Model Reduction and Neural Networks

Derniers papiers

• On the Limits of Interpretable Machine Learning in Quintic Root Classification

  Rohan Thomas, Majid Bani-Yaghoub · 2 mars 2026

  Can Machine Learning (ML) autonomously recover interpretable mathematical structure from raw numerical data? We aim to answer this question using the classification of real-root configurations of polynomials up to degree five as a structured benchmark. We tested an extensive set of ML models, includ…

• Uncertainty-aware data assimilation through variational inference

  Anthony Frion, David S Greenberg · 2 mars 2026

  Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing deterministic machine learning approach, we propose a variational …

• Intrinsic Lorentz Neural Network

  Xianglong Shi, Ziheng Chen, Yunhan Jiang, Nicu Sebe · 2 mars 2026

  Real-world data frequently exhibit latent hierarchical structures, which can be naturally represented by hyperbolic geometry. Although recent hyperbolic neural networks have demonstrated promising results, many existing architectures remain partially intrinsic, mixing Euclidean operations with hyper…

• Neural Operators Can Discover Functional Clusters

  Yicen Li, Jose Antonio Lara Benitez, Ruiyang Hong, Anastasis Kratsios, Paul David McNicholas, Maarten Valentijn de Hoop · 2 mars 2026

  Operator learning is reshaping scientific computing by amortizing inference across infinite families of problems. While neural operators (NOs) are increasingly well understood for regression, far less is known for classification and its unsupervised analogue: clustering. We prove that sample-based n…

• Operator Learning with Domain Decomposition for Geometry Generalization in PDE Solving

  Jianing Huang, Kaixuan Zhang, Youjia Wu, Ze Cheng · 2 mars 2026

  Neural operators have become increasingly popular in solving \textit{partial differential equations} (PDEs) due to their superior capability to capture intricate mappings between function spaces over complex domains. However, the data-hungry nature of operator learning inevitably poses a bottleneck …

• Neural ensemble Kalman filter: Data assimilation for compressible flows with shocks

  Xu-Hui Zhou, Lorenzo Beronilla, Michael K. Sleeman, Hangchuan Hu, Matthias Morzfeld, Andrew M. Stuart, Tamer A. Zaki · 2 mars 2026

  Data assimilation (DA) for compressible flows with shocks is challenging because many classical DA methods generate spurious oscillations and nonphysical features near uncertain shocks. We focus here on the ensemble Kalman filter (EnKF). We show that the poor performance of the standard EnKF may be …

• BLISSNet: Deep Operator Learning for Fast and Accurate Flow Reconstruction from Sparse Sensor Measurements

  Maksym Veremchuk, K. Andrea Scott, Zhao Pan · 2 mars 2026

  Reconstructing fluid flows from sparse sensor measurements is a fundamental challenge in science and engineering. Widely separated measurements and complex, multiscale dynamics make accurate recovery of fine-scale structures difficult. In addition, existing methods face a persistent tradeoff: high-a…

• Structure tensor Reynolds-averaged Navier-Stokes turbulence models with equivariant neural networks

  Aaron Miller, Sahil Kommalapati, Robert Moser, Petros Koumoutsakos · 2 mars 2026

  Accurate and generalizable Reynolds-averaged Navier-Stokes (RANS) models for turbulent flows rely on effective closures, but currently available closures are notoriously unreliable. Kassinos et al. (J. Fluid Mechanics, 428, pp. 213-248, 2001) hypothesized that this unreliability of RANS models was d…

• HyperKKL: Enabling Non-Autonomous State Estimation through Dynamic Weight Conditioning

  Yahia Salaheldin Shaaban, Salem Lahlou, Abdelrahman Sayed Sayed · 27 février 2026

  This paper proposes HyperKKL, a novel learning approach for designing Kazantzis-Kravaris/Luenberger (KKL) observers for non-autonomous nonlinear systems. While KKL observers offer a rigorous theoretical framework by immersing nonlinear dynamics into a stable linear latent space, its practical realiz…

• Efficient Real-Time Adaptation of ROMs for Unsteady Flows Using Data Assimilation

  Isma\"el Zighed, Andrea N\'ovoa, Luca Magri, Taraneh Sayadi · 27 février 2026

  We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while requiring only a fraction of the computational time and relying solely on sparse observations of the full system. The architecture employs an encode-pro…

• Physics-informed neural particle flow for the Bayesian update step

  Domonkos Csuzdi, Tam\'as B\'ecsi, Oliv\'er T\"or\H{o} · 27 février 2026

  The Bayesian update step poses significant computational challenges in high-dimensional nonlinear estimation. While log-homotopy particle flow filters offer an alternative to stochastic sampling, existing formulations usually yield stiff differential equations. Conversely, existing deep learning app…

• Fast and Flexible Probabilistic Forecasting of Dynamical Systems using Flow Matching and Physical Perturbation

  Siddharth Rout, Eldad Haber, Stephane Gaudreault · 27 février 2026

  Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture uncertainty, standard Gaussian or uniform perturbations ofte…

• SODAs: Sparse Optimization for the Discovery of Differential and Algebraic Equations

  Manu Jayadharan, Christina Catlett, Arthur N. Montanari, Niall M. Mangan · 27 février 2026

  Differential-algebraic equations (DAEs) integrate ordinary differential equations (ODEs) with algebraic constraints, providing a fundamental framework for developing models of dynamical systems characterized by timescale separation, conservation laws, and physical constraints. While sparse optimizat…

• Aligning Few-Step Diffusion Models with Dense Reward Difference Learning

  Ziyi Zhang, Li Shen, Sen Zhang, Deheng Ye, Yong Luo, Miaojing Shi, Dongjing Shan, Bo Du, Dacheng Tao · 27 février 2026

  Few-step diffusion models enable efficient high-resolution image synthesis but struggle to align with specific downstream objectives due to limitations of existing reinforcement learning (RL) methods in low-step regimes with limited state spaces and suboptimal sample quality. To address this, we pro…

• MSINO: Curvature-Aware Sobolev Optimization for Manifold Neural Networks

  Suresan Pareth · 27 février 2026

  We introduce Manifold Sobolev Informed Neural Optimization (MSINO), a curvature aware training framework for neural networks defined on Riemannian manifolds. The method replaces standard Euclidean derivative supervision with a covariant Sobolev loss that aligns gradients using parallel transport and…

• Learning Physical Operators using Neural Operators

  Vignesh Gopakumar, Ander Gray, Dan Giles, Lorenzo Zanisi, Matt J. Kusner, Timo Betcke, Stanislas Pamela, Marc Peter Deisenroth · 27 février 2026

  Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work introduces a physics-informed training framework that addres…

• Probing the Geometry of Diffusion Models with the String Method

  Elio Moreau, Florentin Coeurdoux, Gr\'egoire Ferre, Eric Vanden-Eijnden · 26 février 2026

  Understanding the geometry of learned distributions is fundamental to improving and interpreting diffusion models, yet systematic tools for exploring their landscape remain limited. Standard latent-space interpolations fail to respect the structure of the learned distribution, often traversing low-d…

• D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matching

  Meet Hemant Parikh, Yaqin Chen, Jian-Xun Wang · 26 février 2026

  Data assimilation and scientific inverse problems require reconstructing high-dimensional physical states from sparse and noisy observations, ideally with uncertainty-aware posterior samples that remain faithful to learned priors and governing physics. While training-free conditional generation is w…

• Surrogate models for Rock-Fluid Interaction: A Grid-Size-Invariant Approach

  Nathalie C. Pinheiro, Donghu Guo, Hannah P. Menke, Aniket C. Joshi, Claire E. Heaney, Ahmed H. ElSheikh, Christopher C. Pain · 26 février 2026

  Modelling rock-fluid interaction requires solving a set of partial differential equations (PDEs) to predict the flow behaviour and the reactions of the fluid with the rock on the interfaces. Conventional high-fidelity numerical models require a high resolution to obtain reliable results, resulting i…

• Learning Complex Physical Regimes via Coverage-oriented Uncertainty Quantification: An application to the Critical Heat Flux

  Michele Cazzola, Alberto Ghione, Lucia Sargentini, Julien Nespoulous, Riccardo Finotello · 26 février 2026

  A central challenge in scientific machine learning (ML) is the correct representation of physical systems governed by multi-regime behaviours. In these scenarios, standard data analysis techniques often fail to capture the nature of the data, as the system's response varies significantly across the …

• MNO: Multiscale Neural Operator for 3D Computational Fluid Dynamics

  Qinxuan Wang, Chuang Wang, Mingyu Zhang, Jingwei Sun, Peipei Yang, Shuo Tang, Shiming Xiang · 26 février 2026

  Neural operators have emerged as a powerful data-driven paradigm for solving partial differential equations (PDEs), while their accuracy and scalability are still limited, particularly on irregular domains where fluid flows exhibit rich multiscale structures. In this work, we introduce the Multiscal…

• From Basis to Basis: Gaussian Particle Representation for Interpretable PDE Operators

  Zhihao Li, Yu Feng, Zhilu Lai, Wei Wang · 26 février 2026

  Learning PDE dynamics for fluids increasingly relies on neural operators and Transformer-based models, yet these approaches often lack interpretability and struggle with localized, high-frequency structures while incurring quadratic cost in spatial samples. We propose representing fields with a Gaus…

• The Error of Deep Operator Networks Is the Sum of Its Parts: Branch-Trunk and Mode Error Decompositions

  Alexander Heinlein, Johannes Taraz · 26 février 2026

  Operator learning has the potential to strongly impact scientific computing by learning solution operators for differential equations, potentially accelerating multi-query tasks such as design optimization and uncertainty quantification by orders of magnitude. Despite proven universal approximation …

• Shape-informed cardiac mechanics surrogates in data-scarce regimes via geometric encoding and generative augmentation

  Davide Carrara, Marc Hirschvogel, Francesca Bonizzoni, Stefano Pagani, Simone Pezzuto, Francesco Regazzoni · 25 février 2026

  High-fidelity computational models of cardiac mechanics provide mechanistic insight into the heart function but are computationally prohibitive for routine clinical use. Surrogate models can accelerate simulations, but generalization across diverse anatomies is challenging, particularly in data-scar…

• Regularity and Stability Properties of Selective SSMs with Discontinuous Gating

  Nikola Zubi\'c, Davide Scaramuzza · 25 février 2026

  Deep selective State-Space Models (SSMs), whose state-space parameters are modulated online by a selection signal, offer significant expressive power but pose challenges for stability analysis, especially under discontinuous gating. We study continuous-time selective SSMs through the lenses of passi…