Model Reduction and Neural Networks

Derniers papiers

• Bridging Diffusion Guidance and Anderson Acceleration via Hopfield Dynamics

  Kwanyoung Kim · 4 mars 2026

  Classifier-Free Guidance (CFG) has significantly enhanced the generative quality of diffusion models by extrapolating between conditional and unconditional outputs. However, its high inference cost and limited applicability to distilled or single-step models have shifted research focus toward attent…

• Enhancing Physics-Informed Neural Networks with Domain-aware Fourier Features: Towards Improved Performance and Interpretable Results

  Alberto Mi\~no Calero, Luis Salamanca, Konstantinos E. Tatsis · 4 mars 2026

  Physics-Informed Neural Networks (PINNs) incorporate physics into neural networks by embedding partial differential equations (PDEs) into their loss function. Despite their success in learning the underlying physics, PINN models remain difficult to train and interpret. In this work, a novel modeling…

• Physics-informed post-processing of stabilized finite element solutions for transient convection-dominated problems

  S\"uleyman Cengizci, \"Om\"ur U\u{g}ur, Srinivasan Natesan · 4 mars 2026

  The numerical simulation of convection-dominated transient transport phenomena poses significant computational challenges due to sharp gradients and propagating fronts across the spatiotemporal domain. Classical discretization methods often generate spurious oscillations, requiring advanced stabiliz…

• Generalized Discrete Diffusion with Self-Correction

  Linxuan Wang, Ziyi Wang, Yikun Bai, Wei Deng, Guang Lin, Qifan Song · 4 mars 2026

  Self-correction is an effective technique for maintaining parallel sampling in discrete diffusion models with minimal performance degradation. Prior work has explored self-correction at inference time or during post-training; however, such approaches often suffer from limited generalization and may …

• Safe and Robust Domains of Attraction for Discrete-Time Systems: A Set-Based Characterization and Certifiable Neural Network Estimation

  Mohamed Serry, Maxwell Fitzsimmons, Jun Liu · 4 mars 2026

  Analyzing nonlinear systems with attracting robust invariant sets (RISs) requires estimating their domains of attraction (DOAs). Despite extensive research, accurately characterizing DOAs for general nonlinear systems remains challenging due to both theoretical and computational limitations, particu…

• Using the SEKF to Transfer NN Models of Dynamical Systems with Limited Data

  Joshua E. Hammond, Tyler A. Soderstrom, Brian A. Korgel, Michael Baldea · 4 mars 2026

  Data-driven models of dynamical systems require extensive amounts of training data. For many practical applications, gathering sufficient data is not feasible due to cost or safety concerns. This work uses the Subset Extended Kalman Filter (SEKF) to adapt pre-trained neural network models to new, si…

• On Geometry Regularization in Autoencoder Reduced-Order Models with Latent Neural ODE Dynamics

  Mikhail Osipov · 4 mars 2026

  We investigate geometric regularization strategies for learned latent representations in encoder--decoder reduced-order models. In a fixed experimental setting for the advection--diffusion--reaction (ADR) equation, we model latent dynamics using a neural ODE and evaluate four regularization approach…

• Shape Derivative-Informed Neural Operators with Application to Risk-Averse Shape Optimization

  Xindi Gong, Dingcheng Luo, Thomas O'Leary-Roseberry, Ruanui Nicholson, Omar Ghattas · 4 mars 2026

  Shape optimization under uncertainty (OUU) is computationally intensive for classical PDE-based methods due to the high cost of repeated sampling-based risk evaluation across many uncertainty realizations and varying geometries, while standard neural surrogates often fail to provide accurate and eff…

• CFG-Ctrl: Control-Based Classifier-Free Diffusion Guidance

  Hanyang Wang, Yiyang Liu, Jiawei Chi, Fangfu Liu, Ran Xue, Yueqi Duan · 4 mars 2026

  Classifier-Free Guidance (CFG) has emerged as a central approach for enhancing semantic alignment in flow-based diffusion models. In this paper, we explore a unified framework called CFG-Ctrl, which reinterprets CFG as a control applied to the first-order continuous-time generative flow, using the c…

• Thermodynamic Regulation of Finite-Time Gibbs Training in Energy-Based Models: A Restricted Boltzmann Machine Study

  G\"orkem Can S\"uleymano\u{g}lu · 4 mars 2026

  Restricted Boltzmann Machines (RBMs) are typically trained using finite-length Gibbs chains under a fixed sampling temperature. This practice implicitly assumes that the stochastic regime remains valid as the energy landscape evolves during learning. We argue that this assumption can become structur…

• Stabilized Adaptive Loss and Residual-Based Collocation for Physics-Informed Neural Networks

  Divyavardhan Singh, Shubham Kamble, Dimple Sonone, Kishor Upla · 4 mars 2026

  Physics-Informed Neural Networks (PINNs) have been recognized as a mesh-free alternative to solve partial differential equations where physics information is incorporated. However, in dealing with problems characterized by high stiffness or shock-dominated dynamics, traditional PINNs have been found…

• Physics-Informed Neural Networks with Architectural Physics Embedding for Large-Scale Wave Field Reconstruction

  Huiwen Zhang, Feng Ye, Chu Ma · 4 mars 2026

  Large-scale wave field reconstruction requires precise solutions but faces challenges with computational efficiency and accuracy. The physics-based numerical methods like Finite Element Method (FEM) provide high accuracy but struggle with large-scale or high-frequency problems due to prohibitive com…

• From Complex Dynamics to DynFormer: Rethinking Transformers for PDEs

  Pengyu Lai, Yixiao Chen, Dewu Yang, Rui Wang, Feng Wang, Hui Xu · 4 mars 2026

  Partial differential equations (PDEs) are fundamental for modeling complex physical systems, yet classical numerical solvers face prohibitive computational costs in high-dimensional and multi-scale regimes. While Transformer-based neural operators have emerged as powerful data-driven alternatives, t…

• Inverse Reconstruction of Shock Time Series from Shock Response Spectrum Curves using Machine Learning

  Adam Watts (Los Alamos National Laboratory), Andrew Jeon (Los Alamos National Laboratory), Destry Newton (Los Alamos National Laboratory), Ryan Bowering (University of Rochester) · 4 mars 2026

  The shock response spectrum (SRS) is widely used to characterize the response of single-degree-of-freedom (SDOF) systems to transient accelerations. Because the mapping from acceleration time history to SRS is nonlinear and many-to-one, reconstructing time-domain signals from a target spectrum is in…

• Leray-Schauder Mappings for Operator Learning

  Emanuele Zappala · 3 mars 2026

  We present an algorithm for learning operators between Banach spaces, based on the use of Leray-Schauder mappings to learn a finite-dimensional approximation of compact subspaces. We show that the resulting method is a universal approximator of (possibly nonlinear) operators. We demonstrate the effi…

• Towards Generalizable PDE Dynamics Forecasting via Physics-Guided Invariant Learning

  Siyang Li, Yize Chen, Yan Guo, Ming Huang, Hui Xiong · 3 mars 2026

  Advanced deep learning-based approaches have been actively applied to forecast the spatiotemporal physical dynamics governed by partial differential equations (PDEs), which acts as a critical procedure in tackling many science and engineering problems. As real-world physical environments like PDE sy…

• Latent attention on masked patches for flow reconstruction

  Ben Eze, Luca Magri, Andrea N\'ovoa · 3 mars 2026

  Vision transformers have demonstrated outstanding performance on image generation applications, but their adoption in scientific disciplines, like fluid dynamics, has been limited. We introduce the Latent Attention on Masked Patches (LAMP) model, an interpretable regression-based modified vision tra…

• KROM: Kernelized Reduced Order Modeling

  Aras Bacho, Jonghyeon Lee, Houman Owhadi · 3 mars 2026

  We propose KROM, a kernel-based reduced-order framework for fast solution of nonlinear partial differential equations. KROM formulates PDE solution as a minimum-norm (Gaussian-process) recovery problem in an RKHS, and accelerates the resulting kernel solves by sparsifying the precision matrix via sp…

• Landing with the Score: Riemannian Optimization through Denoising

  Andrey Kharitenko, Zebang Shen, Riccardo de Santi, Niao He, Florian Doerfler · 3 mars 2026

  Under the data manifold hypothesis, high-dimensional data are concentrated near a low-dimensional manifold. We study the problem of Riemannian optimization over such manifolds when they are given only implicitly through the data distribution, and the standard manifold operations required by classica…

• A level-wise training scheme for learning neural multigrid smoothers with application to integral equations

  Lingfeng Li, Yin King Chu, Raymond Chan, Justin Wan · 3 mars 2026

  Convolution-type integral equations commonly occur in signal processing and image processing. Discretizing these equations yields large and ill-conditioned linear systems. While the classic multigrid method is effective for solving linear systems derived from partial differential equations (PDE) pro…

• Tackling multiphysics problems via finite element-guided physics-informed operator learning

  Yusuke Yamazaki, Reza Najian Asl, Markus Apel, Mayu Muramatsu, Shahed Rezaei · 3 mars 2026

  This work presents a finite element-guided physics-informed operator learning framework for multiphysics problems with coupled partial differential equations (PDEs) on arbitrary domains. Implemented with Folax, a JAX-based operator-learning platform, the proposed framework learns a mapping from the …

• Super-resolution of turbulent reacting flows on complex meshes using graph neural networks

  Priyabrat Dash, Konduri Aditya, Christos E. Frouzakis, Mathis Bode · 3 mars 2026

  State-of-the-art deep learning models have been extensively utilized to reconstruct small-scale structures from coarse-grained data in turbulent flows. However, their application has predominantly been restricted to structured uniform meshes, limiting their applicability to data associated with comp…

• PhysFormer: A Physics-Embedded Generative Model for Physically Self-Consistent Spectral Synthesis

  Siqi Wang, Mengmeng Zhang, Yude Bu, Chaozhou Mou · 3 mars 2026

  In scientific and engineering domains, modeling high-dimensional complex systems governed by partial differential equations (PDEs) remains challenging in terms of physical consistency and numerical stability. However, existing approaches, such as physics-informed neural networks (PINNs), typically r…

• Randomized Neural Networks for Partial Differential Equation on Static and Evolving Surfaces

  Jingbo Sun, Fei Wang · 3 mars 2026

  Surface partial differential equations arise in numerous scientific and engineering applications. Their numerical solution on static and evolving surfaces remains challenging due to geometric complexity and, for evolving geometries, the need for repeated mesh updates and geometry or solution transfe…

• One Operator to Rule Them All? On Boundary-Indexed Operator Families in Neural PDE Solvers

  Lennon J. Shikhman · 3 mars 2026

  Neural PDE solvers are often described as learning solution operators that map problem data to PDE solutions. In this work, we argue that this interpretation is generally incorrect when boundary conditions vary. We show that standard neural operator training implicitly learns a boundary-indexed fami…