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When Data Driven Reduced Order Modeling Meets Full Waveform Inversion
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| Pengarang | : | Liliana Borcea, Josselin Garnier, Alexander V. Mamonov |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 66 (No. 3) |
| Halaman | : | 501-532 |
| Abstrak | : | Waveform inversion is concerned with estimating a heterogeneous medium, modeled by variable coefficients of wave equations, using sources that emit probing signals and receivers that record the generated waves. It is an old and intensively studied inverse problem with a wide range of applications, but the existing inversion methodologies are still far from satisfactory. The typical mathematical formulation is a nonlinear least squares data fit optimization and the difficulty stems from the nonconvexity of the objective function that displays numerous local minima at which local optimization approaches stagnate. This pathological behavior has at least three unavoidable causes: (1) The mapping from the unknown coefficients to the wave field is nonlinear and complicated. (2) The sources and receivers typically lie on a single side of the medium, so only backscattered waves are measured. (3) The probing signals are band limited and with high frequency content. There is a lot of activity in the computational science and engineering communities that seeks to mitigate the difficulty of estimating the medium by data fitting. In this paper we present a different point of view, based on reduced order models (ROMs) of two operators that control the wave propagation. The ROMs are called data driven because they are computed directly from the measurements, without any knowledge of the wave field inside the inaccessible medium. This computation is noniterative and uses standard numerical linear algebra methods. The resulting ROMs capture features of the physics of wave propagation in a complementary way and have surprisingly good approximation properties that facilitate waveform inversion. |
Persistent Homology for Resource Coverage: A Case Study of Access to Polling Sites
| Pengarang | : | Abigail Hickok, Benjamin Jarman, Michael Johnson, Jiajie Luo, Mason A. Porter |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 66 (No. 3) |
| Halaman | : | 481-500 |
| Abstrak | : | It is important to choose the geographical distributions of public resources in a fair and equitable manner. However, it is complicated to quantify the equity of such a distribution; important factors include distances to resource sites, availability of transportation, and ease of travel. We use persistent homology, which is a tool from topological data analysis, to study the availability and coverage of polling sites. The information from persistent homology allows us to infer holes in a distribution of polling sites. We analyze and compare the coverage of polling sites in Los Angeles County and five cities (Atlanta, Chicago, Jacksonville, New York City, and Salt Lake City), and we conclude that computation of persistent homology appears to be a reasonable approach to analyzing resource coverage. |
A Hyperbolic PDE with Parabolic Behavior
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 46 (No. 1) |
| Halaman | : | 115-127 |
| Abstrak | : | In this paper we present a hyperbolic partial differential equation (PDE) in one space and one time dimension. This equation arose in a study of numerical schemes for simulating evolving river topographies. The solution of this PDE, whose initial data are specified along a characteristic, is very similar to that of the canonical diffusion equation. This interesting example provides insight into the solution of hyperbolic PDEs when data is specified in this pathological way as well as illustrating some connections between the parabolic and hyperbolic classes of evolution equations. |
Cardinality Minimization, Constraints, and Regularization: A Survey
| Pengarang | : | Andreas M. Tillmann, Daniel Bienstock, Andrea Lodi, Alexandra Schwartz |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 66 (No. 3) |
| Halaman | : | 403-477 |
| Abstrak | : | We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function. We provide a unified viewpoint on the general problem classes and models, and we give concrete examples from diverse application fields such as signal and image processing, portfolio selection, and machine learning. The paper discusses general-purpose modeling techniques and broadly applicable as well as problem-specific exact and heuristic solution approaches. While our perspective is that of mathematical optimization, a main goal of this work is to reach out to and build bridges between the different communities in which cardinality optimization problems are frequently encountered. In particular, we highlight that modern mixed-integer programming, which is often regarded as impractical due to the commonly unsatisfactory behavior of black-box solvers applied to generic problem formulations, can in fact produce provably high-quality or even optimal solutions for cardinality optimization problems, even in large-scale real-world settings. Achieving such performance typically involves drawing on the merits of problem-specific knowledge that may stem from different fields of application and, e.g., can shed light on structural properties of a model or its solutions, or can lead to the development of efficient heuristics. We also provide some illustrative examples. |
Connecting Energy and Electricity Instruction to Local Environmental Justice Issues
| Pengarang | : | |
| Nama Majalah/Jurnal | : | The Physics Teacher |
| Volume / Edisi | : | 61 (No. 6) |
| Halaman | : | 519–521 |
| Abstrak | : | Abstrak tidak tersedia. |
Stochastic Linear-Quadratic Control via Primal-Dual Semidefinite Programming
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 46 (No. 1) |
| Halaman | : | 87-111 |
| Abstrak | : | We study stochastic linear-quadratic (LQ) optimal control problems over an infinite time horizon, allowing the cost matrices to be indefinite. We develop a systematic approach based on semidefinite programming (SDP). A central issue is the stability of the feedback control. We show that this can be effectively examined through the complementary duality of the SDP. Furthermore, we establish several implication relations among the SDP complementary duality, the (generalized) Riccati equation, and the optimality of the LQ control problem. Based on these relations, we propose a numerical procedure that provides a thorough treatment of the LQ control problem via primal-dual SDP: it identifies a stabilizing feedback control that is optimal or determines that the problem possesses no optimal solution. For the latter case, we develop an -approximation scheme that is asymptotically optimal. |
Algorithms for Almost Block Diagonal Linear Systems
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 46 (No. 1) |
| Halaman | : | 49-58 |
| Abstrak | : | Codes for solving systems of ordinary differential equations for use in the method of lines for partial differential equations (PDEs) usually provide only a banded system solver. In this context, a frequently occurring structure is almost block diagonal (ABD). Solving ABD systems by imposing banded structure introduces fill-in and is inefficient. Though robust, efficient ABD software has been developed and used in packages for solving boundary value problems with separated boundary conditions for ordinary differential equations (BVODEs), it has not been generally exploited in PDE software. The situation with bordered almost block diagonal system software for BVODEs with nonseparated boundary conditions is less satisfactory. This survey draws on material from a variety of sources, particularly [P. Amodio et al., Numer. Linear Algebra Appl., {7} (2000), pp. 275--317] and [B. Garrett and I. Gladwell, J. Comput. Methods Sci. Engrg., {1} (2001), pp. 75--98] and the references therein. |
Recursive Blocked Algorithms and Hybrid Data Structures for Dense Matrix Library Software
| Pengarang | : | Erik Elmroth |
| Nama Majalah/Jurnal | : | Siam Review |
| Volume / Edisi | : | 46 (No. 1) |
| Halaman | : | 3-45 |
| Abstrak | : | Matrix computations are both fundamental and ubiquitous in computational science and its vast application areas. Along with the development of more advanced computer systems with complex memory hierarchies, there is a continuing demand for new algorithms and library software that efficiently utilize and adapt to new architecture features. This article reviews and details some of the recent advances made by applying the paradigm of recursion to dense matrix computations on today's memory-tiered computer systems. Recursion allows for efficient utilization of a memory hierarchy and generalizes existing fixed blocking by introducing automatic variable blocking that has the potential of matching every level of a deep memory hierarchy. Novel recursive blocked algorithms offer new ways to compute factorizations such as Cholesky and QR and to solve matrix equations. In fact, the whole gamut of existing dense linear algebra factorization is beginning to be reexamined in view of the recursive paradigm. Use of recursion has led to using new hybrid data structures and optimized superscalar kernels. The results we survey include new algorithms and library software implementations for level 3 kernels, matrix factorizations, and the solution of general systems of linear equations and several common matrix equations. The software implementations we survey are robust and show impressive performance on today's high performance computing systems. |
The Physics of Limits
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The Physics Teacher |
| Volume / Edisi | : | 61 (No. 6) |
| Halaman | : | 512–515 |
| Abstrak | : | Abstrak tidak tersedia. |
Enlightening Visualizations of Partially Filled Dielectric Capacitors
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The Physics Teacher |
| Volume / Edisi | : | 61 (No. 6) |
| Halaman | : | 503–505 |
| Abstrak | : | Abstrak tidak tersedia. |