Model Reduction and Neural Networks

Derniers papiers

• Momentum-Conserving Graph Neural Networks for Deformable Objects

  Jiahong Wang, Logan Numerow, Stelian Coros, Christian Theobalt, Vahid Babaei, Bernhard Thomaszewski · 30 avril 2026

  Graph neural networks (GNNs) have emerged as a versatile and efficient option for modeling the dynamic behavior of deformable materials. While GNNs generalize readily to arbitrary shapes, mesh topologies, and material parameters, existing architectures struggle to correctly predict the temporal evol…

• PiGGO: Physics-Guided Learnable Graph Kalman Filters for Virtual Sensing of Nonlinear Dynamic Structures under Uncertainty

  Marcus Haywood-Alexander, Gregory Duth\'e, Eleni Chatzi · 30 avril 2026

  Digital twins provide a powerful paradigm for diagnostic and prognostic tasks in the monitoring and control of engineered systems; however, their deployment for complex structures remains challenged by model-form uncertainty, arising from unknown nonlinear dynamics, and by sparse sensing. These limi…

• Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the $L^p$-sense

  Julia Ackermann, Arnulf Jentzen, Thomas Kruse, Benno Kuckuck, Joshua Lee Padgett · 30 avril 2026

  Recently, several deep learning (DL) methods for approximating high-dimensional partial differential equations (PDEs) have been proposed. The interest that these methods have generated in the literature is in large part due to simulations which appear to demonstrate that such DL methods have the cap…

• A Randomized PDE Energy driven Iterative Framework for Efficient and Stable PDE Solutions

  Yi Bing, Zheng Ran, Fu Jinyang, Liu Long, Peng Xiang · 30 avril 2026

  Efficient and stable solution of partial differential equations (PDEs) is central to scientific and engineering applications, yet existing numerical solvers rely heavily on matrix based discretizations, while learning based methods require costly training and often suffer from limited generalization…

• PINNs in More General Geometry

  Edward Hirst · 29 avril 2026

  Neural architectures trained with losses inspired by differential conditions are the basis for PINN models. Since many constructions in differential geometry may be framed as minimisation of a differential functional, these functionals can be coded as loss functions to align the AI loss-minimisation…

• Teacher Forcing as Generalized Bayes: Optimization Geometry Mismatch in Switching Surrogates for Chaotic Dynamics

  Andre Herz, Daniel Durstewitz, Georgia Koppe · 29 avril 2026

  Identity teacher forcing (ITF) enables stable training of deterministic recurrent surrogates for chaotic dynamical systems and has been highly effective for dynamical systems reconstruction (DSR) with recurrent neural networks (RNNs), including interpretable almost-linear RNNs (AL-RNNs). However, as…

• Residual-loss Anomaly Analysis of Physics-Informed Neural Networks: An Inverse Method for Change-point Detection in Nonlinear Dynamical Systems with Regime Switching

  Yuhe Bai, Chengli Tan, Jiaqi Li, Xiangjun Wang, Zhikun Zhang · 29 avril 2026

  Nonlinear dynamical systems with regime transitions are typically described by ordinary differential equations with jumping parameters parameters. Traditional methods often treat change-point detection and parameter estimation as separate tasks, ignoring the inherent coupling between them. To addres…

• Shearlet Neural Operators for Anisotropic-Shock-Dominated and Multi-scale parametric partial differential equations

  Fabio Pereira dos Santos, Julio de Castro Vargas Fernandes, Adriano Mauricio de Almeida Cortes · 29 avril 2026

  Neural operators have emerged as powerful data-driven surrogates for learning solution operators of parametric partial differential equations (PDEs). However, widely used Fourier Neural Operators (FNOs) rely on global Fourier representations, which can be inefficient for resolving anisotropic struct…

• Dictionary learning for Kernel EDMD

  Erik Lien Bolager, Boumediene Hamzi, Houman Owhadi, Ioannis G. Kevrekidis, Felix Dietrich · 29 avril 2026

  Studying nonlinear dynamical systems through their state space behavior can be challenging, and one possible alternative is to analyze them via their associated Koopman operator. This turns the nonlinear problem into a linear, infinite-dimensional one. To approximate the operator in finite dimension…

• Adaptive Meta-Learning Stochastic Gradient Hamiltonian Monte Carlo Simulation for Bayesian Updating of Structural Dynamic Models

  Xianghao Meng, James L. Beck, Yong Huang, Hui Li · 29 avril 2026

  In the last few decades, Markov chain Monte Carlo (MCMC) methods have been widely applied to Bayesian updating of structural dynamic models in the field of structural health monitoring. Recently, several MCMC algorithms have been developed that incorporate neural networks to enhance their performanc…

• Partition-of-Unity Gaussian Kolmogorov-Arnold Networks

  Amir Nooeizadegan · 29 avril 2026

  Gaussian basis functions provide an efficient and flexible alternative to spline activations in KANs. In this work, we introduce the partition-of-unity Gaussian KAN (PU-GKAN), a Shepard-type normalized Gaussian KAN in which the Gaussian basis values on each edge are divided by their local sum over f…

• GeoFunFlow-3D: A Physics-Guided Generative Flow Matching Framework for High-Fidelity 3D Aerodynamic Inference over Complex Geometries

  Ruiling Jiang, Yong Zhang, Houbiao Li · 28 avril 2026

  Deep generative models and neural operators have demonstrated significant potential for 3D aerodynamic inference. However, they often face inherent challenges in maintaining physical consistency and preserving high-frequency features, primarily due to spectral bias and gradient conflicts within the …

• Solving Nonlinear PDEs with Sparse Radial Basis Function Networks

  Zihan Shao, Konstantin Pieper, Xiaochuan Tian · 28 avril 2026

  We propose a novel framework for solving nonlinear PDEs using sparse radial basis function (RBF) networks. Sparsity-promoting regularization is employed to prevent over-parameterization and reduce redundant features. This work is motivated by longstanding challenges in traditional RBF collocation me…

• Conditional Score-Based Modeling of Effective Langevin Dynamics

  Ludovico T. Giorgini · 28 avril 2026

  Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time trajectory increments, state-space partitioning, or repeated simul…

• Deep Learning of Solver-Aware Turbulence Closures from Nudged LES Dynamics

  Ashwin Suriyanarayanan, Melissa Adrian, Dibyajyoti Chakraborty, Romit Maulik · 28 avril 2026

  Deep learning approaches have shown remarkable promise in turbulence closure modeling for large eddy simulations (LES). The differentiable physics paradigm uses the so-called a-posteriori approach for learning by embedding a neural network closure directly inside the solver and optimizing its learna…

• Adaptive-Distribution Randomized Neural Networks for PDEs: A Low-Dimensional Distribution-Learning Framework

  You Yang, Fei Wang · 28 avril 2026

  Randomized neural networks (RaNNs) are attractive for partial differential equations (PDEs) because they replace expensive end-to-end training with a linear least-squares solve over randomized hidden features. Their practical performance, however, depends strongly on the sampling distribution of the…

• Conflict-Aware Harmonized Rotational Gradient for Multiscale Kinetic Regimes

  Zhangyong Liang · 28 avril 2026

  In this paper, we propose a harmonized rotational gradient method, termed HRGrad, for simultaneously tackling multiscale time-dependent kinetic problems with varying small parameters. These parameters exhibit asymptotic transitions from microscopic to macroscopic physics, making it a challenging m…

• Learning Interpretable PDE Representations for Generative Reconstructions with Structured Sparsity

  Valerie Tsao, Nathaniel Chaney, Manolis Veveakis · 28 avril 2026

  Scientific measurements are often bottlenecked by suboptimal conditions, whether that be noise, incomplete spatial coverage, or limited resolution, rendering accurate field reconstruction a difficult task. We introduce LatentPDE, a latent diffusion framework designed to simultaneously resolve sparse…

• Physics-Guided Dimension Reduction for Simulation-Free Operator Learning of Stiff Differential-Algebraic Systems

  Huy Hoang Le, Haoguang Wang, Christian Moya, Marcos Netto, Guang Lin · 28 avril 2026

  Neural surrogates for stiff differential-algebraic equations (DAEs) face two barriers: soft-constraint methods leave algebraic residuals that stiffness amplifies into errors, and hard-constraint methods require trajectory data from stiff integrators. We introduce an extended Newton implicit layer th…

• When PINNs Go Wrong: Pseudo-Time Stepping Against Spurious Solutions

  Sifan Wang, Shawn Koohy, Yiping Lu, Paris Perdikaris · 28 avril 2026

  Physics-informed neural networks (PINNs) provide a promising machine learning framework for solving partial differential equations, but their training often breaks down on challenging problems, sometimes converging to physically incorrect solutions despite achieving small residual losses. This failu…

• Nonlinear Non-Gaussian Density Steering with Input and Noise Channel Mismatch: Sinkhorn with Memory for Solving the Control-affine Schr\"{o}dinger Bridge Problem

  Georgiy A. Bondar, Asmaa Eldesoukey, Yongxin Chen, Abhishek Halder · 28 avril 2026

  Solutions to the Schr\"{o}dinger bridge problem and its generalizations yield feedback control policies for optimal density steering over a controlled diffusion. To numerically compute the same, the dynamic Sinkhorn recursion has become a standard approach. The mathematical engine behind this approa…

• FLUID: Flow-based Unified Inference for Dynamics

  Tiangang Cui, Xiaodong Feng, Chenlong Pei, Xiaoliang Wan, Tao Zhou · 27 avril 2026

  Bayesian filtering and smoothing for high-dimensional nonlinear dynamical systems are fundamental yet challenging problems in many areas of science and engineering. In this work, we propose FLUID, a flow-based unified amortized inference framework for filtering and smoothing dynamics. The core idea …

• LTBs-KAN: Linear-Time B-splines Kolmogorov-Arnold Networks

  Eduardo Said Merin-Martinez, Andres Mendez-Vazquez, Eduardo Rodriguez-Tello · 27 avril 2026

  Kolmogorov-Arnold Networks (KANs) are a recent neural network architecture offering an alternative to Multilayer Perceptrons (MLPs) with improved explainability and expressibility. However, KANs are significantly slower than MLPs due to the recursive nature of B-spline function computations, limitin…

• Online Distributional Regression

  Simon Hirsch, Jonathan Berrisch, Florian Ziel · 27 avril 2026

  Large-scale streaming data are common in modern machine learning applications and have led to the development of online learning algorithms. Many fields, such as supply chain management, weather and meteorology, energy markets, and finance, have pivoted toward probabilistic forecasting. This results…

• Transferable Physics-Informed Representations via Closed-Form Head Adaptation

  Jian Cheng Wong, Isaac Yin Chung Lai, Pao-Hsiung Chiu, Chin Chun Ooi, Abhishek Gupta, Yew-Soon Ong · 24 avril 2026

  Physics-informed neural networks (PINNs) have garnered significant interest for their potential in solving partial differential equations (PDEs) that govern a wide range of physical phenomena. By incorporating physical laws into the learning process, PINN models have demonstrated the ability to lear…