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Uncertainty Quantification for Geometry Deformations of Superconducting Cavities using Eigenvalue TrackingFeb 08 2018The electromagnetic field distribution as well as the resonating frequency of various modes in superconducting cavities are sensitive to small geometry deformations. The occurring variations are motivated by measurements of an available set of resonators ... More
A mixed finite element for weakly-symmetric elasticityFeb 08 2018We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for $r \geq 0$, discontinuous polynomials of $r$ for the displacement, $H(\mathrm{div})$-conforming ... More
Primal-dual stochastic gradient method for convex programs with many functional constraintsFeb 08 2018Stochastic gradient (SG) method has been popularly applied to solve optimization problems with objective that is stochastic or an average of many functions. Most existing works on SG assume that the underlying problem is unconstrained or has an easy-to-project ... More
Analysis and computation of some tumor growth models with nutrient: from cell density models to free boundary dynamicsFeb 02 2018In this paper, we study the tumor growth equation along with various models for the nutrient component, including the \emph{in vitro} model and the \emph{in vivo} model. At the cell density level, the spatial availability of the tumor density $n$ is governed ... More
Compressed Anomaly Detection with Multiple Mixed ObservationsJan 31 2018We consider a collection of independent random variables that are identically distributed, except for a small subset which follows a different, anomalous distribution. We study the problem of detecting which random variables in the collection are governed ... More
A randomized and fully discrete Galerkin finite element method for semilinear stochastic evolution equationsJan 25 2018In this paper the numerical solution of non-autonomous semilinear stochastic evolution equations driven by an additive Wiener noise is investigated. We introduce a novel fully discrete numerical approximation that combines a standard Galerkin finite element ... More
Invitation to Real Complexity Theory: Algorithmic Foundations to Reliable Numerics with Bit-CostsJan 19 2018While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and efficiency is demonstrated ... More
A Kotel'nikov Representation for WaveletsJan 17 2018This paper presents a wavelet representation using baseband signals, by exploiting Kotel'nikov results. Details of how to obtain the processes of envelope and phase at low frequency are shown. The archetypal interpretation of wavelets as an analysis with ... More
Efficient Computation of the 8-point DCT via Summation by PartsJan 17 2018This paper introduces a new fast algorithm for the 8-point discrete cosine transform (DCT) based on the summation-by-parts formula. The proposed method converts the DCT matrix into an alternative transformation matrix that can be decomposed into sparse ... More
Computation of the State Bias and Initial States for Stochastic State Space Systems in the General 2-D Roesser Model FormJan 14 2018Recently \cite{Ramos2017a} presented a subspace system identification algorithm for 2-D purely stochastic state space models in the general Roesser form. However, since the exact problem requires an oblique projection of $Y_f^h$ projected onto $W_p^h$ ... More
On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scalesJan 13 2018The necessity to find the global optimum of multiextremal functions arises in many applied problems where finding local solutions is insufficient. One of the desirable properties of global optimization methods is \emph{strong homogeneity} meaning that ... More
Numerical Analysis of Automodel Solutions for Superdiffusive TransportJan 09 2018The distributed computing analysis of the accuracy of automodel solutions for the Green's function of a wide class of superdiffusive transport of perturbation on a uniform background is carried out. The approximate automodel solutions have been suggested ... More
Higher-order models for glioma invasion: from a two-scale description to effective equations for mass density and momentumJan 09 2018Starting from a two-scale description involving receptor binding dynamics and a kinetic transport equation for the evolution of the cell density function under velocity reorientations, we deduce macroscopic models for glioma invasion featuring partial ... More
Case study: Approximations of the Bessel FunctionDec 31 2017The purpose of this note is to compare various approximation methods as applied to the inverse of the Bessel function of the first kind, in a given domain of the complex plane.
Coupling of Magneto-Thermal and Mechanical Superconducting Magnet Models by Means of Mesh-Based InterpolationDec 29 2017In this paper we present an algorithm for the coupling of magneto-thermal and mechanical finite element models representing superconducting accelerator magnets. The mechanical models are used during the design of the mechanical structure as well as the ... More
Monotone Difference Schemes for Convection-Dominated Diffusion-Reaction Equations Based on Quadratic SplineDec 22 2017A three-point monotone difference scheme is proposed for solving a one-dimensional non-stationary convection-diffusion-reaction equation with variable coefficients. The scheme is based on a parabolic spline and allows to linearly reproduce the numerical ... More
Sparse Randomized Kaczmarz for Support Recovery of Jointly Sparse Corrupted Multiple Measurement VectorsNov 07 2017Jan 03 2018While single measurement vector (SMV) models have been widely studied in signal processing, there is a surging interest in addressing the multiple measurement vectors (MMV) problem. In the MMV setting, more than one measurement vector is available and ... More
Stochastic Greedy Algorithms For Multiple Measurement VectorsNov 05 2017Sparse representation of a single measurement vector (SMV) has been explored in a variety of compressive sensing applications. Recently, SMV models have been extended to solve multiple measurement vectors (MMV) problems, where the underlying signal is ... More
PDE-Net: Learning PDEs from DataOct 26 2017Jan 01 2018In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two objectives at the ... More
Multilevel ensemble Kalman filtering for spatio-temporal processesOct 19 2017This work concerns state-space models, in which the state-space is an infinite-dimensional spatial field, and the evolution is in continuous time, hence requiring approximation in space and time. The multilevel Monte Carlo (MLMC) sampling strategy is ... More
Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gainOct 10 2017In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. ... More
A note on preconditioning weighted linear least squares, with consequences for weakly-constrained variational data assimilationSep 26 2017The effect of preconditioning linear weighted least-squares using an approximation of the model matrix is analyzed, showing the interplay of the eigenstructures of both the model and weighting matrices. A small example is given illustrating the resulting ... More
A stencil scaling approach for accelerating matrix-free finite element implementationsSep 20 2017We present a novel approach to fast on-the-fly low order finite element assembly for scalar elliptic partial differential equations of Darcy type with variable coefficients optimized for matrix-free implementations. Our approach introduces a new operator ... More
A Stabilized Normal Form Algorithm for Generic Systems of Polynomial EquationsAug 25 2017We propose a numerical linear algebra based method to find the multiplication operators of the quotient ring $\mathbb{C}[x]/I$ associated to a zero-dimensional ideal $I$ generated by $n$ $\mathbb{C}$-polynomials in $n$ variables. We assume that the polynomials ... More
Optimal Monte Carlo integration on closed manifoldsJul 15 2017Jan 24 2018The worst case integration error in reproducing kernel Hilbert spaces of standard Monte Carlo methods with n random points decays as $n^{-1/2}$. However, re-weighting of random points can sometimes be used to improve the convergence order. This paper ... More
Lagrangian Transport Through Surfaces in Compressible FlowsJul 03 2017Sep 28 2017A material-based, i.e., Lagrangian, methodology for exact integration of flux by volume-preserving flows through a surface has been developed recently in [Karrasch, SIAM J. Appl. Math., 76 (2016), pp. 1178-1190]. In the present paper, we first generalize ... More
Multiscale differential Riccati equations for linear quadratic regulator problemsJun 14 2017We consider approximations to the solutions of differential Riccati equations in the context of linear quadratic regulator problems, where the state equation is governed by a multiscale operator. Similarly to elliptic and parabolic problems, standard ... More
Compression, inversion, and approximate PCA of dense kernel matrices at near-linear computational complexityJun 07 2017Nov 10 2017Dense kernel matrices $\Theta \in \mathbb{R}^{N \times N}$ obtained from point evaluations of a covariance function $G$ at locations $\{ x_{i} \}_{1 \leq i \leq N}$ arise in statistics, machine learning, and numerical analysis. For covariance functions ... More
Third-order Limiting for Hyperbolic Conservation Laws applied to Adaptive Mesh Refinement and Non-Uniform 2D GridsMay 26 2017In this paper we extend the recently developed third-order limiter function $H_{3\text{L}}^{(c)}$ [J. Sci. Comput., (2016), 68(2), pp.~624--652] to make it applicable for more elaborate test cases in the context of finite volume schemes. This work covers ... More
Operator learning approach for the limited view problem in photoacoustic tomographyMay 07 2017In photoacoustic tomography, one is interested to recover the initial pressure distribution inside a tissue from the corresponding measurements of the induced acoustic wave on the boundary of a region enclosing the tissue. In the limited view problem, ... More
A robust parallel algorithm for combinatorial compressed sensingApr 28 2017In previous work two of the authors have shown that a vector $x \in \mathbb{R}^n$ with at most $k < n$ nonzeros can be recovered from an expander sketch $Ax$ in $\mathcal{O}(\mathrm{nnz}(A)\log k)$ operations via the Parallel-$\ell_0$ decoding algorithm, ... More
Control Synthesis of Nonlinear Sampled Switched Systems using Euler's MethodApr 11 2017In this paper, we propose a symbolic control synthesis method for nonlinear sampled switched systems whose vector fields are one-sided Lipschitz. The main idea is to use an approximate model obtained from the forward Euler method to build a guaranteed ... More
Hybrid collocation perturbation for PDEs with random domainsMar 29 2017In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by $N$ random variables. The random domain is split ... More
Uncertainty Quantification of geochemical and mechanical compaction in layered sedimentary basinsMar 10 2017Jul 25 2017In this work we propose an Uncertainty Quantification methodology for sedimentary basins evolution under mechanical and geochemical compaction processes, which we model as a coupled, time-dependent, non-linear, monodimensional (depth-only) system of PDEs ... More
On the Power of Truncated SVD for General High-rank Matrix Estimation ProblemsFeb 22 2017Nov 05 2017We show that given an estimate $\widehat{A}$ that is close to a general high-rank positive semi-definite (PSD) matrix $A$ in spectral norm (i.e., $\|\widehat{A}-A\|_2 \leq \delta$), the simple truncated SVD of $\widehat{A}$ produces a multiplicative approximation ... More
Automatic implementation of material laws: Jacobian calculation in a finite element code with TAPENADEFeb 21 2017In an effort to increase the versatility of finite element codes, we explore the possibility of automatically creating the Jacobian matrix necessary for the gradient-based solution of nonlinear systems of equations. Particularly, we aim to assess the ... More
Benchmarks for single-phase flow in fractured porous mediaJan 05 2017This paper presents several test cases intended to be benchmarks for numerical schemes for single-phase fluid flow in fractured porous media. A number of solution strategies are compared, including a vertex and a cell-centered finite volume method, a ... More
Solving piecewise linear equations in abs-normal formJan 03 2017With the ultimate goal of iteratively solving piecewise smooth (PS) systems, we consider the solution of piecewise linear (PL) equations. PL models can be derived in the fashion of automatic or algorithmic differentiation as local approximations of PS ... More
Revisiting Hammel et al. (1987): Does the shadowing property hold for modern computers?Dec 07 2016Computational techniques are extensively applied in nonlinear science. However, while the use of computers for research has been expressive, the evaluation of numerical results does not grow in the same pace. Hammel et al. (Journal of Complexity, 1987, ... More
Deterministic and Probabilistic Conditions for Finite Completability of Low Rank TensorDec 06 2016We investigate the fundamental conditions on the sampling pattern, i.e., locations of the sampled entries, for finite completability of a low-rank tensor given some components of its Tucker rank. In order to find the deterministic necessary and sufficient ... More
Implementation and evaluation of data-compression algorithms for irregular-grid iterative methods on the PEZY-SC processorDec 02 2016Iterative methods on irregular grids have been used widely in all areas of comptational science and engineering for solving partial differential equations with complex geometry. They provide the flexibility to express complex shapes with relatively low ... More
Monge's Optimal Transport Distance with Applications for Nearest Neighbour Image ClassificationDec 01 2016This paper focuses on a similarity measure, known as the Wasserstein distance, with which to compare images. The Wasserstein distance results from a partial differential equation (PDE) formulation of Monge's optimal transport problem. We present an efficient ... More
Full-Projection scheme for monotone BSDEs with polynomial growthNov 30 2016We study a new modified explicit scheme for BSDEs with monotone drivers of polynomial growth which preserves the strict monotonicity of the driver, by projecting at each step the input on a ball of predefined radius. We provide a full analysis on the ... More
Adapted time steps explicit scheme for monotone BSDEsNov 30 2016We study the numerical strong stability of explicit schemes for the numerical approximation of the solution to a BSDE where the driver has polynomial growth in the primary variable and satisfies a monotone decreasing condition, and we introduce an explicit ... More
Towards a Global Controller Design for Guaranteed Synchronization of Switched Chaotic SystemsNov 29 2016In this paper, synchronization of identical switched chaotic systems is explored based on Lyapunov theory of guaranteed stability. Concepts from robust control principles and switched linear systems are merged together to derive a sufficient condition ... More
A duality-based optimization approach for model adaptivity in heterogeneous multiscale problemsNov 28 2016This paper introduces a novel framework for model adaptivity in the context of heterogeneous multiscale problems. The framework is based on the idea to interpret model adaptivity as a minimization problem of local error indicators, that are derived in ... More
Fast Multipole Method based filtering of non-uniformly sampled dataNov 28 2016Non-uniform fast Fourier Transform (NUFFT) and inverse NUFFT (INUFFT) algorithms, based on the Fast Multipole Method (FMM) are developed and tested. Our algorithms are based on a novel factorization of the FFT kernel, and are implemented with attention ... More
Variational inequality approach to enforce the non-negative constraint for advection-diffusion equationsNov 26 2016Predictive simulations are crucial for the success of many subsurface applications, and it is highly desirable to obtain accurate non-negative solutions for transport equations in these numerical simulations. In this paper, we propose a computational ... More
Variational inequality approach to enforce the non-negative constraint for advection-diffusion equationsNov 26 2016Dec 04 2016Predictive simulations are crucial for the success of many subsurface applications, and it is highly desirable to obtain accurate non-negative solutions for transport equations in these numerical simulations. In this paper, we propose a computational ... More
Improved error bound for multivariate Chebyshev polynomial interpolationNov 26 2016Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For efficiency, ... More
A Defect Corrected Finite Element Approach for the Accurate Evaluation of Magnetic Fields on Unstructured GridsNov 25 2016In electromagnetic simulations of magnets and machines one is often interested in a highly accurate and local evaluation of the magnetic field uniformity. Based on local post-processing of the solution, a defect correction scheme is proposed as an easy ... More
A Unified Convex Surrogate for the Schatten-$p$ NormNov 25 2016The Schatten-$p$ norm ($0<p<1$) has been widely used to replace the nuclear norm for better approximating the rank function. However, existing methods are either 1) not scalable for large scale problems due to relying on singular value decomposition (SVD) ... More
How to overcome the Courant-Friedrichs-Lewy condition of explicit discretizations?Nov 24 2016This manuscript contains some thoughts on the discretization of the classical heat equation. Namely, we discuss the advantages and disadvantages of explicit and implicit schemes. Then, we show how to overcome some disadvantages while preserving some advantages. ... More
Multi-level Monte Carlo methods with the Truncated Euler-Maruyama Scheme for Stochastic Differential EquationsNov 23 2016In this paper, the truncated Euler-Maruyama (EM) method is employed together with the Multi-level Monte Carlo (MLMC) method to approximate the expectations of functions of solutions to stochastic differential equations (SDEs). The convergence rate and ... More
Multilevel Monte-Carlo for measure valued solutionsNov 23 2016We propose a Multilevel Monte-Carlo (MLMC) method for computing entropy measure valued solutions of hyperbolic conservation laws. Sharp bounds for the narrow convergence of MLMC for the entropy measure valued solutions are proposed. An optimal work-vs-error ... More
Generalized Fourier-Bessel operator and almost-periodic interpolation and approximationNov 23 2016We consider functions $f$ of two real variables, given as trigonometric functions over a finite set $F$ of frequencies. This set is assumed to be closed under rotations in the frequency plane of angle $\frac{2k\pi}{M}$ for some integer $M$. Firstly, we ... More
Randomized Distributed Mean Estimation: Accuracy vs CommunicationNov 22 2016We consider the problem of estimating the arithmetic average of a finite collection of real vectors stored in a distributed fashion across several compute nodes subject to a communication budget constraint. Our analysis does not rely on any statistical ... More
Low-Dimensional Stochastic Modeling of the Electrical Properties of Biological TissuesNov 22 2016Uncertainty quantification plays an important role in biomedical engineering as measurement data is often unavailable and literature data shows a wide variability. Using state-of-the-art methods one encounters difficulties when the number of random inputs ... More
Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables - with Application to Lognormal Elliptic Diffusion ProblemsNov 22 2016We give a convergence proof of sparse collocation to approximate Hilbert space-valued functions depending on countably many Gaussian random variables. Such functions appear as solutions or quantities of interest associated with elliptic PDEs with lognormal ... More
Correlation Clustering with Low-Rank MatricesNov 21 2016Correlation clustering is a technique for aggregating data based on qualitative information about which pairs of objects are labeled 'similar' or 'dissimilar.' Because the optimization problem is NP-hard, much of the previous literature focuses on finding ... More
Numerical optimal control for HIV prevention with dynamic budget allocationNov 21 2016This paper is about numerical control of HIV propagation. The contribution of the paper is threefold: first, a novel model of HIV propagation is proposed; second, the methods from numerical optimal control are successfully applied to the developed model ... More
Multiple Right-Hand Side Techniques in Semi-Explicit Time Integration Methods for Transient Eddy Current ProblemsNov 21 2016The spatially discretized magnetic vector potential formulation of magnetoquasistatic field problems is transformed from an infinitely stiff differential algebraic equation system into a finitely stiff ordinary differential equation (ODE) system by application ... More
Bidiagonalization with Parallel Tiled AlgorithmsNov 18 2016We consider algorithms for going from a "full" matrix to a condensed "band bidiagonal" form using orthogonal transformations. We use the framework of "algorithms by tiles". Within this framework, we study: (i) the tiled bidiagonalization algorithm BiDiag, ... More
Robust and Scalable Column/Row Sampling from Corrupted Big DataNov 18 2016Conventional sampling techniques fall short of drawing descriptive sketches of the data when the data is grossly corrupted as such corruptions break the low rank structure required for them to perform satisfactorily. In this paper, we present new sampling ... More
Reweighted Low-Rank Tensor Decomposition and its Applications in Video DenoisingNov 18 2016A tensor is decomposed into low-rank and sparse components by simultaneously minimizing tensor nuclear norm and the $l_1$ norm in Tensor Principal Component Pursuit (TPCP). Inspired by reweighted $l_1$ norm minimization for sparsity enhancement, this ... More
Minimal Problems for the Calibrated Trifocal VarietyNov 18 2016We determine the algebraic degree of minimal problems for the calibrated trifocal variety in computer vision. We rely on numerical algebraic geometry and the homotopy continuation software Bertini.
Force-Based Atomistic/Continuum Blending for MultilatticesNov 18 2016We formulate the blended force-based quasicontinuum (BQCF) method for multilattices and develop rigorous error estimates in terms of the approximation parameters: atomistic region, blending region and continuum finite element mesh. Balancing the approximation ... More
Splitting schemes for unsteady problems involving the grad-div operatorNov 17 2016In this paper we consider various splitting schemes for unsteady problems containing the grad-div operator. The fully implicit discretization of such problems would yield at each time step a linear problem that couples all components of the solution vector. ... More
Analytical Approximate Solutions of Systems of Multi-pantograph Delay Differential Equations Using Residual Power-series MethodNov 16 2016Dec 03 2016This paper investigates analytical approximate solutions for a system of multipantograph delay differential equations using the residual power series method (RPSM), which obtains a Taylor expansion of the solutions and produces the exact form in terms ... More
Analytical Approximate Solutions of Systems of Multi-pantograph Delay Differential Equations Using Residual Power-series MethodNov 16 2016This paper investigates analytical approximate solutions for a system of multipantograph delay differential equations using the residual power series method (RPSM), which obtains a Taylor expansion of the solutions and produces the exact form in terms ... More
Strict upper and lower bounds for quantities of interest in static response sensitivity analysisNov 16 2016In this paper, a goal-oriented error estimation technique for static response sensitivity analysis is proposed based on the constitutive relation error (CRE) estimation for finite element analysis (FEA). Strict upper and lower bounds of various quantities ... More
Pseudospectral bounds on transient growth for higher order and constant delay differential equationsNov 16 2016Asymptotic dynamics of ordinary differential equations (ODEs) are commonly understood by looking at eigenvalues of a matrix, and transient dynamics can be bounded above and below by considering the corresponding pseudospectra. While asymptotics for other ... More
Accelerated Stochastic ADMM with Variance ReductionNov 13 2016Alternating Direction Method of Multipliers (ADMM) is a popular method in solving Machine Learning problems. Stochastic ADMM was firstly proposed in order to reduce the per iteration computational complexity, which is more suitable for big data problems. ... More
Accelerated Stochastic ADMM with Variance ReductionNov 13 2016Nov 30 2016Alternating Direction Method of Multipliers (ADMM) is a popular method in solving Machine Learning problems. Stochastic ADMM was firstly proposed in order to reduce the per iteration computational complexity, which is more suitable for big data problems. ... More
Riemannian Tensor Completion with Side InformationNov 12 2016Riemannian optimization methods have shown to be both fast and accurate in recovering a large-scale tensor from its incomplete observation. However, in almost all recent Riemannian tensor completion methods, only low rank constraint is considered. Another ... More
SLIM-Decomposition: Nearest-Neighbor Interaction Systems in the Tensor Train FormatNov 11 2016Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods anymore due to ... More
On Explicit Approximations for Lévy Driven SDEs with Super-linear Diffusion CoefficientsNov 10 2016Motivated by the results of \cite{sabanis2015}, we propose explicit Euler-type schemes for SDEs with random coefficients driven by L\'evy noise when the drift and diffusion coefficients can grow super-linearly. As an application of our results, one can ... More
Sharper Bounds for Regression and Low-Rank Approximation with RegularizationNov 10 2016The technique of matrix sketching, such as the use of random projections, has been shown in recent years to be a powerful tool for accelerating many important statistical learning techniques. Research has so far focused largely on using sketching for ... More
Faster Kernel Ridge Regression Using Sketching and PreconditioningNov 10 2016Random feature maps, such as random Fourier features, have recently emerged as a powerful technique for speeding up and scaling the training of kernel-based methods such as kernel ridge regression. However, random feature maps only provide crude approximations ... More
Faster Kernel Ridge Regression Using Sketching and PreconditioningNov 10 2016Nov 26 2016Kernel Ridge Regression (KRR) is a simple yet powerful technique for non-parametric regression whose computation amounts to solving a linear system. This system is usually dense and highly ill-conditioned. In addition, the dimensions of the matrix are ... More
The Little Engine that Could: Regularization by Denoising (RED)Nov 09 2016Removal of noise from an image is an extensively studied problem in image processing. Indeed, the recent advent of sophisticated and highly effective denoising algorithms lead some to believe that existing methods are touching the ceiling in terms of ... More
Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval ArithmeticNov 09 2016Arb is a C library for arbitrary-precision interval arithmetic using the midpoint-radius representation, also known as ball arithmetic. It supports real and complex numbers, polynomials, power series, matrices, and evaluation of many special functions. ... More
A Big-Data Approach to Handle Many Process Variations: Tensor Recovery and ApplicationsNov 07 2016Fabrication process variations are a major source of yield degradation in the nano-scale design of integrated circuits (IC), microelectromechanical systems (MEMS) and photonic circuits. Stochastic spectral methods are a promising technique to quantify ... More
Numerical methods for the 2nd moment of stochastic ODEsNov 07 2016Numerical methods for stochastic ordinary differential equations typically estimate moments of the solution from sampled paths. Instead, in this paper we directly target the deterministic equation satisfied by the first and second moments. For the canonical ... More
Data-driven Structured RealizationNov 07 2016We present a framework for constructing structured realizations of linear dynamical systems having transfer functions of the form $C(\sum_{k=1}^K h_k(s)A_k)^{-1}B$ where $h_1,h_2,\ldots,h_K$ are prescribed functions that specify the surmised structure ... More
Mean Field Type Control with Congestion (II): An Augmented Lagrangian MethodNov 07 2016This work deals with a numerical method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential equations arising ... More
Certified Lower Bounds of Roundoff Errors using Semidefinite ProgrammingNov 04 2016Nov 07 2016A longstanding problem related to floating-point implementation of numerical programs is to provide efficient yet precise analysis of output errors. We present a framework to compute lower bounds of absolute roundoff errors for numerical programs implementing ... More
Certified Lower Bounds of Roundoff Errors using Semidefinite ProgrammingNov 04 2016A longstanding problem related to floating-point implementation of numerical programs is to provide efficient yet precise analysis of output errors. We present a framework to compute lower bounds of absolute roundoff errors for numerical programs implementing ... More
Sensitivity analysis on chaotic dynamical system by Non-Intrusive Least Square Shadowing (NILSS)Nov 03 2016Nov 26 2016This paper develops the tangent Non-Intrusive Least Square Shadowing (NILSS) method, which computes the sensitivity for long-time averaged objectives in chaotic dynamical systems. In NILSS, we represent a tangent solution as a linear combination of a ... More
Sensitivity analysis on chaotic dynamical system by Non-Intrusive Least Square Shadowing (NILSS)Nov 03 2016Nov 21 2016This paper develops the tangent Non-Intrusive Least Square Shadowing (NILSS) method, which computes the sensitivity for long-time averaged objectives in chaotic dynamical systems. In NILSS, we represent a tangent solution as a linear combination of a ... More
Sensitivity analysis on chaotic dynamical system by Non-Intrusive Least Square Shadowing (NILSS)Nov 03 2016Nov 08 2016This paper develops the tangent Non-Intrusive Least Square Shadowing (NILSS) method, which computes sensitivity for chaotic dynamical systems. In NILSS, a tangent solution is represented as a linear combination of a inhomogeneous tangent solution and ... More
Sensitivity analysis on chaotic dynamical system by Non-Intrusive Least Square Shadowing (NILSS)Nov 03 2016This paper develops the tangent Non-Intrusive Least Square Shadowing (NILSS) method, which computes sensitivity for chaotic dynamical systems. In NILSS, a tangent solution is represented as a linear combination of a inhomogeneous tangent solution and ... More
Regularity results for transmission problems with sign-changing coefficients: a modal approachNov 01 2016We investigate some scalar transmission problems between a classical positive material and a negative one, whose physical coefficients are negative. First, we consider cases where the negative inclusion is a disk in 2d and a ball in 3d. Thanks to asymptotics ... More
Algebraic Multigrid Preconditioners for Multiphase Flow in Porous MediaNov 01 2016Multiphase flow is a critical process in a wide range of applications, including carbon sequestration, contaminant remediation, and groundwater management. Typically, this process is modeled by a nonlinear system of partial differential equations derived ... More
A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson--Nernst--Planck systemsOct 31 2016We design an arbitrary-order free energy satisfying discontinuous Galerkin (DG) method for solving time-dependent Poisson-Nernst-Planck systems. Both the semi-discrete and fully discrete DG methods are shown to satisfy the corresponding discrete free ... More
A Primal-Dual Homotopy Algorithm for $\ell_{1}$-Minimization with $\ell_{\infty}$-ConstraintsOct 31 2016In this paper we propose a primal-dual homotopy method for $\ell_1$-minimization problems with infinity norm constraints in the context of sparse reconstruction. The natural homotopy parameter is the value of the bound for the constraints and we show ... More
Deconfliction and Surface Generation from Bathymetry Data Using LR B-splinesOct 31 2016A set of bathymetry point clouds acquired by different measurement techniques at different times, having different accuracy and varying patterns of points, are approximated by an LR B-spline surface. The aim is to represent the sea bottom with good accuracy ... More
Multilevel and Multi-index Monte Carlo methods for McKean-Vlasov equationsOct 31 2016We address the approximation of functionals depending on a system of particles, described by stochastic differential equations (SDEs), in the mean-field limit when the number of particles approaches infinity. This problem is equivalent to estimating the ... More
Multilevel and Multi-index Monte Carlo methods for the McKean-Vlasov equationOct 31 2016May 01 2017We address the approximation of functionals depending on a system of particles, described by stochastic differential equations (SDEs), in the mean-field limit when the number of particles approaches infinity. This problem is equivalent to estimating the ... More
Anisotropic mesh adaptation in Firedrake with PETSc DMPlexOct 31 2016Despite decades of research in this area, mesh adaptation capabilities are still rarely found in numerical simulation software. We postulate that the primary reason for this is lack of usability. Integrating mesh adaptation into existing software is difficult ... More