and practicality of our method by applying the proposed method to clinical data of 206 GBM patients. We analyze the extracted biomarkers and relate tumor origin with patient overall survival by mapping the former into a common atlas space. We present preliminary results that suggest improved accuracy for prediction of patient overall survival when a set of imaging features is augmented with estimated biophysical parameters. All extracted features, tumor initial positions, and biophysical growth parameters are made publicly available for further analysis. To our knowledge, this is the first fully automatic scheme that can handle multifocal tumors and can localize the TIL to a few millimeters.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Integrated Biophysical Modeling and Image Analysis: Application to Neuro-Oncology

Central nervous system (CNS) tumors come with the vastly heterogeneous histologic, molecular and radiographic landscape, rendering their precise characterization challenging. The rapidly growing fields of biophysical modeling and radiomics have shown promise in better characterizing the molecular, spatial, and temporal heterogeneity of tumors. Integrative analysis of CNS tumors, including clinically-acquired multi-parametric magnetic resonance imaging (mpMRI) and the inverse problem of calibrating biophysical models to mpMRI data, assists in identifying macroscopic quantifiable tumor patterns of invasion and proliferation, potentially leading to improved (i) detection/segmentation of tumor sub-regions, and (ii) computer-aided diagnostic/prognostic/predictive modeling. This paper presents a summary of (i) biophysical growth modeling and simulation, (ii) inverse problems for model calibration, (iii) their integration with imaging workflows, and (iv) their application on clinically-relevant studies. We anticipate that such quantitative integrative analysis may even be beneficial in a future revision of the World Health Organization (WHO) classification for CNS tumors, ultimately improving patient survival prospects.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Multiatlas Calibration of Biophysical Brain Tumor Growth Models with Mass Effect

We present a 3D fully-automatic method for the calibration of partial differential equation (PDE) models of glioblastoma (GBM) growth with mass effect, the deformation of brain tissue due to the tumor. We quantify the mass effect, tumor proliferation, tumor migration, and the localized tumor initial condition from a single multiparameteric Magnetic Resonance Imaging (mpMRI) patient scan. The PDE is a reaction-advection-diffusion partial differential equation coupled with linear elasticity equations to capture mass effect. The single-scan calibration model is notoriously difficult because the precancerous (healthy) brain anatomy is unknown. To solve this inherently ill-posed and ill-conditioned optimization problem, we introduce a novel inversion scheme that uses multiple brain atlases as proxies for the healthy precancer patient brain resulting in robust and reliable parameter estimation. We apply our method on both synthetic and clinical datasets representative of the heterogeneous spatial landscape typically observed in glioblastomas to demonstrate the validity and performance of our methods. In the synthetic data, we report calibration errors (due to the ill-posedness and our solution scheme) in the 10\%-20\% range. In the clinical data, we report good quantitative agreement with the observed tumor and qualitative agreement with the mass effect (for which we do not have a ground truth). Our method uses a minimal set of parameters and provides both global and local quantitative measures of tumor infiltration and mass effect.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Stable shapes of three-dimensional vesicles in unconfined and confined Poiseuille flow

We use numerical simulations to study the dynamics of three dimensional vesicles in unconfined and confined Poiseuille flow. Previous numerical studies have shown that when the fluid viscosity inside and outside the vesicle is same (no viscosity contrast), a transition from asymmetric slippers to symmetric parachutes takes place as viscous forcing or capillary number is increased. At higher viscosity contrast, an outward migration tendency has also been observed in unconfined flow simulations. In this paper, we study how the presence of viscosity contrast and confining walls affect the dynamics of vesicles and present phase diagrams for confined Poiseuille flow with and without viscosity contrast. To our knowledge, this is the first study that provides a phase diagram for 3D vesicles with viscosity contrast in confined Poiseuille flow. The confining walls push the vesicle towards the center while the viscosity contrast has the opposite effect. This interplay leads to important differences in the dynamics like bistability at high capillary numbers.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

CLAIRE: A distributed-memory solver for constrained large deformation diffeomorphic image registration

With this work, we release CLAIRE, a distributed-memory implementation of an effective solver for constrained large deformation diffeomorphic image registration problems in three dimensions. We consider an optimal control formulation. We invert for a stationary velocity field that parameterizes the deformation map. Our solver is based on a globalized, preconditioned, inexact reduced space Gauss--Newton--Krylov scheme. We exploit state-of-the-art techniques in scientific computing to develop an effective solver that scales to thousands of distributed memory nodes on high-end clusters. We present the formulation, discuss algorithmic features, describe the software package, and introduce an improved preconditioner for the reduced space Hessian to speed up the convergence of our solver. We test registration performance on synthetic and real data. We demonstrate registration accuracy on several neuroimaging datasets. We compare the performance of our scheme against different flavors of the Demons algorithm for diffeomorphic image registration. We study convergence of our preconditioner and our overall algorithm. We report scalability results on state-of-the-art supercomputing platforms. We demonstrate that we can solve registration problems for clinically relevant data sizes in two to four minutes on a standard compute node with 20 cores, attaining excellent data fidelity. With the present work we achieve a speedup of (on average) 5$\times$ with a peak performance of up to 17$\times$ compared to our former work.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Image-Driven Biophysical Tumor Growth Model Calibration

We present a novel formulation for the calibration of a biophysical tumor growth model from a single-time snapshot, MRI scan of a glioblastoma patient. Tumor growth models are typically nonlinear parabolic partial differential equations (PDEs). Thus, we have to generate a second snapshot to be able to extract significant information from a single patient snapshot. We create this two-snapshot scenario as follows. We use an atlas (an average of several scans of healthy individuals) as a substitute for an earlier, pretumor, MRI scan of the patient. Then, using the patient scan and the atlas, we combine image-registration algorithms and parameter estimation algorithms to achieve a better estimate of the healthy patient scan and the tumor growth parameters that are consistent with the data. Our scheme is based on our recent work (Scheufele et al, "Biophysically constrained diffeomorphic image registration, Tumor growth, Atlas registration, Adjoint-based methods, Parallel algorithms", CMAME, 2018), but apply a different and novel scheme where the tumor growth simulation in contrast to the previous work is executed in the patient brain domain and not in the atlas domain yielding more meaningful patient-specific results. As a basis, we use a PDE-constrained optimization framework. We derive a modified Picard-iteration-type solution strategy in which we alternate between registration and tumor parameter estimation in a new way. In addition, we consider an $\ell_1$ sparsity constraint on the initial condition for the tumor and integrate it with the new joint inversion scheme. We solve the subproblems with a reduced-space, inexact Gauss-Newton-Krylov/quasi-Newton methods. We present results using real brain data with synthetic tumor data that show that the new scheme reconstructs the tumor parameters in a more accurate and reliable way compared to our earlier scheme.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Where did the tumor start? An inverse solver with sparse localization for tumor growth models

We present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction-diffusion partial differential equation (PDE) for the tumor concentration. We use a PDE-constrained optimization formulation for the inverse problem. The unknown parameters are the reaction coefficient (proliferation), the diffusion coefficient (infiltration), and the initial condition field for the tumor PDE. Segmentation of Magnetic Resonance Imaging (MRI) scans from a single time snapshot drive the inverse problem where segmented tumor regions serve as partial observations of the tumor concentration. The precise time relative to tumor initiation is unknown, which poses an additional difficulty for inversion. We perform a frozen-coefficient spectral analysis and show that the inverse problem is severely ill-posed. We introduce a biophysically motivated regularization on the tumor initial condition. In particular, we assume that the tumor starts at a few locations (enforced with a sparsity constraint) and that the initial condition magnitude in the maximum norm equals one. We solve the resulting optimization problem using an inexact quasi-Newton method combined with a compressive sampling algorithm for the sparsity constraint. Our implementation uses PETSc and AccFFT libraries. We conduct numerical experiments on synthetic and clinical images to highlight the improved performance of our solver over an existing solver that uses a two-norm regularization for the calibration parameters. The existing solver is unable to localize the initial condition. Our new solver can localize the initial condition and recover infiltration and proliferation. In clinical datasets (for which the ground truth is unknown), our solver results in qualitatively different solutions compared to the existing solver.

0 citations0 reviewsNo code linkedOpen access