Sepehr Mousavi

Sai Keerthana Karnam, Abhisek Dash, Antariksh Das et al.

The GDPR's Right of Access aims to empower users with control over their personal data via Data Download Packages (DDPs). However, their effectiveness is often compromised by inconsistent platform implementations, questionable data reliability, and poor user comprehensibility. This paper conducts a comprehensive audit of DDPs from three social media platforms (TikTok, Instagram, and YouTube) to systematically assess these critical drawbacks. Despite offering similar services, we find that these platforms demonstrate significant inconsistencies in implementing the Right of Access, evident in varying levels of shared data. Critically, the failure to disclose processing purposes, retention periods, and other third-party data recipients serves as a further indicator of non-compliance. Our reliability evaluations, using bots and user-donated data, reveal that while TikTok's DDPs offer more consistent and complete data, others exhibit notable shortcomings. Similarly, our assessment of comprehensibility, based on surveys with 400 participants, indicates that current DDPs substantially fall short of GDPR's standards. To improve the comprehensibility, we propose and demonstrate a two-layered approach by: (1)~enhancing the data representation itself using stakeholder interpretations; and (2)~incorporating a user-friendly extension (\textit{Know Your Data}) for intuitive data visualization where users can control the level of transparency they prefer. Our findings underscore the need for clearer and non-conflicting regulatory guidance, stricter enforcement, and platform commitment to realize the goal of GDPR's Right of Access.

Sepehr Mousavi, Shizheng Wen, Levi Lingsch et al.

Learning the solution operators of PDEs on arbitrary domains is challenging due to the diversity of possible domain shapes, in addition to the often intricate underlying physics. We propose an end-to-end graph neural network (GNN) based neural operator to learn PDE solution operators from data on point clouds in arbitrary domains. Our multi-scale model maps data between input/output point clouds by passing it through a downsampled regional mesh. The approach includes novel elements aimed at ensuring spatio-temporal resolution invariance. Our model, termed RIGNO, is tested on a challenging suite of benchmarks composed of various time-dependent and steady PDEs defined on a diverse set of domains. We demonstrate that RIGNO is significantly more accurate than neural operator baselines and robustly generalizes to unseen resolutions both in space and in time. Our code is publicly available at github.com/camlab-ethz/rigno.

Shizheng Wen, Arsh Kumbhat, Levi Lingsch et al.

The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator learning algorithms to approximate such PDEs, we find that accurate models are not necessarily computationally efficient and vice versa. We address this issue by proposing a geometry aware operator transformer (GAOT) for learning PDEs on arbitrary domains. GAOT combines novel multiscale attentional graph neural operator encoders and decoders, together with geometry embeddings and (vision) transformer processors to accurately map information about the domain and the inputs into a robust approximation of the PDE solution. Multiple innovations in the implementation of GAOT also ensure computational efficiency and scalability. We demonstrate this significant gain in both accuracy and efficiency of GAOT over several baselines on a large number of learning tasks from a diverse set of PDEs, including achieving state of the art performance on three large scale three-dimensional industrial CFD datasets.

Sepehr Mousavi, Siddhartha Mishra, Laura De Lorenzis

Neural operators have emerged as powerful surrogates for the solution of partial differential equations (PDEs), yet their ability to handle general, highly variable boundary conditions (BCs) remains limited. Existing approaches often fail when the solution operator exhibits strong sensitivity to boundary forcings. We propose a general framework for conditioning neural operators on complex non-homogeneous BCs through function extensions. Our key idea is to map boundary data to latent pseudo-extensions defined over the entire spatial domain, enabling any standard operator learning architecture to consume boundary information. The resulting operator, coupled with an arbitrary domain-to-domain neural operator, can learn rich dependencies on complex BCs and input domain functions at the same time. To benchmark this setting, we construct 18 challenging datasets spanning Poisson, linear elasticity, and hyperelasticity problems, with highly variable, mixed-type, component-wise, and multi-segment BCs on diverse geometries. Our approach achieves state-of-the-art accuracy, outperforming baselines by large margins, while requiring no hyperparameter tuning across datasets. Overall, our results demonstrate that learning boundary-to-domain extensions is an effective and practical strategy for imposing complex BCs in existing neural operator frameworks, enabling accurate and robust scientific machine learning models for a broader range of PDE-governed problems.