arXiv subjects

Yaël Frégier

Publications and source records attributed to Yaël Frégier.

7 recordsLinked to original sources

arXiv2026

ED-CSP: Crystal Structure Prediction from Electron Diffraction

Recovering a periodic 3D crystal structure from sparse, unindexed electron diffraction (ED) observations is a challenging generative inverse problem. Existing ED-based learning methods mainly predict crystallographic labels, reconstruct structures from indexed reflections, or retrieve candidates from finite structure libraries. Here, we introduce ED-CSP, a machine learning framework that predicts crystal structures from chemical composition, atom count, and multiple detector-plane ED spot sets. ED-CSP combines a relational set encoder, permutation-invariant multi-view aggregation, and a periodic flow generator to jointly predict lattice parameters and fractional atomic coordinates. To train the model, we construct ED-CS, a dataset of 4.85 million simulated multi-view ED crystal structures, deduplicated across seven materials repositories and filtered to exclude CHILI-100K overlaps. On 2,075 held-out CHILI-100K materials, ED-CSP trained only on CHILI achieves a structural match rate of 57.49% MR@5, outperforming PXRDGen (52.92%), a state-of-the-art crystal structure prediction model conditioned on powder X-ray diffraction. Scaling training data further improves performance: initializing from a one-million-structure precursor raises MR@5 to 66.27%. On 1,024 compositions absent from the training retrieval library, the model still achieves 53.52% MR@5, demonstrating true generative capability beyond exact-formula retrieval. Replacing target ED observations with diffraction from non-isomorphic structures of identical composition decreases MR@5 by 22.09 percentage points, confirming that predictions depend on the input diffraction patterns rather than composition alone. ED-CSP and ED-CS establish a benchmark for generative crystal structure prediction from sparse ED observations and provide a foundation for future transfer to experimental data.

cs.LG↗

arXiv2025

Diffusion-based translation between unpaired spontaneous premature neonatal EEG and fetal MEG

Background and objective: Brain activity in premature newborns has traditionally been studied using electroencephalography (EEG), leading to substantial advances in our understanding of early neural development. However, since brain development takes root at the fetal stage, a critical window of this process remains largely unknown. The only technique capable of recording neural activity in the intrauterine environment is fetal magnetoencephalography (fMEG), but this approach presents challenges in terms of data quality and scarcity. Using artificial intelligence, the present research aims to transfer the well-established knowledge from EEG studies to fMEG to improve understanding of prenatal brain development, laying the foundations for better detection and treatment of potential pathologies. Methods: We developed an unpaired diffusion translation method based on dual diffusion bridges, which notably includes numerical integration improvements to obtain more qualitative results at a lower computational cost. Models were trained on our unpaired dataset of bursts of spontaneous activity from 30 high-resolution premature newborns EEG recordings and 44 fMEG recordings. Results: We demonstrate that our method achieves significant improvement upon previous results obtained with Generative Adversarial Networks (GANs), by almost 5% on the mean squared error in the time domain, and completely eliminating the mode collapse problem in the frequency domain, thus achieving near-perfect signal fidelity. Conclusion: We set a new state of the art in the EEG-fMEG unpaired translation problem, as our developed tool completely paves the way for early brain activity analysis. Overall, we also believe that our method could be reused for other unpaired signal translation applications.

eess.SP↗

arXiv2023

Unified Model for Crystalline Material Generation

One of the greatest challenges facing our society is the discovery of new innovative crystal materials with specific properties. Recently, the problem of generating crystal materials has received increasing attention, however, it remains unclear to what extent, or in what way, we can develop generative models that consider both the periodicity and equivalence geometric of crystal structures. To alleviate this issue, we propose two unified models that act at the same time on crystal lattice and atomic positions using periodic equivariant architectures. Our models are capable to learn any arbitrary crystal lattice deformation by lowering the total energy to reach thermodynamic stability. Code and data are available at https://github.com/aklipf/GemsNet.

cond-mat.mtrl-sci↗

arXiv2023

Optimized Crystallographic Graph Generation for Material Science

Graph neural networks are widely used in machine learning applied to chemistry, and in particular for material science discovery. For crystalline materials, however, generating graph-based representation from geometrical information for neural networks is not a trivial task. The periodicity of crystalline needs efficient implementations to be processed in real-time under a massively parallel environment. With the aim of training graph-based generative models of new material discovery, we propose an efficient tool to generate cutoff graphs and k-nearest-neighbours graphs of periodic structures within GPU optimization. We provide pyMatGraph a Pytorch-compatible framework to generate graphs in real-time during the training of neural network architecture. Our tool can update a graph of a structure, making generative models able to update the geometry and process the updated graph during the forward propagation on the GPU side. Our code is publicly available at https://github.com/aklipf/mat-graph.

cond-mat.mtrl-sci↗

arXiv2020

Mind2Mind : transfer learning for GANs

Training generative adversarial networks (GANs) on high quality (HQ) images involves important computing resources. This requirement represents a bottleneck for the development of applications of GANs. We propose a transfer learning technique for GANs that significantly reduces training time. Our approach consists of freezing the low-level layers of both the critic and generator of the original GAN. We assume an autoencoder constraint in order to ensure the compatibility of the internal representations of the critic and the generator. This assumption explains the gain in training time as it enables us to bypass the low-level layers during the forward and backward passes. We compare our method to baselines and observe a significant acceleration of the training. It can reach two orders of magnitude on HQ datasets when compared with StyleGAN. We prove rigorously, within the framework of optimal transport, a theorem ensuring the convergence of the learning of the transferred GAN. We moreover provide a precise bound for the convergence of the training in terms of the distance between the source and target dataset.

cs.LG↗

arXiv2020

Deformation-obstruction theory for diagrams of algebras and applications to geometry

Let $X$ be a smooth complex algebraic variety and let $\operatorname{Coh} (X)$ denote its Abelian category of coherent sheaves. By the work of W. Lowen and M. Van den Bergh, it is known that the deformation theory of $\operatorname{Coh} (X)$ as an Abelian category can be seen to be controlled by the Gerstenhaber-Schack complex associated to the restriction of the structure sheaf $\mathcal O_X \vert_{\mathfrak U}$ to a cover of affine open sets. We construct an explicit $L_\infty$ algebra structure on the Gerstenhaber-Schack complex controlling the higher deformation theory of $\mathcal O_X \vert_{\mathfrak U}$ in case $X$ can be covered by two acyclic open sets, giving an explicit deformation-obstruction calculus for such deformations. Deformations of complex structures and deformation quantizations of $X$ are recovered as degenerate cases, as is shown by means of concrete examples.

math.QA↗

arXiv2007

Dequantized Differential Operators between Tensor Densities as Modules over the Lie Algebra of Contact Vector Fields

In recent years, algebras and modules of differential operators have been extensively studied. Equivariant quantization and dequantization establish a tight link between invariant operators connecting modules of differential operators on tensor densities, and module morphisms that connect the corresponding dequantized spaces. In this paper, we investigate dequantized differential operators as modules over a Lie subalgebra of vector fields that preserve an additional structure. More precisely, we take an interest in invariant operators between dequantized spaces, viewed as modules over the Lie subalgebra of infinitesimal contact or projective contact transformations. The principal symbols of these invariant operators are invariant tensor fields. We first provide full description of the algebras of such affine-contact- and contact-invariant tensor fields. These characterizations allow showing that the algebra of projective-contact-invariant operators between dequantized spaces implemented by the same density weight, is generated by the vertical cotangent lift of the contact form and a generalized contact Hamiltonian. As an application, we prove a second key-result, which asserts that the Casimir operator of the Lie algebra of infinitesimal projective contact transformations, is diagonal. Eventually, this upshot entails that invariant operators between spaces induced by different density weights, are made up by a small number of building bricks that force the parameters of the source and target spaces to verify Diophantine-type equations.

math.RT↗