arXiv subjects

Olivier Peltre

Publications and source records attributed to Olivier Peltre.

14 recordsLinked to original sources

arXiv2026

E3J: An Efficient and Open-Source Backend for Euclidean Equivariant Operations on GPU and TPU

We present e3j, a fast Euclid-equivariance backend for geometric deep learning applications with JAX bindings for GPU and TPU. Leveraging both optimized CUDA and Pallas kernels and algorithmic improvements, the library achieves state-of-the-art throughput and runtime on both forward and backward paths. On a machine learning interatomic potential (MLIP) use case, it outperforms established backends, measuring up to 34% speed-up over cuEquivariance on water box NPT simulation using MACE, while remaining fully open source. E3j achieves over 80% efficiency over the H100 maximum memory bandwidth on tensor product operations, and in many cases more than doubles throughput of message passing convolutions forward compared to previously available backends. In addition, with the release of dedicated Pallas TPU kernel, e3j opens the possibility of large scale equivariant deep learning workloads on TPU architectures, which has so far been difficult to achieve. Our benchmarks show that e3j also achieves over 80% of a TPUv6e memory bandwidth, up to one order of magnitude more than e3nn-jax. The library is available on GitHub, PyPI and is released under an open source Apache 2.0 license.

cs.LG↗

arXiv2026

Machine Learning Interatomic Potentials: Advancing Open-Source Software for Efficient and Scalable Molecular Simulation

Machine learning interatomic potentials (MLIPs) enable atomistic simulations with near ab initio accuracy at significantly reduced computational cost, but their broader adoption is often limited by fragmented tooling, limited scalability, and inflexible software design. We present mlip v2, a new generation of the mlip library that advances efficient and scalable molecular simulation through a unified and extensible framework. The new release features a targeted API redesign with improved modularity and control, enabling flexible customization of training, data processing, and simulation workflows. It further integrates a new high-performance backend for equivariant operations, e3j, significantly accelerating model inference and simulations. In addition, the framework introduces a range of entirely new capabilities, including the eSEN architecture with a Mixture-of-Experts formulation for scalable training on large and diverse datasets, improved handling of electrostatics through more physically grounded charge modeling and long-range interaction treatment, and advanced simulation features such as NPT ensembles and nudged elastic band methods. Together, these extensions significantly broaden the scope of MLIP applications, enabling efficient modeling of complex, reactive, and out-of-equilibrium systems, and bridging the gap between ML research and practical molecular simulation applications. The library is available on GitHub and on PyPI under the Apache license 2.0.

physics.chem-ph↗

arXiv2026

Pretrained Model Representations as Acquisition Signals for Active Learning of MLIPs

Training machine learning interatomic potentials (MLIPs) for reactive chemistry is often bottlenecked by the high cost of quantum chemical labels and the scarcity of transition state configurations in candidate pools. Active learning (AL) can mitigate these costs, but its effectiveness hinges on the acquisition rule. We investigate whether the latent space of a pretrained MLIP already contains the information necessary for effective acquisition, eliminating the need for auxiliary uncertainty heads, Bayesian training and fine-tuning, or committee ensembles. We introduce two acquisition signals derived directly from a pretrained MACE potential: a finite-width neural tangent kernel (NTK) and an activation kernel built from hidden latent space features. On reactive-chemistry benchmarks, both kernels consistently outperform fixed-descriptor baselines, committee disagreement, and random acquisition, reducing the data required to reach performance targets by an average of 38% for energy error and 28% for force error. We further show that the pretrained model induces similarity spaces that preserve chemically meaningful structure and provide more reliable residual uncertainty estimates than randomly initialised or fixed-descriptor-based kernels. Our results suggest that pretraining aligns latent-space geometry with model error, yielding a practical and sufficient acquisition signal for reactive MLIP fine-tuning.

cs.LG↗

arXiv2026

Force-Aware Neural Tangent Kernels for Scalable and Robust Active Learning of MLIPs

Active learning for machine-learning interatomic potentials (MLIPs) must address several challenges to be practical: scaling to large candidate pools, leveraging energy-force supervision, and maintaining robustness when candidate pools are biased relative to the target distribution. In this work, we jointly address these challenges. We first introduce a linearly scaling acquisition framework based on chunked feature-space posterior-variance shortlisting. By avoiding materialisation of the candidate and train set kernels, this approach enables screening of ~200k structures within hours and applies broadly to acquisition strategies that score candidates based on molecular similarity metrics. We then extend the Neural Tangent Kernel (NTK) to a force-aware setting via mixed parameter-coordinate derivatives, yielding a force NTK and a joint energy-force NTK that provide natural similarity metrics for vector-field prediction. We demonstrate the effectiveness of the joint energy-force NTK on the OC20 dataset, where force-aware acquisition is crucial: it achieves the lowest energy and force MAE and RMSE across all metrics and distribution splits. Across T1x, PMechDB, and RGD benchmarks, our force NTK methods remain competitive with established baselines while being significantly more efficient than committee-based approaches. Under a controlled candidate-pool shift case study on T1x, acquisition based on pretrained MLIP embeddings and NTKs remains robust, whereas committee-based methods exhibit higher variance. Overall, these results show that a single pretrained MLIP can enable scalable, force-aware, and distribution-robust active learning for foundation-model fine-tuning.

cs.LG↗

arXiv2025

Machine Learning Interatomic Potentials: library for efficient training, model development and simulation of molecular systems

Machine Learning Interatomic Potentials (MLIP) are a novel in silico approach for molecular property prediction, creating an alternative to disrupt the accuracy/speed trade-off of empirical force fields and density functional theory (DFT). In this white paper, we present our MLIP library which was created with two core aims: (1) provide to industry experts without machine learning background a user-friendly and computationally efficient set of tools to experiment with MLIP models, (2) provide machine learning developers a framework to develop novel approaches fully integrated with molecular dynamics tools. The library includes in this release three model architectures (MACE, NequIP, and ViSNet), and two molecular dynamics (MD) wrappers (ASE, and JAX-MD), along with a set of pre-trained organics models. The seamless integration with JAX-MD, in particular, facilitates highly efficient MD simulations, bringing MLIP models significantly closer to industrial application. The library is available on GitHub and on PyPI under the Apache license 2.0.

physics.chem-ph↗

arXiv2025

Universally applicable and tunable graph-based coarse-graining for Machine learning force fields

Coarse-grained (CG) force field methods for molecular systems are a crucial tool to simulate large biological macromolecules and are therefore essential for characterisations of biomolecular systems. While state-of-the-art deep learning (DL)-based models for all-atom force fields have improved immensely over recent years, we observe and analyse significant limitations of the currently available approaches for DL-based CG simulations. In this work, we present the first transferable DL-based CG force field approach (i.e., not specific to only one narrowly defined system type) applicable to a wide range of biosystems. To achieve this, our CG algorithm does not rely on hard-coded rules and is tuned to output coarse-grained systems optimised for minimal statistical noise in the ground truth CG forces, which results in significant improvement of model training. Our force field model is also the first CG variant that is based on the MACE architecture and is trained on a custom dataset created by a new approach based on the fragmentation of large biosystems covering protein, RNA and lipid chemistry. We demonstrate that our model can be applied in molecular dynamics simulations to obtain stable and qualitatively accurate trajectories for a variety of systems, while also discussing cases for which we observe limited reliability.

physics.chem-ph↗

arXiv2023

Local Max-Entropy and Free Energy Principles, Belief Diffusions and their Singularities

A comprehensive picture of three Bethe-Kikuchi variational principles including their relationship to belief propagation (BP) algorithms on hypergraphs is given. The structure of BP equations is generalized to define continuous-time diffusions, solving localized versions of the max-entropy principle (A), the variational free energy principle (B), and a less usual equilibrium free energy principle (C), Legendre dual to A. Both critical points of Bethe-Kikuchi functionals and stationary beliefs are shown to lie at the non-linear intersection of two constraint surfaces, enforcing energy conservation and marginal consistency respectively. The hypersurface of singular beliefs, accross which equilibria become unstable as the constraint surfaces meet tangentially, is described by polynomial equations in the convex polytope of consistent beliefs. This polynomial is expressed by a loop series expansion for graphs of binary variables.

math-ph↗

arXiv2023

Equivariant Message Passing Neural Network for Crystal Material Discovery

Automatic material discovery with desired properties is a fundamental challenge for material sciences. Considerable attention has recently been devoted to generating stable crystal structures. While existing work has shown impressive success on supervised tasks such as property prediction, the progress on unsupervised tasks such as material generation is still hampered by the limited extent to which the equivalent geometric representations of the same crystal are considered. To address this challenge, we propose EMPNN a periodic equivariant message-passing neural network that learns crystal lattice deformation in an unsupervised fashion. Our model equivalently acts on lattice according to the deformation action that must be performed, making it suitable for crystal generation, relaxation and optimisation. We present experimental evaluations that demonstrate the effectiveness of our approach.

cs.LG↗

arXiv2022

Local Max-Entropy and Free Energy Principles Solved by Belief Propagation

A statistical system is classically defined on a set of microstates $E$ by a global energy function $H : E \to \mathbb{R}$, yielding Gibbs probability measures (softmins) $ρ^β(H)$ for every inverse temperature $β= T^{-1}$. Gibbs states are simultaneously characterized by free energy principles and the max-entropy principle, with dual constraints on inverse temperature $β$ and mean energy ${\cal U}(β) = \mathbb{E}_{ρ^β}[H]$ respectively. The Legendre transform relates these diverse variational principles which are unfortunately not tractable in high dimension. The global energy is generally given as a sum $H(x) = \sum_{\rm a \subset Ω} h_{\rm a}(x_{|\rm a})$ of local short-range interactions $h_{\rm a} : E_{\rm a} \to \mathbb{R}$ indexed by bounded subregions ${\rm a} \subset Ω$, and this local structure can be used to design good approximation schemes on thermodynamic functionals. We show that the generalized belief propagation (GBP) algorithm solves a collection of local variational principles, by converging to critical points of Bethe-Kikuchi approximations of the free energy $F(β)$, the Shannon entropy $S(\cal U)$, and the variational free energy ${\cal F}(β) = {\cal U} - β^{-1} S(\cal U)$, extending an initial correspondence by Yedidia et al. This local form of Legendre duality yields a possible degenerate relationship between mean energy ${\cal U}$ and $β$.

cond-mat.stat-mech↗

arXiv2020

Extra-fine sheaves and interaction decompositions

We introduce an original notion of extra-fine sheaf on a topological space, and a variant (hyper-extra-fine) for which Čech cohomology in strictly positive degree vanishes. We provide a characterization of such sheaves when the topological space is a partially ordered set (poset) equipped with the Alexandrov topology. Then we further specialize our results to some sheaves of vector spaces and injective maps, where extra-fineness is (essentially) equivalent to the decomposition of the sheaf into a direct sum of subfunctors, known as interaction decomposition, and can be expressed by a sum-intersection condition. We use these results to compute the dimension of the space of global sections when the presheaves are freely generated over a functor of sets, generalizing classical counting formulae for the number of solutions of the linearized marginal problem (Kellerer and Matúš). We finish with a comparison theorem between the Čech cohomology associated to a covering and the topos cohomology of the poset with coefficients in the presheaf, which is also the cohomology of a cosimplicial local system over the nerve of the poset. For that, we give a detailed treatment of cosimplicial local systems on simplicial sets. The appendixes present presheaves, sheaves and Čech cohomology, and their application to the marginal problem.

math.AT↗

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

Message-Passing Algorithms and Homology

This PhD thesis lays out algebraic and topological structures relevant for the study of probabilistic graphical models. Marginal estimation algorithms are introduced as diffusion equations of the form $\dot u = δφ$. They generalise the traditional belief propagation (BP) algorithm, and provide an alternative for contrastive divergence (CD) or Markov chain Monte Carlo (MCMC) algorithms, typically involved in estimating a free energy functional and its gradient w.r.t. model parameters. We propose a new homological picture where parameters are a collections of local interaction potentials $(u_α) \in A_0$, for $α$ running over the factor nodes of a given region graph. The boundary operator $δ$ mapping heat fluxes $(φ_{αβ}) \in A_1$ to a subspace $δA_1 \subseteq A_0$ is the discrete analog of a divergence. The total energy $H = \sum_αu_α$ defining the global probability $p = e^{-H} / Z$ is in one-to-one correspondence with a homology class $[u] = u + δA_1$ of interaction potentials, so that total energy remains constant when $u$ evolves up to a boundary term $δφ$. Stationary states of diffusion are shown to lie at the intersection of a homology class of potentials with a non-linear constraint surface enforcing consistency of the local marginals estimates. This picture allows us to precise and complete a proof on the correspondence between stationary states of BP and critical points of a local free energy functional (obtained by Bethe-Kikuchi approximations) and to extend the uniqueness result for acyclic graphs (i.e. trees) to a wider class of hypergraphs. In general, bifurcations of equilibria are related to the spectral singularities of a local diffusion operator, yielding new explicit examples of the degeneracy phenomenon. Work supervised by Pr. Daniel Bennequin

math-ph↗

arXiv2020

Geomstats: A Python Package for Riemannian Geometry in Machine Learning

We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more. We provide object-oriented and extensively unit-tested implementations. Among others, manifolds come equipped with families of Riemannian metrics, with associated exponential and logarithmic maps, geodesics and parallel transport. Statistics and learning algorithms provide methods for estimation, clustering and dimension reduction on manifolds. All associated operations are vectorized for batch computation and provide support for different execution backends, namely NumPy, PyTorch and TensorFlow, enabling GPU acceleration. This paper presents the package, compares it with related libraries and provides relevant code examples. We show that Geomstats provides reliable building blocks to foster research in differential geometry and statistics, and to democratize the use of Riemannian geometry in machine learning applications. The source code is freely available under the MIT license at \url{geomstats.ai}.

cs.LG↗

arXiv2019

A Homological Approach to Belief Propagation and Bethe Approximations

We introduce a differential complex of local observables given a decomposition of a global set of random variables into subsets. Its boundary operator allows us to define a transport equation equivalent to Belief Propagation. This definition reveals a set of conserved quantities under Belief Propagation and gives new insight on the relationship of its equilibria with the critical points of Bethe free energy.

math-ph↗