In many engineering and physics domains, the shape or geometry of an object directly influences its performance with regard to some metric. Simple examples include the shape of an airplane wing affecting its lift-to-drag ratio, or the geometry/structure of a bridge influencing the maximum load weight which can safely traverse it. “Shape optimization” refers to the task of identifying the ideal shape/geometry of such an object which can maximize or minimize a metric of interest with respect to that object. This project looks to leverage Physics Informed Neural Networks (PINN) and Coordinate Projection Networks (also called shape networks in the literature) to develop machine learning architectures which can quickly and efficiently perform this task.
Total project length: 175 hours.
Recent research has demonstrated the feasibility of using PINNs (Paper 1) for performing shape optimization (Paper 2). Since that initial research, a number of techniques have been proposed and verified to help improve the performance of PINNs in general to overcome the shortcomings that generally plague PINNs: slow convergence, overfitting, and spectral bias in which low frequency solutions are preferentially converged towards during training. In particular, the use of grid-based structures (PIXEL, see Paper 3), and their further development into Physics-Informed Gaussians (PIG, see Paper 4), have improved upon many of these shortcomings. In this work, we look to apply these new techniques to the task of shape optimization. We additionally look to apply them to novel use-cases to demonstrate the usefulness of this approach. One use-case of particular interest is in the design optimization of Paul Traps, which are used in many applications ranging from quantum computing to mass spectrometry and atomic clocks (see Paper 5). The following task ideas are therefore proposed for this project:
Advanced
Please use this link to access the test for this project.
Please DO NOT contact mentors directly by email. Questions should instead be directed to ml4-sci@cern.ch which is forwarded to mentors. To submit your proposal, CV, and test task solutions, please use this Google form.