Periodic Reporting for period 1 - GRAPES (learninG, pRocessing, And oPtimising shapES)
Reporting period: 2019-12-01 to 2021-11-30
To devise robust and general methods for the aforementioned issues, GRAPES aims at advancing the state of the art in a variety of fields ranging from Computational and Numerical Mathematics, to Geometric Modelling and CAD, up to Data Science and Machine Learning. Besides applicable research, we address the technological challenge by creating synergies between Universities, Research Centers, and private companies. Our focus is the training of 15 PhD candidates; our structure allows them to benefit from top-notch research as well as a strong innovation component through a nexus of intersectoral secondments and Network-wide workshops.
The main results achieved so far can be partitioned into 3 scientific domains:
1. High-order methods and alternative representations deal with nonlinear methods for accurately representing complex shapes, while different representations offer complementary advantages. We have advanced in algebraic methods supporting such methods, including some prototype software for testing the new algorithms. Our emphasis has been on methods that exploit the structure of the given equations, such as their sparseness, aiming at techniques whose runtimes depend on the intrinsic rather than nominal input complexity.
2. Algebraic & numeric tools in shape optimisation and analysis have focused on isogeometric analysis, which allows for combining geometric modeling with computational fluid mechanics (typically governed by partial differential equations). Software engineering is a core target in bridging algorithms design with industrial-strength applications. A concrete example is modeling of ship parts for simulation, such as ship hulls, and propelers.
3. Machine Learning for shapes has concentrated on supervised methods for representing shapes and for offering robust methods in similarity search and object segmentation. We have pioneered specific neural network architectures for 3d objects as well as the combination of 2d image and 3d information (typically point clouds, but also meshes, implicit functions) for handling deformable objects. A more applied series of results concerns large scale 3D modeling and reconstruction with industrial partner GeometryFactory.
Applied results that may have a direct socio-economic impact include highly sophisticated methods for re-using geometric models across different platforms (with industrial partner ITI), shape optimisation for sensitivity analysis and other maritime applications by implementing viable search spaces, and modeling of dangerous geological regions. These innovation directions are expected to bear fruit within the lifetime of the Project. A more general direction of the Project that shall lead to tangible outcomes is to allow for complex geometric operations by novel AI algorithms in an accurate, efficient and, hopefully, predictable and understandable way.