Interior over-penalized enriched Galerkin methods for second order elliptic equations

In this paper we propose a variant of enriched Galerkin methods for second order elliptic equations with over-penalization of interior jump terms. The bilinear form with interior over-penalization gives a non-standard norm which is different from the discrete energy norm in the classical discontinuous Galerkin methods. Nonetheless we prove that optimal a priori error estimates with the standard discrete energy norm can be obtained by combining a priori and a posteriori error analysis techniques. We also show that the interior over-penalization is advantageous for constructing preconditioners robust to mesh refinement by analyzing spectral equivalence of bilinear forms. Numerical results are included to illustrate the convergence and preconditioning results.Comment: preconditioning for anisotropic cases is improve

Optimal design of chemoepitaxial guideposts for directed self-assembly of block copolymer systems using an inexact-Newton algorithm

Directed self-assembly (DSA) of block-copolymers (BCPs) is one of the most promising developments in the cost-effective production of nanoscale devices. The process makes use of the natural tendency for BCP mixtures to form nanoscale structures upon phase separation. The phase separation can be directed through the use of chemically patterned substrates to promote the formation of morphologies that are essential to the production of semiconductor devices. Moreover, the design of substrate pattern can formulated as an optimization problem for which we seek optimal substrate designs that effectively produce given target morphologies. In this paper, we adopt a phase field model given by a nonlocal Cahn--Hilliard partial differential equation (PDE) based on the minimization of the Ohta--Kawasaki free energy, and present an efficient PDE-constrained optimization framework for the optimal design problem. The design variables are the locations of circular- or strip-shaped guiding posts that are used to model the substrate chemical pattern. To solve the ensuing optimization problem, we propose a variant of an inexact Newton conjugate gradient algorithm tailored to this problem. We demonstrate the effectiveness of our computational strategy on numerical examples that span a range of target morphologies. Owing to our second-order optimizer and fast state solver, the numerical results demonstrate five orders of magnitude reduction in computational cost over previous work. The efficiency of our framework and the fast convergence of our optimization algorithm enable us to rapidly solve the optimal design problem in not only two, but also three spatial dimensions.Comment: 35 Pages, 17 Figure

Bayesian model calibration for diblock copolymer thin film self-assembly using power spectrum of microscopy data

Identifying parameters of computational models from experimental data, or model calibration, is fundamental for assessing and improving the predictability and reliability of computer simulations. In this work, we propose a method for Bayesian calibration of models that predict morphological patterns of diblock copolymer (Di-BCP) thin film self-assembly while accounting for various sources of uncertainties in pattern formation and data acquisition. This method extracts the azimuthally-averaged power spectrum (AAPS) of the top-down microscopy characterization of Di-BCP thin film patterns as summary statistics for Bayesian inference of model parameters via the pseudo-marginal method. We derive the analytical and approximate form of a conditional likelihood for the AAPS of image data. We demonstrate that AAPS-based image data reduction retains the mutual information, particularly on important length scales, between image data and model parameters while being relatively agnostic to the aleatoric uncertainties associated with the random long-range disorder of Di-BCP patterns. Additionally, we propose a phase-informed prior distribution for Bayesian model calibration. Furthermore, reducing image data to AAPS enables us to efficiently build surrogate models to accelerate the proposed Bayesian model calibration procedure. We present the formulation and training of two multi-layer perceptrons for approximating the parameter-to-spectrum map, which enables fast integrated likelihood evaluations. We validate the proposed Bayesian model calibration method through numerical examples, for which the neural network surrogate delivers a fivefold reduction of the number of model simulations performed for a single calibration task

Rapid turnover of T cells in acute infectious mononucleosis.

During acute infectious mononucleosis (AIM), large clones of Epstein-Barr virus-specific T lymphocytes are produced. To investigate the dynamics of clonal expansion, we measured cell proliferation during AIM using deuterated glucose to label DNA of dividing cells in vivo, analyzing cells according to CD4, CD8 and CD45 phenotype. The proportion of labeled CD8(+)CD45R0(+) T lymphocytes was dramatically increased in AIM subjects compared to controls (mean 17.5 versus 2.8%/day; p<0.005), indicating very rapid proliferation. Labeling was also increased in CD4(+)CD45R0(+) cells (7.1 versus 2.1%/day; p<0.01), but less so in CD45RA(+) cells. Mathematical modeling, accounting for death of labeled cells and changing pool sizes, gave estimated proliferation rates in CD8(+)CD45R0(+) cells of 11-130% of cells proliferating per day (mean 47%/day), equivalent to a doubling time of 1.5 days and an appearance rate in blood of about 5 x 10(9) cells/day (versus 7 x 10(7) cells/day in controls). Very rapid death rates were also observed amongst labeled cells (range 28-124, mean 57%/day),indicating very short survival times in the circulation. Thus, we have shown direct evidence for massive proliferation of CD8(+)CD45R0(+) T lymphocytes in AIM and demonstrated that rapid cell division continues concurrently with greatly accelerated rates of cell disappearance

Success and Failure in the Simulation of an Accident and Emergency Department

Healthcare simulation has the potential to offer many benefits but the implementation is often problematic. This paper describes the development of a simulation of an Accident and Emergency Department in an NHS hospital. The early experience of the client provoked great enthusiasm but ultimately the simulation failed to meet all expectations. The simulation delivered a number of benefits, notably in terms of stimulating constructive debate and helping the stakeholders appreciate the complete Accident and Emergency system. The project produced a technically proficient tool that was delivered too late to have the desired impact. This mixed record of success appears typical of many simulations. Important lessons were learned, both technically and in the management of client expectations, which have contributed to subsequent successful implementation in other departments of the hospital. The experience suggests that both potential clients and analysts need to establish realistic expectations and appreciate the particular challenges of simulation in a healthcare environment

Dynamic Data Driven Methods for Self-aware Aerospace Vehicles

A self-aware aerospace vehicle can dynamically adapt the way it performs missions by gathering information about itself and its surroundings and responding intelligently. Achieving this DDDAS paradigm enables a revolutionary new generation of self-aware aerospace vehicles that can perform missions that are impossible using current design, flight, and mission planning paradigms. To make self-aware aerospace vehicles a reality, fundamentally new algorithms are needed that drive decision-making through dynamic response to uncertain data, while incorporating information from multiple modeling sources and multiple sensor fidelities.In this work, the specific challenge of a vehicle that can dynamically and autonomously sense, plan, and act is considered. The challenge is to achieve each of these tasks in real time executing online models and exploiting dynamic data streams–while also accounting for uncertainty. We employ a multifidelity approach to inference, prediction and planning an approach that incorporates information from multiple modeling sources, multiple sensor data sources, and multiple fidelities

Synthesis and characterization of [Fe(BPMEN)-ACC]SbF 6 : a structural and functional mimic of ACC-oxidase †

International audienceA mononuclear Fe(II) complex bearing 1-aminocyclopropane-1-carboxylic acid (ACCH) was synthesized and characterized. X-ray crystallography demonstrated that ACC binds to the Fe(II) ion in a bidentate mode constituting the first structural mimic of the expected binding of ACC to the Fe(II) center of the ethylene forming enzyme ACC-oxidase (ACCO). [Fe(BPMEN)ACC]SbF 6 also constitutes a functional biomimetic complex of ACCO, as it reacts with hydrogen peroxide producing ethylene

Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems

We explore using neural operators, or neural network representations of nonlinear maps between function spaces, to accelerate infinite-dimensional Bayesian inverse problems (BIPs) with models governed by nonlinear parametric partial differential equations (PDEs). Neural operators have gained significant attention in recent years for their ability to approximate the parameter-to-solution maps defined by PDEs using as training data solutions of PDEs at a limited number of parameter samples. The computational cost of BIPs can be drastically reduced if the large number of PDE solves required for posterior characterization are replaced with evaluations of trained neural operators. However, reducing error in the resulting BIP solutions via reducing the approximation error of the neural operators in training can be challenging and unreliable. We provide an a priori error bound result that implies certain BIPs can be ill-conditioned to the approximation error of neural operators, thus leading to inaccessible accuracy requirements in training. To reliably deploy neural operators in BIPs, we consider a strategy for enhancing the performance of neural operators, which is to correct the prediction of a trained neural operator by solving a linear variational problem based on the PDE residual. We show that a trained neural operator with error correction can achieve a quadratic reduction of its approximation error, all while retaining substantial computational speedups of posterior sampling when models are governed by highly nonlinear PDEs. The strategy is applied to two numerical examples of BIPs based on a nonlinear reaction--diffusion problem and deformation of hyperelastic materials. We demonstrate that posterior representations of the two BIPs produced using trained neural operators are greatly and consistently enhanced by error correction