一周活动预告（4.3-4.9）
Direct imaging method for reconstructing penetrable locally rough surfaces from phaseless totalfield data (张海文)
Tensor Numerical Methods in Scientific Computing with Applications（Boris Khoromskij）
Projection-based and data-driven reduced order models for parametric bifurcation problems (Federico Pichi)
Analysis and numerical approximation of optimal mixing via fluid flows (Yangwen Zhang)
Analysis of Seismic Inversion with Optimal Transportation and Softplus Encoding（邱凌云）
1. Direct imaging method for reconstructing penetrable locally rough surfaces from phaseless totalfield data
报告人: 张海文 （中科院）
报告时间: 2023-4.4 14:00-15:00
报告链接: 腾讯会议ID: 685 3507 8479
信息来源: https://math.jlu.edu.cn/info/1555/14412.htm
报告摘要:
This talk is concerned with inverse scattering of time-harmonic acoustic plane waves by a two-layered medium with a locally rough interface in 2D. A direct imaging method is proposed to reconstruct the penetrable locally rough surface from the phaseless total-field data measured on the upper part of the circle with a sufficiently large radius. The presence of the two-layered background medium leads to the difficulties in the theoretical analysis of our inversion method. To overcome the difficulties, we give the asymptotic analysis for relevant oscillatory integrals. It is worth mentioning that our recent work [L. Li, J. Yang, B. Zhang and H. Zhang, arXiv:2208.00456] on the uniform far-field asymptotics of the scattered wave to the acoustic two-layered medium scattering problem provides a theoretical foundation for the proposed direct imaging method. Finally, numerical experiments are carried out to demonstrate the feasibility and robustness of our imaging algorithm.
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2. Tensor Numerical Methods in Scientific Computing with Applications
Speaker: Boris Khoromskij（Max-Planck-Institute for Mathematics in the Sciences）
Time: 2023-04-04 16:00-17:00
Venue: Zoom Meeting ID: 676 1358 3250 Passcode: 102717
Info Source:
https://ins.sjtu.edu.cn/seminars/2309
Abstract:
Recent progress in understanding of rank-structured tensor decompositions in Rd and development of related tensor numerical methods enables efficient techniques for solution of the multidimensional problems in scientific computing and data science, avoiding the curse of dimensionality.
However, application of the advantageous tensor-structured numerical methods to particular problems in scientific computing requires interdisciplinary cooperation and nontrivial bridging of tensor approaches with many other special numerical techniques, for example, computational quantum chemistry and bio-molecular modeling, domain-specific rank structured parametrizations/formats, low-rank approximation of operators and functions, adaptation to geometries, preconditioned iteration on rank-structured tensor manifolds or matching to stochastic/parametric features of the problem.
In this talk I shall discuss how old and new tensor formats can be applied to numerical modeling of multi-particle systems, PDE constrained optimal control problems, stochastic homog[1]enization of elliptic PDEs with random input, and tensor interpolation of multi-dimensional scattered data.
References
Boris N. Khoromskij. Tensor numerical methods in scientific computing. De Gruyter, Berlin, 2018.
Venera Khoromskaia and Boris N. Khoromskij. Tensor numerical methods in quantum chemistry. De Gruyter, Berlin, 2018.
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3. Projection-based and data-driven reduced order models for parametric bifurcation problems
Speaker: Federico Pichi (École Polytechnique Fédérale de Lausanne)
Time: 2023-4-4, 16:00 CEST+0200 (Europe/Rome)
Registration and Source Link:
https://na-g-roms.github.io/seminars/Federico_Pichi_2023.html
Abstract:
Bifurcating phenomena, i.e. sudden changes in the system’s qualitative behavior linked to the solution’s non-uniqueness, naturally arise in several fields. We discuss both intrusive and non-intrusive Reduced Order Models for reconstructing bifurcation diagrams, whose associated cost is unaffordable using high-fidelity simulations. POD and deflated Greedy approaches are investigated and compared with data-driven ones based on neural networks. The proposed methodologies are tested on classical bifurcating benchmarks in fluid dynamics held by the Navier-Stokes equations and linked to Coanda’s effect.
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4. Analysis and numerical approximation of optimal mixing via fluid flows
Speaker: Yangwen Zhang, Carnegie Mellon University
Time: 2023-4-5, 4:10PM-5PM Berkeley time
Venue:
https://berkeleyams.lbl.gov/spring23/zhang.html
Source Link:
https://berkeley.zoom.us/j/98667278310
Abstract:
The question of what fluid flow maximizes mixing rate, slows it down, or even steers a quantity of interest toward a desired target distribution draws great attention from a broad range of scientists and engineers in the area of complex dynamical systems. Our methodology is to place these problems within a flexible computational framework, and to develop a solution strategy based on optimal control tools. Theoretically, we investigate the well-posedness, regularity of the solution for various control designs. Computationally, we propose a novel model order reduction method to reduce computational costs. Numerical analysis and experiments demonstrate the effectiveness of our reduced order models.
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5. Analysis of Seismic Inversion with Optimal Transportation and Softplus Encoding
Speaker: 邱凌云（清华大学丘成桐数学科学中心）
Time: 2023-04-06 14:00-15:00
Venue: Tencent Meeting ID:278851696 Password:449899
Info Source:
https://ins.sjtu.edu.cn/seminars/2314
Abstract:
This work is devoted to theoretical and numerical investigation of the local minimum issue in seismic full waveform inversion (FWI). We provide a mathematical analysis of optimal transportation type objective function's differentiability and proves that the gradient obtained in the adjoint-state method does not depend on the particular choice of the Kantorovich potentials. A novel approach using the softplus encoding method is presented to generalize and impose the OT metric on FWI. This approach improves the convexity of the objective function and mitigates the cycle-skipping problem. The effectiveness of the proposed method is demonstrated numerically on an inversion task with the benchmark Marmousi model.
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