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Computational Engineering, Finance, and Science

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Papers in this area

24 featured work(s)

preprint2019arXiv

Reconstruction of Hydraulic Data by Machine Learning

Numerical simulation models associated with hydraulic engineering take a wide array of data into account to produce predictions: rainfall contribution to the drainage basin (characterized by soil nature, infiltration capacity and moisture), current water height in the river, topography, nature and geometry of the river bed, etc. This data is tainted with uncertainties related to an imperfect knowledge of the field, measurement errors on the physical parameters calibrating the equations of physics, an approximation of the latter, etc. These uncertainties can lead the model to overestimate or underestimate the flow and height of the river. Moreover, complex assimilation models often require numerous evaluations of physical solvers to evaluate these uncertainties, limiting their use for some real-time operational applications. In this study, we explore the possibility of building a predictor for river height at an observation point based on drainage basin time series data. An array of data-driven techniques is assessed for this task, including statistical models, machine learning techniques and deep neural network approaches. These are assessed on several metrics, offering an overview of the possibilities related to hydraulic time-series. An important finding is that for the same hydraulic quantity, the best predictors vary depending on whether the data is produced using a physical model or real observations.

preprint2019arXiv

A numerical scheme for the quantile hedging problem

We consider the numerical approximation of the quantile hedging price in a non-linear market. In a Markovian framework, we propose a numerical method based on a Piecewise Constant Policy Timestepping (PCPT) scheme coupled with a monotone finite difference approximation. We prove the convergence of our algorithm combining BSDE arguments with the Barles & Jakobsen and Barles & Souganidis approaches for non-linear equations. In a numerical section, we illustrate the efficiency of our scheme by considering a financial example in a market with imperfections.

preprint2018arXiv

Development of a Computationally Efficient Fabric Model for Optimization of Gripper Trajectories in Automated Composite Draping

An automated prepreg fabric draping system is being developed which consists of an array of actuated grippers. It has the ability to pick up a fabric ply and place it onto a double-curved mold surface. A previous research effort based on a nonlinear Finite Element model showed that the movements of the grippers should be chosen carefully to avoid misplacement and induce of wrinkles in the draped configuration. Thus, the present study seeks to develop a computationally efficient model of the mechanical behavior of a fabric based on 2D catenaries which can be used for optimization of the gripper trajectories. The model includes bending stiffness, large deflections, large ply shear and a simple contact formulation. The model is found to be quick to evaluate and gives very reasonable predictions of the displacement field.

preprint2020arXiv

Fractional-Order Models for the Static and Dynamic Analysis of Nonlocal Plates

This study presents the analytical formulation and the finite element solution of fractional order nonlocal plates under both Mindlin and Kirchoff formulations. By employing consistent definitions for fractional-order kinematic relations, the governing equations and the associated boundary conditions are derived based on variational principles. Remarkably, the fractional-order nonlocal model gives rise to a self-adjoint and positive-definite system that accepts a unique solution. Further, owing to the difficulty in obtaining analytical solutions to this fractional-order differ-integral problem, a 2D finite element model for the fractional-order governing equations is presented. Following a thorough validation with benchmark problems, the 2D fractional finite element model is used to study the static as well as the free dynamic response of fractional-order plates subject to various loading and boundary conditions. It is established that the fractional-order nonlocality leads to a reduction in the stiffness of the plate structure thereby increasing the displacements and reducing the natural frequency of vibration of the plates. Further, it is seen that the effect of nonlocality is stronger on the higher modes of vibration when compared to the fundamental mode. These effects of the fractional-order nonlocality are noted irrespective of the nature of the boundary conditions. More specifically, the fractional-order model of nonlocal plates is free from boundary effects that lead to paradoxical predictions such as hardening and absence of nonlocal effects in classical integral approaches to nonlocal elasticity. This consistency in the predictions is a result of the well-posed nature of the fractional-order governing equations that accept a unique solution.

preprint2020arXiv

Rapid multi-component phase-split calculations using volume functions and reduction methods

We present a new family of fast and robust methods for the calculation of the vapor-liquid equilibrium at isobaric-isothermal (PT-flash), isochoric-isothermal (VT-flash), isenthalpic-isobaric (HP-flash), and isoenergetic-isochoric (UV-flash) conditions. The framework is provided by formulating phase-equilibrium conditions for multi-component mixtures in an effectively reduced space based on the molar specific value of the recently introduced volume function derived from the Helmholtz free energy. The proposed algorithmic implementation can fully exploit the optimum quadratic convergence of a Newton method with the analytical Jacobian matrix. This paper provides all required exact analytic expressions for the general cubic equation of state. Computational results demonstrate the effectivity and efficiency of the new methods. Compared to conventional methods, the proposed reduced-space iteration leads to a considerable speed-up as well as to improved robustness and better convergence behavior near the spinodal and coexistence curves of multi-component mixtures, where the preconditioning by the reduction method is most effective.

preprint2020arXiv

Topology optimization of 2D structures with nonlinearities using deep learning

The field of optimal design of linear elastic structures has seen many exciting successes that resulted in new architected materials and structural designs. With the availability of cloud computing, including high-performance computing, machine learning, and simulation, searching for optimal nonlinear structures is now within reach. In this study, we develop convolutional neural network models to predict optimized designs for a given set of boundary conditions, loads, and optimization constraints. We have considered the case of materials with a linear elastic response with and without stress constraint. Also, we have considered the case of materials with a hyperelastic response, where material and geometric nonlinearities are involved. For the nonlinear elastic case, the neo-Hookean model is utilized. For this purpose, we generate datasets composed of the optimized designs paired with the corresponding boundary conditions, loads, and constraints, using a topology optimization framework to train and validate the neural network models. The developed models are capable of accurately predicting the optimized designs without requiring an iterative scheme and with negligible inference computational time. The suggested pipeline can be generalized to other nonlinear mechanics scenarios and design domains.

preprint2020arXiv

A Hybrid Lagrangian/Eulerian Collocated Advection and Projection Method for Fluid Simulation

We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. We interchangeably use particle and grid representations of transported quantities to balance efficiency and accuracy. A novel Backward Semi-Lagrangian method is derived to improve accuracy of grid based advection. Our approach utilizes the implicit formula associated with solutions of Burgers' equation. We solve this equation using Newton's method enabled by $C^1$ continuous grid interpolation. We enforce incompressibility over collocated, rather than staggered grids. Our projection technique is variational and designed for B-spline interpolation over regular grids where multiquadratic interpolation is used for velocity and multilinear interpolation for pressure. Despite our use of regular grids, we extend the variational technique to allow for cut-cell definition of irregular flow domains for both Dirichlet and free surface boundary conditions.

preprint2020arXiv

Data-driven optimization of building layouts for energy efficiency

One of the primary driving factors in building energy performance is occupant behavioral dynamics. As a result, the layout of building occupant workstations is likely to influence energy consumption. In this paper, we introduce methods for relating lighting zone energy to zone-level occupant dynamics, simulating energy consumption of a lighting system based on this relationship, and optimizing the layout of buildings through the use of both a clustering-based approach and a genetic algorithm in order to reduce energy consumption. We find in a case study that nonhomogeneous behavior (i.e., high diversity) among occupant schedules positively correlates with the energy consumption of a highly controllable lighting system. We additionally find through data-driven simulation that the naïve clustering-based optimization and the genetic algorithm (which makes use of the energy simulation engine) produce layouts that reduce energy consumption by roughly 5% compared to the existing layout of a real office space comprised of 165 occupants. Overall, this study demonstrates the merits of utilizing low-cost dynamic design of existing building layouts as a means to reduce energy usage. Our work provides an additional path to reach our sustainable energy goals in the built environment through new non-capital-intensive interventions.

preprint2020arXiv

Processing of Crowdsourced Observations of Aircraft in a High Performance Computing Environment

As unmanned aircraft systems (UASs) continue to integrate into the U.S. National Airspace System (NAS), there is a need to quantify the risk of airborne collisions between unmanned and manned aircraft to support regulation and standards development. Both regulators and standards developing organizations have made extensive use of Monte Carlo collision risk analysis simulations using probabilistic models of aircraft flight. We've previously determined that the observations of manned aircraft by the OpenSky Network, a community network of ground-based sensors, are appropriate to develop models of the low altitude environment. This works overviews the high performance computing workflow designed and deployed on the Lincoln Laboratory Supercomputing Center to process 3.9 billion observations of aircraft. We then trained the aircraft models using more than 250,000 flight hours at 5,000 feet above ground level or below. A key feature of the workflow is that all the aircraft observations and supporting datasets are available as open source technologies or been released to the public domain.

preprint2020arXiv

VoxCap: FFT-Accelerated and Tucker-Enhanced Capacitance Extraction Simulator for Voxelized Structures

VoxCap, a fast Fourier transform (FFT)-accelerated and Tucker-enhanced integral equation simulator for capacitance extraction of voxelized structures, is proposed. The VoxCap solves the surface integral equations (SIEs) for conductor and dielectric surfaces with three key attributes that make the VoxCap highly CPU and memory efficient for the capacitance extraction of the voxelized structures: (i) VoxCap exploits the FFTs for accelerating the matrix-vector multiplications during the iterative solution of linear system of equations arising due to the discretization of SIEs. (ii) During the iterative solution, VoxCap uses a highly effective and memory-efficient preconditioner that reduces the number of iterations significantly. (iii) VoxCap employs Tucker decompositions to compress the block Toeplitz and circulant tensors, requiring the largest memory in the simulator. By doing so, it reduces the memory requirement of these tensors from hundreds of gigabytes to a few megabytes and the CPU time required to obtain Toeplitz tensors from tens of minutes (even hours) to a few seconds for very large scale problems. VoxCap is capable of accurately computing capacitance of arbitrarily shaped and large-scale voxelized structures on a desktop computer.

preprint2020arXiv

SEMDOT: Smooth-Edged Material Distribution for Optimizing Topology Algorithm

Element-based topology optimization algorithms capable of generating smooth boundaries have drawn serious attention given the significance of accurate boundary information in engineering applications. The basic framework of a new element-based continuum algorithm is proposed in this paper. This algorithm is based on a smooth-edged material distribution strategy that uses solid/void grid points assigned to each element. Named Smooth-Edged Material Distribution for Optimizing Topology (SEMDOT), the algorithm uses elemental volume fractions which depend on the densities of grid points in the Finite Element Analysis (FEA) model rather than elemental densities. Several numerical examples are studied to demonstrate the application and effectiveness of SEMDOT. In these examples, SEMDOT proved to be capable of obtaining optimized topologies with smooth and clear boundaries showing better or comparable performance compared to other topology optimization methods. Through these examples, first, the advantages of using the Heaviside smooth function are discussed in comparison to the Heaviside step function. Then, the benefits of introducing multiple filtering steps in this algorithm are shown. Finally, comparisons are conducted to exhibit the differences between SEMDOT and some well-established element-based algorithms. The validation of the sensitivity analysis method adopted in SEMDOT is conducted using a typical compliant mechanism design case. In addition, this paper provides the Matlab code of SEMDOT for educational and academic purposes.

preprint2020arXiv

GPU acceleration of CaNS for massively-parallel direct numerical simulations of canonical fluid flows

This work presents the GPU acceleration of the open-source code CaNS for very fast massively-parallel simulations of canonical fluid flows. The distinct feature of the many-CPU Navier-Stokes solver in CaNS is its fast direct solver for the second-order finite-difference Poisson equation, based on the method of eigenfunction expansions. The solver implements all the boundary conditions valid for this type of problems in a unified framework. Here, we extend the solver for GPU-accelerated clusters using CUDA Fortran. The porting makes extensive use of CUF kernels and has been greatly simplified by the unified memory feature of CUDA Fortran, which handles the data migration between host (CPU) and device (GPU) without defining new arrays in the source code. The overall implementation has been validated against benchmark data for turbulent channel flow and its performance assessed on a NVIDIA DGX-2 system (16 Tesla V100 32Gb, connected with NVLink via NVSwitch). The wall-clock time per time step of the GPU-accelerated implementation is impressively small when compared to its CPU implementation on state-of-the-art many-CPU clusters, as long as the domain partitioning is sufficiently small that the data resides mostly on the GPUs. The implementation has been made freely available and open-source under the terms of an MIT license.

preprint2020arXiv

Towards Accuracy and Scalability: Combining Isogeometric Analysis with Deflation to Obtain Scalable Convergence for the Helmholtz Equation

Finding fast yet accurate numerical solutions to the Helmholtz equation remains a challenging task. The pollution error (i.e. the discrepancy between the numerical and analytical wave number k) requires the mesh resolution to be kept fine enough to obtain accurate solutions. A recent study showed that the use of Isogeometric Analysis (IgA) for the spatial discretization significantly reduces the pollution error. However, solving the resulting linear systems by means of a direct solver remains computationally expensive when large wave numbers or multiple dimensions are considered. An alternative lies in the use of (preconditioned) Krylov subspace methods. Recently, the use of the exact Complex Shifted Laplacian Preconditioner (CSLP) with a small complex shift has shown to lead to wave number independent convergence while obtaining more accurate numerical solutions using IgA. In this paper, we propose the use of deflation techniques combined with an approximated inverse of the CSLP using a geometric multigrid method. Numerical results obtained for both one- and two-dimensional model problems, including constant and non-constant wave numbers, show scalable convergence with respect to the wave number and approximation order p of the spatial discretization. Furthermore, when kh is kept constant, the proposed approach leads to a significant reduction of the computational time compared to the use of the exact inverse of the CSLP with a small shift.

preprint2020arXiv

Accelerating computational modeling and design of high-entropy alloys

With huge design spaces for unique chemical and mechanical properties, we remove a roadblock to computational design of {high-entropy alloys} using a metaheuristic hybrid Cuckoo Search (CS) for "on-the-fly" construction of Super-Cell Random APproximates (SCRAPs) having targeted atomic site and pair probabilities on arbitrary crystal lattices. Our hybrid-CS schema overcomes large, discrete combinatorial optimization by ultrafast global solutions that scale linearly in system size and strongly in parallel, e.g. a 4-element, 128-atom model [a $10^{73+}$ space] is found in seconds -- a reduction of 13,000+ over current strategies. With model-generation eliminated as a bottleneck, computational alloy design can be performed that is currently impossible or impractical. We showcase the method for real alloys with varying short-range order. Being problem-agnostic, our hybrid-CS schema offers numerous applications in diverse fields.

preprint2020arXiv

Falling balls in a viscous fluid with contact: Comparing numerical simulations with experimental data

We evaluate a number of different finite element approaches for fluid-structure (contact) interaction problems against data from physical experiments. For this we take the data from experiments by Hagemeier [Mendeley Data, doi: 10.17632/mf27c92nc3.1]. This consists of trajectories of single particles falling through a highly viscous fluid and rebounding off the bottom fluid tank wall. The resulting flow is in the transitional regime between creeping and turbulent flows. This type of configuration is particularly challenging for numerical methods due to the large change of the fluid domain and the contact between the wall and particle. In the numerical simulations we consider both rigid body and linear elasticity models for the falling particles. In the first case, we compare results obtained with the well established Arbitrary Lagrangian Eulerian (ALE) approach and a moving domain CutFEM method together with a simple and common approach for contact avoidance. For the full fluid-structure interaction (FSI) problem with contact, we use a fully Eulerian approach in combination with a unified FSI-contact treatment using Nitsche's method. For higher computational efficiency we use the geometrical symmetry of the experimental set up to reformulate the FSI system into two spatial dimensions. Finally, we show full three dimensional ALE computations to study the effects of small perturbations in the initial state of the particle to investigate deviations from a perfectly vertical fall observed in the experiment. The methods are implemented in open-source finite element libraries and the results are made freely available to aide reproducibility.

preprint2020arXiv

Identifying and tracking bubbles and drops in simulations: a toolbox for obtaining sizes, lineages, and breakup and coalescence statistics

Knowledge of bubble and drop size distributions in two-phase flows is important for characterizing a wide range of phenomena, including combustor ignition, sonar communication, and cloud formation. The physical mechanisms driving the background flow also drive the time evolution of these distributions. Accurate and robust identification and tracking algorithms for the dispersed phase are necessary to reliably measure this evolution and thereby quantify the underlying mechanisms in interface-resolving flow simulations. The identification of individual bubbles and drops traditionally relies on an algorithm used to identify connected regions. This traditional algorithm can be sensitive to the presence of spurious structures. A cost-effective refinement is proposed to maximize volume accuracy while minimizing the identification of spurious bubbles and drops. An accurate identification scheme is crucial for distinguishing bubble and drop pairs with large size ratios. The identified bubbles and drops need to be tracked in time to obtain breakup and coalescence statistics that characterize the evolution of the size distribution, including breakup and coalescence frequencies, and the probability distributions of parent and child bubble and drop sizes. An algorithm based on mass conservation is proposed to construct bubble and drop lineages using simulation snapshots that are not necessarily from consecutive time-steps. These lineages are then used to detect breakup and coalescence events, and obtain the desired statistics. Accurate identification of large-size-ratio bubble and drop pairs enables accurate detection of breakup and coalescence events over a large size range. Together, these algorithms enable insights into the mechanisms behind bubble and drop formation and evolution in flows of practical importance.

preprint2020arXiv

Inverse problems for semiconductors: models and methods

We consider the problem of identifying discontinuous doping profiles in semiconductor devices from data obtained by different models connected to the voltage-current map. Stationary as well as transient settings are discussed and a framework for the corresponding inverse problems is established. Numerical implementations for the so-called stationary unipolar and stationary bipolar cases show the effectiveness of a level set approach to tackle the inverse problem.

preprint2020arXiv

Concurrent consideration of cortical and cancellous bone within continuum bone remodelling

Continuum bone remodelling is an important tool for predicting the effects of mechanical stimuli on bone density evolution. While the modelling of only cancellous bone is considered in many studies based on continuum bone remodelling, this work presents an approach of modelling also cortical bone and the interaction of both bone types. The distinction between bone types is made by introducing an initial volume fraction. A simple point-wise example is used to study the behaviour of novel model options, as well as a proximal femur example, where the interaction of both bone types is demonstrated using initial density distributions. The results of the proposed model options indicate that the consideration of cortical bone remarkably changes the density evolution of cancellous bone, and should therefore not be neglected.

preprint2020arXiv

Construction of Minimum Spanning Trees from Financial Returns using Rank Correlation

The construction of minimum spanning trees (MSTs) from correlation matrices is an often used method to study relationships in the financial markets. However most of the work on this topic tends to use the Pearson correlation coefficient, which relies on the assumption of normality and can be brittle to the presence of outliers, neither of which is ideal for the study of financial returns. In this paper we study the inference of MSTs from daily US, UK and German financial returns using Pearson and two rank correlation methods, Spearman and Kendall's $τ$. MSTs constructed using these rank methods tend to be more stable and maintain more edges over the dataset than those constructed using Pearson correlation. The edge agreement between the Pearson and rank MSTs varies significantly depending on the state of the markets, but the rank MSTs generally show strong agreement at all times. Deviation from univariate normality can be related to changes in the correlation matrices but is more difficult to connect to changes in the MSTs. Irrelevant of coefficient, the trees tend to have similar topologies. Portfolios constructed from the MST correlation matrices have a smaller turnover than those from the full covariance matrix for the larger markets, but not for the smaller German market. Using a bootstrap method we find that the correlation matrices constructed using the rank correlations are more robust, but there is little difference between the robustness of the MSTs.

preprint2020arXiv

A convolutional neural-network model of human cochlear mechanics and filter tuning for real-time applications

Auditory models are commonly used as feature extractors for automatic speech-recognition systems or as front-ends for robotics, machine-hearing and hearing-aid applications. Although auditory models can capture the biophysical and nonlinear properties of human hearing in great detail, these biophysical models are computationally expensive and cannot be used in real-time applications. We present a hybrid approach where convolutional neural networks are combined with computational neuroscience to yield a real-time end-to-end model for human cochlear mechanics, including level-dependent filter tuning (CoNNear). The CoNNear model was trained on acoustic speech material and its performance and applicability were evaluated using (unseen) sound stimuli commonly employed in cochlear mechanics research. The CoNNear model accurately simulates human cochlear frequency selectivity and its dependence on sound intensity, an essential quality for robust speech intelligibility at negative speech-to-background-noise ratios. The CoNNear architecture is based on parallel and differentiable computations and has the power to achieve real-time human performance. These unique CoNNear features will enable the next generation of human-like machine-hearing applications.

preprint2020arXiv

A finite element model updating method based on global optimization

Finite element model updating of a structure made of linear elastic materials is based on the solution of a minimization problem. The goal is to find some unknown parameters of the finite element model (elastic moduli, mass densities, constraints and boundary conditions) that minimize an objective function which evaluates the discrepancy between experimental and numerical dynamic properties. The objective function depends nonlinearly on the parameters and may have multiple local minimum points. This paper presents a numerical method able to find a global minimum point and assess its reliability. The numerical method has been tested on two simulated examples - a masonry tower and a domed temple - and validated via a generic genetic algorithm and a global sensitivity analysis tool. A real case study monitored under operational conditions has also been addressed, and the structure's experimental modal properties have been used in the model updating procedure to estimate the mechanical properties of its constituent materials.

preprint2020arXiv

Quantifying the predictability of visual scanpaths using active information storage

Entropy-based measures are an important tool for studying human gaze behavior under various conditions. In particular, gaze transition entropy (GTE) is a popular method to quantify the predictability of fixation transitions. However, GTE does not account for temporal dependencies beyond two consecutive fixations and may thus underestimate a scanpath's actual predictability. Instead, we propose to quantify scanpath predictability by estimating the active information storage (AIS), which can account for dependencies spanning multiple fixations. AIS is calculated as the mutual information between a processes' multivariate past state and its next value. It is thus able to measure how much information a sequence of past fixations provides about the next fixation, hence covering a longer temporal horizon. Applying the proposed approach, we were able to distinguish between induced observer states based on estimated AIS, providing first evidence that AIS may be used in the inference of user states to improve human-machine interaction.

preprint2020arXiv

A second-order self-adjusting steepness based remapping method for arbitrary quadrilateral meshes

In this paper, based on the idea of self-adjusting steepness based schemes[5], a two-dimensional calculation method of steepness parameter is proposed, and thus a two-dimensional self-adjusting steepness based limiter is constructed. With the application of such limiter to the over-intersection based remapping framework, a low dissipation remapping method has been proposed that can be applied to the existing ALE method.

preprint2020arXiv

Robust 3D reconstruction of dynamic scenes from single-photon lidar using Beta-divergences

In this paper, we present a new algorithm for fast, online 3D reconstruction of dynamic scenes using times of arrival of photons recorded by single-photon detector arrays. One of the main challenges in 3D imaging using single-photon lidar in practical applications is the presence of strong ambient illumination which corrupts the data and can jeopardize the detection of peaks/surface in the signals. This background noise not only complicates the observation model classically used for 3D reconstruction but also the estimation procedure which requires iterative methods. In this work, we consider a new similarity measure for robust depth estimation, which allows us to use a simple observation model and a non-iterative estimation procedure while being robust to mis-specification of the background illumination model. This choice leads to a computationally attractive depth estimation procedure without significant degradation of the reconstruction performance. This new depth estimation procedure is coupled with a spatio-temporal model to capture the natural correlation between neighboring pixels and successive frames for dynamic scene analysis. The resulting online inference process is scalable and well suited for parallel implementation. The benefits of the proposed method are demonstrated through a series of experiments conducted with simulated and real single-photon lidar videos, allowing the analysis of dynamic scenes at 325 m observed under extreme ambient illumination conditions.

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