Armand Kassaï Koupaï

Louis Serrano, Lise Le Boudec, Armand Kassaï Koupaï et al.

Machine learning approaches for solving partial differential equations require learning mappings between function spaces. While convolutional or graph neural networks are constrained to discretized functions, neural operators present a promising milestone toward mapping functions directly. Despite impressive results they still face challenges with respect to the domain geometry and typically rely on some form of discretization. In order to alleviate such limitations, we present CORAL, a new method that leverages coordinate-based networks for solving PDEs on general geometries. CORAL is designed to remove constraints on the input mesh, making it applicable to any spatial sampling and geometry. Its ability extends to diverse problem domains, including PDE solving, spatio-temporal forecasting, and inverse problems like geometric design. CORAL demonstrates robust performance across multiple resolutions and performs well in both convex and non-convex domains, surpassing or performing on par with state-of-the-art models.

Armand K. Koupai, Mohammud J. Bocus, Raul Santos-Rodriguez et al.

The pervasiveness of Wi-Fi signals provides significant opportunities for human sensing and activity recognition in fields such as healthcare. The sensors most commonly used for passive Wi-Fi sensing are based on passive Wi-Fi radar (PWR) and channel state information (CSI) data, however current systems do not effectively exploit the information acquired through multiple sensors to recognise the different activities. In this paper, we explore new properties of the Transformer architecture for multimodal sensor fusion. We study different signal processing techniques to extract multiple image-based features from PWR and CSI data such as spectrograms, scalograms and Markov transition field (MTF). We first propose the Fusion Transformer, an attention-based model for multimodal and multi-sensor fusion. Experimental results show that our Fusion Transformer approach can achieve competitive results compared to a ResNet architecture but with much fewer resources. To further improve our model, we propose a simple and effective framework for multimodal and multi-sensor self-supervised learning (SSL). The self-supervised Fusion Transformer outperforms the baselines, achieving a F1-score of 95.9%. Finally, we show how this approach significantly outperforms the others when trained with as little as 1% (2 minutes) of labelled training data to 20% (40 minutes) of labelled training data.

Armand Kassaï Koupaï, Lise Le Boudec, Patrick Gallinari

We introduce ECHO, a transformer-operator framework for generating million-point PDE trajectories. While existing neural operators (NOs) have shown promise for solving partial differential equations, they remain limited in practice due to poor scalability on dense grids, error accumulation during dynamic unrolling, and task-specific design. ECHO addresses these challenges through three key innovations. (i) It employs a hierarchical convolutional encode-decode architecture that achieves a 100 $\times$ spatio-temporal compression while preserving fidelity on mesh points. (ii) It incorporates a training and adaptation strategy that enables high-resolution PDE solution generation from sparse input grids. (iii) It adopts a generative modeling paradigm that learns complete trajectory segments, mitigating long-horizon error drift. The training strategy decouples representation learning from downstream task supervision, allowing the model to tackle multiple tasks such as trajectory generation, forward and inverse problems, and interpolation. The generative model further supports both conditional and unconditional generation. We demonstrate state-of-the-art performance on million-point simulations across diverse PDE systems featuring complex geometries, high-frequency dynamics, and long-term horizons.

Armand Kassaï Koupaï, Jorge Mifsut Benet, Yuan Yin et al.

Solving parametric partial differential equations (PDEs) presents significant challenges for data-driven methods due to the sensitivity of spatio-temporal dynamics to variations in PDE parameters. Machine learning approaches often struggle to capture this variability. To address this, data-driven approaches learn parametric PDEs by sampling a very large variety of trajectories with varying PDE parameters. We first show that incorporating conditioning mechanisms for learning parametric PDEs is essential and that among them, $\textit{adaptive conditioning}$, allows stronger generalization. As existing adaptive conditioning methods do not scale well with respect to the number of parameters to adapt in the neural solver, we propose GEPS, a simple adaptation mechanism to boost GEneralization in Pde Solvers via a first-order optimization and low-rank rapid adaptation of a small set of context parameters. We demonstrate the versatility of our approach for both fully data-driven and for physics-aware neural solvers. Validation performed on a whole range of spatio-temporal forecasting problems demonstrates excellent performance for generalizing to unseen conditions including initial conditions, PDE coefficients, forcing terms and solution domain. $\textit{Project page}$: https://geps-project.github.io

Alex Iacob, Pedro P. B. Gusmão, Nicholas D. Lane et al.

Human Activity Recognition (HAR) training data is often privacy-sensitive or held by non-cooperative entities. Federated Learning (FL) addresses such concerns by training ML models on edge clients. This work studies the impact of privacy in federated HAR at a user, environment, and sensor level. We show that the performance of FL for HAR depends on the assumed privacy level of the FL system and primarily upon the colocation of data from different sensors. By avoiding data sharing and assuming privacy at the human or environment level, as prior works have done, the accuracy decreases by 5-7%. However, extending this to the modality level and strictly separating sensor data between multiple clients may decrease the accuracy by 19-42%. As this form of privacy is necessary for the ethical utilisation of passive sensing methods in HAR, we implement a system where clients mutually train both a general FL model and a group-level one per modality. Our evaluation shows that this method leads to only a 7-13% decrease in accuracy, making it possible to build HAR systems with diverse hardware.