Article
Business, Finance
Omid M. Ardakani
Summary: This study introduces a multivariate entropic Value at Risk (mEVaR) risk measure, expanding the traditional Value at Risk approach to a multi-asset scenario. The mEVaR is coherent and captures the integrated risk of various assets in a portfolio. Moreover, a new theoretical result incorporates mutual information into the mEVaR to capture tail dependence during extreme market events. The findings suggest that greater mutual dependence among assets increases risk and reduces the benefits of diversification. Examples, simulations, and empirical studies demonstrate the applicability of these risk measures for managing and optimizing investment portfolios.
FINANCE RESEARCH LETTERS
(2023)
Article
Mathematics, Applied
Sebastian Garreis, Thomas M. Surowiec, Michael Ulbrich
Summary: In the presence of uncertainty in engineering and natural science models, the incorporation of random parameters in partial differential equations is necessary. This leads to infinite-dimensional stochastic optimization problems, which often require the use of risk measures in the objective function. The proposed log-barrier risk measure method offers a novel approach to solving risk-averse PDE-constrained optimization problems.
SIAM JOURNAL ON OPTIMIZATION
(2021)
Article
Mathematics, Applied
Saskia Dietze, Martin A. Grepl
Summary: Model Predictive Control (MPC) is a well-established approach for solving infinite horizon optimal control problems, but its application to large-scale systems is computationally expensive. In this study, the reduced basis method is employed as a low-dimensional surrogate model for the finite time optimal control problem, allowing for efficient offline-online computation. The proposed RB-MPC approach guarantees asymptotic stability of the closed-loop system and offers an adaptive strategy for choosing the prediction horizon. Numerical results illustrate the theoretical properties of the approach.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Automation & Control Systems
Zhen Huang, Nabarun Deb, Bodhisattva Sen
Summary: We propose a simple and interpretable method called kernel partial correlation coefficient to measure the conditional dependence between two random variables given a third variable. We describe two consistent methods for estimating this coefficient and use it to develop a model-free variable selection algorithm. Extensive simulation and real-data examples demonstrate the superior performance of our methods compared to existing procedures.
JOURNAL OF MACHINE LEARNING RESEARCH
(2022)
Article
Mathematics, Applied
Michael Hinze, Denis Korolev
Summary: This paper proposes a certified reduced basis method for quasilinear parabolic problems with strongly monotone spatial differential operator. A residual-based a posteriori error estimate and efficiently computable bound are provided for the space-time formulation. The approach combines a POD-Greedy approximation with a space-time Galerkin method, allowing for the construction of reduced-basis spaces and application of the Empirical Interpolation Method for efficient offline-online computational procedure.
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2021)
Article
Agronomy
Achim Grelle, Hannes Keck
Summary: The relaxed eddy accumulation (REA) technique is used for measuring fluxes of atmospheric tracers above ecosystems, particularly when eddy covariance (EC) technique is limited. The REA system developed here is capable of simultaneously measuring CO2, CH4, N2O, and H2O fluxes with only one gas analyser, making it versatile and robust for field campaigns. The REA system has been tested in Nordic climate and showed promising results in capturing fluxes of various gases.
AGRICULTURAL AND FOREST METEOROLOGY
(2021)
Article
Mathematics, Applied
G. M. M. Reddy, P. Nanda, M. Vynnycky, J. A. Cuminato
Summary: This article introduces a novel computational technique for efficiently solving the inverse boundary identification problem with uncertain data in two dimensions. The method relies on a posteriori error indicators using Tikhonov regularized solutions obtained by the method of fundamental solutions (MFS) and given data. An adaptive stochastic optimization strategy is used for stable solutions, avoiding unstable regions.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Jehanzeb H. Chaudhry, Donald Estep, Simon J. Tavener
Summary: In this paper, a space-time parallel method for solving parabolic partial differential equations is proposed, which combines the parareal algorithm with overlapping domain decomposition. The goal is to obtain a parallel discretization that can be efficiently solved on parallel computers. However, this introduces significant sources of error that need to be evaluated. By reformulating the original parareal algorithm as a variational method and implementing a finite element discretization in space, an adjoint-based a posteriori error analysis can be performed to distinguish between errors arising from temporal and spatial discretizations, as well as incomplete parareal iterations and incomplete iterations of the domain decomposition solver.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Engineering, Mechanical
Sangjin Ryu, Ethan Davis, Jae Sung Park, Haipeng Zhang, Jung Yul Yoo
Summary: This study investigates turbulent coherent structures in a boundary layer flow by measuring wall shear stress fluctuations and analyzing their relationships with streamwise velocity fluctuations. The results suggest that events detected simultaneously by two probes indicate stronger fluctuations in streamwise velocity, indicating the presence of stronger coherent structures.Additionally, different detection methods reveal correlations between wall shear stress fluctuations and coherent structures, which may inform flow control strategies in exploiting these relationships.
JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME
(2021)
Article
Engineering, Mechanical
Shuai Huang, Wenwen Jin, Bo Wu, Xin Zhang, Aman Elmi, Youmin Hu
Summary: In this study, a robust ensemble of metamodels (EMs) is proposed by combining three regression stand-alone metamodels in a weighted sum form, with the weight factor adaptively determined according to a hybrid error metric. Three typical individual metamodels that can filter noise are selected to construct the EMs, extending their application in practical engineering problems. Results show that the proposed EMs have higher accuracy and robustness than individual metamodels and other typical EMs in major cases.
FRONTIERS OF MECHANICAL ENGINEERING
(2021)
Article
Automation & Control Systems
Masako Kishida, Ahmet Cetinkaya
Summary: This paper considers stochastic linear quadratic control problems from the viewpoint of risks. The study focuses on three problems: finding the optimal feedback gain that minimizes the risk of the quadratic cost, solving the one-step problem, and addressing the infinite time horizon problem. The presented theorems are illustrated with numerical examples.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Operations Research & Management Science
Tasuku Soma, Yuichi Yoshida
Summary: In this paper, we propose an online algorithm for maximizing the conditional value at risk (CVaR) of a monotone stochastic submodular function. The algorithm generates a sequence of solutions that converge to an approximate solution with a certain convergence rate. Compared to previous offline algorithms, the online algorithm requires less space.
ANNALS OF OPERATIONS RESEARCH
(2023)
Article
Computer Science, Artificial Intelligence
Anushri Dixit, Mohamadreza Ahmadi, Joel W. Burdick
Summary: This paper investigates the problem of risk-averse receding horizon motion planning for agents with uncertain dynamics in the presence of stochastic, dynamic obstacles. The proposed model predictive control (MPC) scheme formulates the obstacle avoidance constraint using coherent risk measures. A waypoint following algorithm using the MPC scheme is also proposed and proved to be risk-sensitive and recursively feasible while guaranteeing finite-time task completion. The paper further explores commonly used coherent risk metrics and proposes a tractable incorporation within MPC. Simulation studies are conducted to illustrate the framework.
ARTIFICIAL INTELLIGENCE
(2023)
Article
Mathematics, Applied
Jianwei Zhou, Huiyuan Li, Zhimin Zhang
Summary: In this paper, the authors investigate a posteriori error estimates of the Galerkin spectral methods for second-order equations. They propose a simple type of error estimator based on the expansion coefficients of known quantities such as the right-hand term. The authors show that the decay rate of the high frequency coefficients of the right-hand term serves as an ideal a posteriori error estimator. They also establish a posteriori error estimates on the Galerkin spectral method applied to the singular perturbation problem, where the efficiency is given by the approximation errors of the weighted L-2-projection of the right-hand function and the reliability is determined by the truncation errors of the right-hand function together with the low frequency coefficients.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Computer Science, Software Engineering
Jamie Fairbrother, Amanda Turner, Stein W. Wallace
Summary: Scenario generation is the process of constructing a discrete random vector to represent uncertain parameters in stochastic programming. Most methods are distribution-driven, but this paper proposes an analytic approach that is problem-driven and can better represent tail risk.
MATHEMATICAL PROGRAMMING
(2022)
Article
Automation & Control Systems
D. P. Kouri, T. M. Surowiec
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
(2020)
Article
Operations Research & Management Science
Drew P. Kouri, Thomas M. Surowiec
MATHEMATICS OF OPERATIONS RESEARCH
(2020)
Article
Computer Science, Software Engineering
Drew P. Kouri, Thomas M. Surowiec
Summary: The paper developed an algorithm to solve risk-averse optimization problems efficiently in reflexive Banach space, addressing the issue of nonsmoothness in objective functions resulting from popular risk models. By proposing a primal-dual algorithm inspired by classical methods and epigraphical regularization, the algorithm solves a sequence of smooth optimization problems using derivative-based methods, proving convergence even with inexact subproblem solutions and demonstrating efficiency through numerical examples.
MATHEMATICAL PROGRAMMING
(2022)
Article
Mathematics, Applied
Drew P. Kouri, Denis Ridzal, Ray Tuminaro
Summary: This paper investigates preconditioners for linear systems arising from optimal control and inverse problems involving the Helmholtz equation, focusing on two block preconditioners and extending prior convergence results to Helmholtz-based optimization applications. The analysis shows that solver convergence rates remain stable as the mesh is refined or the wavenumber increases, with accelerated convergence for one preconditioner as the wavenumber increases. In cases where control and observation subregions are disjoint, solver convergence rates show a weak dependence on the regularization parameter, and the performance of the preconditioners is illustrated on acoustic testing control problems.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Operations Research & Management Science
D. P. Kouri
Summary: The paper presents a matrix-free trust-region algorithm for solving convex-constrained optimization problems using the spectral projected gradient method. By reformulating and solving the dual projection problem as a one-dimensional root finding problem, the algorithm shows superior performance compared to existing methods. Additionally, it is simple to implement.
OPTIMIZATION LETTERS
(2022)
Article
Engineering, Multidisciplinary
Sean Hardesty, Harbir Antil, Drew P. Kouri, Denis Ridzal
Summary: A major challenge in shape optimization is efficiently computing shape derivatives in finite element method (FEM) codes. The volume and boundary methods are two approaches, each with its own drawback. We introduce the strip method, which computes shape derivatives on a strip adjacent to the boundary. The strip method is faster than the volume method and achieves higher accuracy than the boundary method.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2022)
Article
Mathematics, Applied
Tianyi Shi, Harbir Antil, Drew P. Kouri
Summary: This paper introduces a spectral method based on ultraspherical polynomial discretization to solve fractional PDEs and presents both serial and parallel domain decomposition solvers. The authors demonstrate the numerical performance of their method through experiments and apply it to optimization problems.
COMPUTATIONAL METHODS IN APPLIED MATHEMATICS
(2022)
Article
Engineering, Industrial
John D. Jakeman, Drew P. Kouri, J. Gabriel Huerta
Summary: This paper presents a surrogate modeling framework for conservatively estimating risk measures from limited experimental or simulation data. The framework allows for faster convergence to the true value and avoids over-confidence in reliability and safety assessments.
RELIABILITY ENGINEERING & SYSTEM SAFETY
(2022)
Article
Mathematics, Interdisciplinary Applications
Drew P. Kouri, John D. Jakeman, J. Gabriel Huerta
Summary: This paper introduces a new optimality criterion, R-optimality, which aims to minimize the risk associated with large prediction variances. The effectiveness of this criterion is demonstrated through numerical methods and various examples.
SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION
(2022)
Article
Computer Science, Software Engineering
Robert J. J. Baraldi, Drew P. P. Kouri
Summary: This study develops a novel trust-region method for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function. The method allows and controls the use of inexact objective function and derivative evaluations. It is demonstrated to be effective in data science and PDE-constrained optimization.
MATHEMATICAL PROGRAMMING
(2023)
Article
Mathematics, Applied
Harbir Antil, Drew P. Kouri, Denis Ridzal
Summary: ALESQP is a new algorithm for infinite-dimensional optimization with general constraints, which uses an augmented Lagrangian method to penalize inequality constraints and solve equality-constrained nonlinear optimization subproblems at every iteration. A key feature of ALESQP is a constraint decomposition strategy that allows it to exploit problem-specific variable scalings and inner products. We analyze convergence of ALESQP under different assumptions and show that strong accumulation points are stationary in finite dimensions while weak accumulation points are feasible in many practical situations in infinite dimensions. Several infinite-dimensional examples demonstrate the remarkable discretization-independent performance of ALESQP in all its iterative components, requiring a modest number of iterations to meet constraint tolerances at the level of machine precision. Additionally, we present a fully matrix-free solution of an infinite-dimensional problem with nonlinear inequality constraints.
SIAM JOURNAL ON OPTIMIZATION
(2023)
Article
Operations Research & Management Science
Drew P. P. Kouri, Mathias Staudigl, Thomas M. M. Surowiec
Summary: This paper investigates a class of convex risk-neutral PDE-constrained optimization problems with pointwise control and state constraints. Due to the challenges of pointwise state evaluations, the paper suggests a relaxation approach using a smooth functional bound with similar properties to probability constraints. The theoretical analysis is extended by implementing an online convex optimization algorithm in an infinite-dimensional setting, which includes periodic restarts for improved solution quality.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Ramchandran Muthukumar, Drew P. Kouri, Madeleine Udell
Summary: This paper proposes a novel limited-memory method to solve dynamic optimization problems, particularly suitable for problems with PDE constraints, by compressing the state to address the high memory requirements.
SIAM JOURNAL ON OPTIMIZATION
(2021)
Article
Automation & Control Systems
Harbir Antil, Drew P. Kouri, Johannes Pfefferer
Summary: This paper introduces and analyzes a new class of optimal control problems constrained by elliptic equations with uncertain fractional exponents. It formulates the optimization problem using risk measures, develops a functional analytic framework, studies the existence of solution, and rigorously derives the first-order optimality conditions. The study also employs sample-based approximation for uncertain exponents and finite element method for spatial discretization, proving the convergence rate for the optimal risk neutral controls using quadrature approximation for uncertain exponents, and concludes with illustrative examples.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2021)
Article
Mathematics, Interdisciplinary Applications
Matthew J. Zahr, Kevin T. Carlberg, Drew P. Kouri
SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION
(2019)
Article
Engineering, Multidisciplinary
Akshay J. Thomas, Mateusz Jaszczuk, Eduardo Barocio, Gourab Ghosh, Ilias Bilionis, R. Byron Pipes
Summary: We propose a physics-guided transfer learning approach to predict the thermal conductivity of additively manufactured short-fiber reinforced polymers using micro-structural characteristics obtained from tensile tests. A Bayesian framework is developed to transfer the thermal conductivity properties across different extrusion deposition additive manufacturing systems. The experimental results demonstrate the effectiveness and reliability of our method in accounting for epistemic and aleatory uncertainties.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Zhen Zhang, Zongren Zou, Ellen Kuhl, George Em Karniadakis
Summary: In this study, deep learning and artificial intelligence were used to discover a mathematical model for the progression of Alzheimer's disease. By analyzing longitudinal tau positron emission tomography data, a reaction-diffusion type partial differential equation for tau protein misfolding and spreading was discovered. The results showed different misfolding models for Alzheimer's and healthy control groups, indicating faster misfolding in Alzheimer's group. The study provides a foundation for early diagnosis and treatment of Alzheimer's disease and other misfolding-protein based neurodegenerative disorders using image-based technologies.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jonghyuk Baek, Jiun-Shyan Chen
Summary: This paper introduces an improved neural network-enhanced reproducing kernel particle method for modeling the localization of brittle fractures. By adding a neural network approximation to the background reproducing kernel approximation, the method allows for the automatic location and insertion of discontinuities in the function space, enhancing the modeling effectiveness. The proposed method uses an energy-based loss function for optimization and regularizes the approximation results through constraints on the spatial gradient of the parametric coordinates, ensuring convergence.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Bodhinanda Chandra, Ryota Hashimoto, Shinnosuke Matsumi, Ken Kamrin, Kenichi Soga
Summary: This paper proposes new and robust stabilization strategies for accurately modeling incompressible fluid flow problems in the material point method (MPM). The proposed approach adopts a monolithic displacement-pressure formulation and integrates two stabilization strategies to ensure stability. The effectiveness of the proposed method is validated through benchmark cases and real-world scenarios involving violent free-surface fluid motion.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Chao Peng, Alessandro Tasora, Dario Fusai, Dario Mangoni
Summary: This article discusses the importance of the tangent stiffness matrix of constraints in multibody systems and provides a general formulation based on quaternion parametrization. The article also presents the analytical expression of the tangent stiffness matrix derived through linearization. Examples demonstrate the positive effect of this additional stiffness term on static and eigenvalue analyses.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Thibaut Vadcard, Fabrice Thouverez, Alain Batailly
Summary: This contribution presents a methodology for detecting isolated branches of periodic solutions to nonlinear mechanical equations. The method combines harmonic balance method-based solving procedure with the Melnikov energy principle. It is able to predict the location of isolated branches of solutions near families of autonomous periodic solutions. The relevance and accuracy of this methodology are demonstrated through academic and industrial applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Weisheng Zhang, Yue Wang, Sung-Kie Youn, Xu Guo
Summary: This study proposes a sketch-guided topology optimization approach based on machine learning, which incorporates computer sketches as constraint functions to improve the efficiency of computer-aided structural design models and meet the design intention and requirements of designers.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Leilei Chen, Zhongwang Wang, Haojie Lian, Yujing Ma, Zhuxuan Meng, Pei Li, Chensen Ding, Stephane P. A. Bordas
Summary: This paper presents a model order reduction method for electromagnetic boundary element analysis and extends it to computer-aided design integrated shape optimization of multi-frequency electromagnetic scattering problems. The proposed method utilizes a series expansion technique and the second-order Arnoldi procedure to reduce the order of original systems. It also employs the isogeometric boundary element method to ensure geometric exactness and avoid re-meshing during shape optimization. The Grey Wolf Optimization-Artificial Neural Network is used as a surrogate model for shape optimization, with radar cross section as the objective function.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
C. Pilloton, P. N. Sun, X. Zhang, A. Colagrossi
Summary: This paper investigates the smoothed particle hydrodynamics (SPH) simulations of violent sloshing flows and discusses the impact of volume conservation errors on the simulation results. Different techniques are used to directly measure the particles' volumes and stabilization terms are introduced to control the errors. Experimental comparisons demonstrate the effectiveness of the numerical techniques.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Ye Lu, Weidong Zhu
Summary: This work presents a novel global digital image correlation (DIC) method based on a convolution finite element (C-FE) approximation. The C-FE based DIC provides highly smooth and accurate displacement and strain results with the same element size as the usual finite element (FE) based DIC. The proposed method's formulation and implementation, as well as the controlling parameters, have been discussed in detail. The C-FE method outperformed the FE method in all tested examples, demonstrating its potential for highly smooth, accurate, and robust DIC analysis.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Mojtaba Ghasemi, Mohsen Zare, Amir Zahedi, Pavel Trojovsky, Laith Abualigah, Eva Trojovska
Summary: This paper introduces Lung performance-based optimization (LPO), a novel algorithm that draws inspiration from the efficient oxygen exchange in the lungs. Through experiments and comparisons with contemporary algorithms, LPO demonstrates its effectiveness in solving complex optimization problems and shows potential for a wide range of applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jingyu Hu, Yang Liu, Huixin Huang, Shutian Liu
Summary: In this study, a new topology optimization method is proposed for structures with embedded components, considering the tension/compression asymmetric interface stress constraint. The method optimizes the topology of the host structure and the layout of embedded components simultaneously, and a new interpolation model is developed to determine interface layers between the host structure and embedded components.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Qiang Liu, Wei Zhu, Xiyu Jia, Feng Ma, Jun Wen, Yixiong Wu, Kuangqi Chen, Zhenhai Zhang, Shuang Wang
Summary: In this study, a multiscale and nonlinear turbulence characteristic extraction model using a graph neural network was designed. This model can directly compute turbulence data without resorting to simplified formulas. Experimental results demonstrate that the model has high computational performance in turbulence calculation.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jacinto Ulloa, Geert Degrande, Jose E. Andrade, Stijn Francois
Summary: This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. The proper generalized decomposition (PGD) is leveraged to decompose the displacements into multiple time scales, separating the spatial and intra-cyclic dependence from the inter-cyclic variation, thereby reducing computational burden.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Utkarsh Utkarsh, Valentin Churavy, Yingbo Ma, Tim Besard, Prakitr Srisuma, Tim Gymnich, Adam R. Gerlach, Alan Edelman, George Barbastathis, Richard D. Braatz, Christopher Rackauckas
Summary: This article presents a high-performance vendor-agnostic method for massively parallel solving of ordinary and stochastic differential equations on GPUs. The method integrates with a popular differential equation solver library and achieves state-of-the-art performance compared to hand-optimized kernels.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)