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We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…

Verification, validation and uncertainty quantification (VVUQ) have become a common practice in thermal-hydraulics analysis. An important step in the uncertainty analysis is the sensitivity analysis of various uncertain input parameters.…

We present a physics informed deep neural network (DNN) method for estimating parameters and unknown physics (constitutive relationships) in partial differential equation (PDE) models. We use PDEs in addition to measurements to train DNNs…

A gradient discretisation method (GDM), Gradient schemes, Convergence analysis, Existence of weak solutions, Anisotropic reaction diffusion models, Dirichlet and Neumann boundary conditions, Non conforming finite element methods, Finite…

Diffusion adaptation is a powerful strategy for distributed estimation and learning over networks. Motivated by the concept of combining adaptive filters, this work proposes a combination framework that aggregates the operation of multiple…

Targeting signaling pathways that drive cancer cell migration or proliferation is a common therapeutic approach. A popular experimental technique, the scratch assay, measures the migration and proliferation-driven cell closure of a defect…

In this paper, we investigate several techniques for modeling the one-dimensional advection equation for a specific class of problems with discontinuous initial and boundary conditions using physics-informed neural networks (PINNs). To…

In this paper, an innovative microwave imaging (MI) approach for breast tumor diagnosis is proposed that employs a differential formulation of the inverse scattering problem (ISP) at hand to exploit arbitrary-fidelity priors on the…

We pursue a computational analysis of the biomedical problem on the identification of the cancerous tumor at an early stage of development based on the Electrical Impedance Tomography (EIT) and optimal control of elliptic partial…

In this paper, we study adaptive neuron enhancement (ANE) method for solving self-adjoint second-order elliptic partial differential equations (PDEs). The ANE method is a self-adaptive method generating a two-layer spline NN and a numerical…

The aim of this paper is to discuss potential advances in PET kinetic models and direct reconstruction of kinetic parameters. As a prominent example we focus on a typical task in perfusion imaging and derive a system of…

We consider a mathematical model of cancer cell invasion of the extracellular matrix (ECM), comprising a strongly degenerate parabolic partial differential equation for the cell volume fraction, coupled with an ordinary differential…

In this paper we consider two-stage adaptive dose-response study designs, where the study design is changed at an interim analysis based on the information collected so far. In a simulation study, two approaches will be compared for these…

In this paper, we propose a new mathematical model nonlinear reaction-diffusion PDE's describing the dynamics of propagation of cancer. Here the mixed problem for the proposed PDE's is investigated and by applying obtained results…

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…

Given a partial differential equation (PDE), goal-oriented error estimation allows us to understand how errors in a diagnostic quantity of interest (QoI), or goal, occur and accumulate in a numerical approximation, for example using the…

Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…

In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on…

We derive the adjoint path-kernel method for computing parameter-gradients (linear responses) of SDEs. Its cost is almost independent of the number of parameters, and it works for non-hyperbolic systems with parameter-controlled…

Deep neural networks (DNNs) offer significant promise for improving breast cancer diagnosis in medical imaging. However, these models are highly susceptible to adversarial attacks--small, imperceptible changes that can mislead…