Centre for Mathematical Imaging Techniques (CMIT)
- CMIT Research Seminar 2023/24 -

Semester 2 (Current)

  • 28 February 2024 15:00-16:00 UK time. In-Person and online (Math Building, Room 104).

  • Maciej Buze (UK).

    Title. Anisotropic power diagrams for polycrystal modelling: efficient generation of curved grains via optimal transport
    Abstract. The microstructure of metals and foams is often modelled using power diagrams, a general class of tessellations which includes the well-known Voronoi diagrams. While power diagram-based approaches can generate complex microstructures in a matter of seconds and require a relatively small number of parameters, the idealised grains they produce are inherently unrealistic - they have flat boundaries and any spatial anisotropy they possess is solely determined by the relative location of seed points of neighbouring grains and not by the preferred growth directions of each grain. Curved boundaries and control over the anisotropy of individual grains can be achieved by employing anisotropic power diagrams (APDs), with several promising APD-based approaches explored in recent years by various authors. One obstacle in the wider adoption of APDs as a practical tool for modelling the microstructure of metals is the computational cost of generating them. Known efficient methods for generating power diagrams do not translate to the anisotropic setup and known techniques for generating APDs are drastically slower - while the usual runtime to generate a power diagram with grains of given volumes is (tens of) seconds, for APDs it ranges from (tens of) minutes to (tens of) hours. In this talk I will begin by providing a brief overview of (anisotropic) power diagram methods in geometric modelling of polycrystalline materials and subsequently present a novel approach to generating APDs with prescribed statistical properties, in which we combine semi-discrete optimal transport techniques with modern GPU-oriented computational tools, originally developed for the Sinkhorn algorithm. Our method succeeds in bringing the runtime to generate optimal APDs down to (tens of) seconds, which is fast enough to be used, e.g. in computational homogenisation. I will finish by showcasing the speed and the versatility of our method with several examples, including ones based on Electron Backscatter Diffraction (EBSD) measurements provided by our industrial partner, Tata Steel. This is joint work with David Bourne (Heriot-Watt), Jean Feydy (Inria Paris), Steve Roper (Glasgow) and Karo Sedighiani (Tata Steel).

    Semester 1 2023/24

  • 6 December 2023 10:00-11:00 UK time. Online on Zoom (link will be announced by email)

  • Zhicheng Wang (CN).

    Title. Solution multiplicity and effects of data and eddy viscosity on Navier-Stokes solutions inferred by physics-informed neural networks
    Abstract. Physics-informed neural networks (PINNs) have emerged as a new simulation paradigm for fluid flows and are especially effective for inverse and hybrid problems. However, vanilla PINNs often fail in forward problems, especially at high Reynolds (Re) number flows. Herein, we study systematically the classical lid-driven cavity flow at Re=2,000, 3,000 and 5,000. We observe that vanilla PINNs obtain two classes of solutions, one class that agrees with direct numerical simulations (DNS), and another that is an unstable solution to the Navier-Stokes equations and not physically realizable. We attribute this solution multiplicity to singularities and unbounded vorticity, and we propose regularization methods that restore a unique solution within 1\% difference from the DNS solution. In particular, we introduce a parameterized entropy-viscosity method as artificial eddy viscosity and identify suitable parameters that drive the PINNs solution towards the DNS solution. Furthermore, we solve the inverse problem by subsampling the DNS solution, and identify a new eddy viscosity distribution that leads to velocity and pressure fields almost identical to their DNS counterparts. Surprisingly, a single measurement at a random point suffices to obtain a unique PINNs DNS-like solution even without artificial viscosity, which suggests possible pathways in simulating high Reynolds number turbulent flows using vanilla PINNs.

  • 1 December 2023 14:00-15:00 UK time. Online on Zoom (link will be announced by email)

  • Paolo Dulio (Department of Mathematics, Polytechnic University of Milan, IT).

    Title. Convex Ghosts in Discrete Tomography
    Abstract. In Computerized Axial Tomography, the problem of reconstructing an unknown object from X-ray projections is considered. The original theoretical model bases on the inversion of the Radon transform, but, in view of application, several items must be refined. Among them, the necessary constraint of using only a finite number of projections leads to the lost of injectivity of the Radon transform. This introduces ghosts in the tomographic problem, namely, non trivial images having zero projections along all the considered directions. As a consequence, uniqueness of reconstruction can never be ensured, even from a theoretical point of view, without assuming some kind of prior knowledge, so to understand the structure of the space of ghosts. In this view, I will focus on the extra information that the set to be reconstructed has some kind of convexity, pointing out properties of the cross-ratio associated to the involved ghosts. In particular, I will present results obtained when only horizontal and vertical convexity is assumed, and how the corresponding ghosts can be numerically characterized in terms of integer sequences.

  • 25 October 2023 10:00-11:00 UK time. Online on Zoom (link will be announced by email)

  • Luying Gui (School of Mathematics and Statistics, Nanjing University of Science and Technology, CN).

    Title. Histopathology image analysis of pancreatic ductal adenocarcinoma based on Unsupervised and weakly-supervised learning algorithms.
    Abstract. Histopathology images are considered the most reliable method for detecting and diagnosing cancer. However, analyzing these images is a complex task that requires a great deal of expertise. Pathologists need to search for useful information in huge pathology images to diagnose diseases in clinical applications. Additionally, analyzing pathology images can predict disease trends and prognosis. The development of deep neural networks has brought many breakthroughs in automated histopathology image analysis. However, these methods rely heavily on the availability of a large number of pixel-level labels, which is a labor-intensive and time-consuming task. To overcome these challenges, we investigated algorithms for histopathology image analysis using unlabeled or a small number of coarse-grained labels. We applied these algorithms to analyze histopathological images of pancreatic ductal adenocarcinoma (PDAC). Our experimental results demonstrate that these weakly-supervised and unsupervised-based algorithms accurately segment the components of the pathology images, thus laying the foundation for further image analysis and prognosis prediction studies.

  • 17 October 2023 11:00-12:00 UK time. In-Person and online (Math Building, Room 303). Joint CMIT-RCMM seminar talk.

  • Federico Sabina (Universidad Nacional Autónoma de México, MX).

    Title. Towards asymptotic modeling of seismic surface metabarriers: Transient scattering of a Rayleigh wave by a cluster of subwavelength resonators.
    Abstract. A seismic metabarrier (intended for surface waves mitigation effect) is modeled as a cluster of single-degree-of-freedom resonator units deposited on the surface of an isotropic homogeneous elastic half-space. It is assumed that each resonator has a frictionless rigid base of diameter much smaller than the wavelength of an incoming surface wave. The slow-motions asymptotic method is applied for constructing the first-order asymptotic model of multiple time-dependent scattering of a pulsed Rayleigh wave with respect to the vertical displacements of the resonators (including their rigid bases and inertial elements) and the normal contact forces (time-dependent integral characteristics of the contact reactions beneath the resonator bases). Both the stationary and transient multiple scattering scenarios are considered. The variation of the amplitude reduction factor due to the model parameters variation is studied in detail.

    Past Semesters

    Semester 2, 2022/23

    Semester 1, 2022/23