Compressed sensing algorithms approximate functions using limited evaluations by searching for a sparse representation among a dictionary of basis functions. Orthogonal matching pursuit (OMP) is a ...greedy algorithm for selecting basis functions whose computational cost scales with the size of the dictionary. For polynomial chaos (PC) approximations, the size of the dictionary grows quickly with the number of model inputs and the maximum polynomial degree, making them often prohibitive to use with greedy methods. We propose two new algorithms for efficiently constructing sparse PC expansions for problems with high-dimensional inputs. The first algorithm is a parallel OMP method coupled with an incremental QR factorization scheme, wherein the model construction step is interleaved with a ν-fold cross-validation procedure. The second approach is a randomized greedy algorithm that leverages a probabilistic argument to only evaluate a subset of basis functions from the dictionary at each iteration of the incremental algorithm. The randomized algorithm is demonstrated to recover model outputs with a similar level of sparsity and accuracy as OMP, but with a cost that is independent of the dictionary size. Both algorithms are validated with a numerical comparison of their performance on a series of algebraic test problems and PDEs with high-dimensional inputs.
•We consider the problem of efficiently learning sparse polynomial chaos expansions.•A novel parallelization strategy is proposed.•A randomized greedy algorithm is developed to handle large-scale problems.•A detailed theoretical analysis is carried out to evaluate the proposed algorithms.
We provide theoretical analyses and numerical comparisons of boundary-based and volumetric shape derivative expressions of linear objective functionals encountered in topology optimization of linear ...elastic structures. The two expressions yield identical results if the domain is smooth and the governing equation is solved exactly; however, the finite element approximation of the expressions for less regular domains yield different results. We first review the two expressions to show that the volumetric shape derivative places weaker regularity requirements, which, unlike the requirements for boundary-based shape derivatives, are satisfied in most finite element approximations. We then analyze the error in the degree-k polynomial finite element approximations of the two expressions; we show that, for sufficiently regular problems, the boundary-based and volumetric shape derivatives provide kth and 2k-th order accurate approximations, respectively, of the true shape derivative. We finally assess, through numerical examples, the practical implications of using the volumetric vs boundary-based shape derivatives in topology optimization problems; we demonstrate that methods based on the volumetric shape derivative yield more robust solutions to topology optimization problems.
•Shape derivatives can be formulated as volumetric or boundary based integrals.•Volumetric shape derivatives require less regularity and converge faster for FEM.•Volumetric shape derivatives provide practical advantages for level set optimization.
AIREBO is one of the commonly utilized interatomic potential (IP) for performing molecular dynamics (MD) simulations of graphene and carbon nanostructures. With its parameters fitted to a limited ...dataset, property prediction outside of the original training set can be challenging and can lead to uncertainty in the predicted values. This is especially important for 2D materials such as graphene which have limited experimental data and have widely varying predicted properties in the literature. In this study, we conducted a comprehensive Uncertainty Quantification (UQ) analysis of AIREBO potential parameters and their corresponding effect on the predicted properties of graphene. We found that computed output properties were highly sensitive to small variations in IP parameters. For instance, a 0.5% change in IP parameters led to a 66% change in the predicted elastic constants. Based on our UQ analysis, we developed a new robust IP parameter set for the AIREBO potential with significantly reduced sensitivity towards output properties. The robust parameters were derived using a Markov Chain Monte Carlo scheme, considering gaussian noise in available DFT data. We were also able to obtain realistic error bars on MD predictions by using posterior probability distributions and propagating the underlying variance to the final properties.
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Abstract Interpatient variability is often overlooked in orthopaedic computational studies due to the substantial challenges involved in sourcing and generating large numbers of bone models. A ...statistical model of the whole femur incorporating both geometric and material property variation was developed as a potential solution to this problem. The statistical model was constructed using principal component analysis, applied to 21 individual computer tomography scans. To test the ability of the statistical model to generate realistic, unique, finite element (FE) femur models it was used as a source of 1000 femurs to drive a study on femoral neck fracture risk. The study simulated the impact of an oblique fall to the side, a scenario known to account for a large proportion of hip fractures in the elderly and have a lower fracture load than alternative loading approaches. FE model generation, application of subject specific loading and boundary conditions, FE processing and post processing of the solutions were completed automatically. The generated models were within the bounds of the training data used to create the statistical model with a high mesh quality, able to be used directly by the FE solver without remeshing. The results indicated that 28 of the 1000 femurs were at highest risk of fracture. Closer analysis revealed the percentage of cortical bone in the proximal femur to be a crucial differentiator between the failed and non-failed groups. The likely fracture location was indicated to be intertrochantic. Comparison to previous computational, clinical and experimental work revealed support for these findings.
We consider the problem of learning a multivariate function from a set of scattered observations using a sparse low-rank separated representation (SSR) model. The model structure considered here is ...promising for high-dimensional learning problems; however, existing training algorithms based on alternating least-squares (ALS) are known to have convergence difficulties, particularly when the rank of the model is greater than 1. In the present work, we supplement the model structure with sparsity constraints to ensure the well posedness of the approximation problem. We propose two fast training algorithms to estimate the model parameters: (i) a cyclic coordinate descent algorithm and (ii) a block coordinate descent (BCD) algorithm. While the first algorithm is not provably convergent owing to the non-convexity of the optimization problem, the BCD algorithm guarantees convergence to a Nash equilibrium point. The computational cost of the proposed algorithms is shown to scale linearly with respect to all of the parameters in contrast to methods based on ALS. Numerical studies on synthetic and real-world regression datasets indicate that the proposed SSR model structure holds significant potential for machine learning problems.
Abstract
We present a method to model interatomic interactions such as energy and forces in a computationally efficient way. The proposed model approximates the energy/forces using a linear ...combination of random features, thereby enabling fast parameter estimation by solving a linear least-squares problem. We discuss how random features based on stationary and non-stationary kernels can be used for energy approximation and provide results for three classes of materials, namely two-dimensional materials, metals and semiconductors. Force and energy predictions made using the proposed method are in close agreement with density functional theory calculations, with training time that is 96% lower than standard kernel models. Molecular Dynamics calculations using random features based interatomic potentials are shown to agree well with experimental and density functional theory values. Phonon frequencies as computed by random features based interatomic potentials are within 0.1% of the density functional theory results. Furthermore, the proposed random features-based potential addresses scalability issues encountered in this class of machine learning problems.
Abstract Femoral resurfacing has become an increasingly popular procedure, especially for young, active patients. The procedure is known to alter load transfer through the proximal femur and this has ...been linked with the most commonly observed complication, neck fracture. An intriguing observation noted by registry data and clinical studies is an inverse relationship between implant size and revision rate. While computational analysis has become an established part of biomedical engineering, the majority of work uses a single or small set of bone models, with a single implant size, due to the constraints of time and data availability. Therefore, it has been infeasible to run a study incorporating natural inter-patient variability or the performance of smaller implants could not be meaningfully studied. In previous work a statistical model of the whole femur was used to generate large numbers of unique, realistic, FE-ready femur models describing both geometry and material properties. The current study demonstrates a methodology for virtually implanting and performing stress analysis of cemented femoral resurfacing components, with model specific sizing and orientation. Automated analysis of 400 generated femurs, in both implanted and intact configurations showed the strain changes induced by resurfacing. This produced a statistically meaningful number of results and allowed the examination of outliers. Results showed increased femoral neck strain changes potentially increasing the risk of neck fracture, associated with smaller, less dense femurs and smaller implant sizes; agreeing with clinical observations. The study demonstrates a methodology for more comprehensive analyses, based on populations rather than individuals.
Aim
The effect of anacardic acid impregnation on catheter surfaces for the prevention of Staphylococcus aureus attachments and biofilm formations were evaluated.
Methods and Results
Silicon catheter ...tubes were impregnated using different concentrations of anacardic acids (0·002–0·25%). Anacardic acids are antibacterial phenolic lipids from cashew nut (Anacardium occidentale) shell oil. Anacardic acid‐impregnated silicon catheters revealed no significant haemolytic activity and were cytocompatible against fibroblast cell line (L929). Sustained release of anacardic acids was observed for 4 days. Anacardic acid‐impregnated silicon catheters efficiently inhibited S. aureus colonization and the biofilm formation on its surface. The in vivo antibiofilm activity of anacardic acid‐impregnated catheters was tested in an intraperitoneal catheter‐associated medaka fish infection model. Significant reduction in S. aureus colonization on anacardic acid‐impregnated catheter tubes was observed.
Conclusions
Our data suggest that anacardic acid‐impregnated silicon catheters may help in preventing catheter‐related staphylococcal infections.
Significance and Impact of the Study
This study opens new directions for designing antimicrobial phytochemical‐coated surfaces with ideal antibiofilm properties and could be of great interest for biomedical research scientists.
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