Model Reduction and Neural Networks

Derniers papiers

• Optimal scenario design for climate emulation

  Christopher B. Womack, Shahine Bouabid, Andrei Sokolov, Popat Salunke, Glenn Flierl, Sebastian D. Eastham, Noelle E. Selin · 18 juin 2026

  As deep learning for physical systems continues to grow in popularity, efforts to improve generalizability have primarily focused on designing architectures that embed physical constraints. However, for machine-learning surrogate climate models (emulators), we show that the low structural diversity …

• A Link between Shock-wave Theory and Symmetry-reduced Stochastic Gradient Descent for Artificial Neural Networks

  Taiki Miyagawa · 18 juin 2026

  We develop a mathematically explicit link between shock-wave theory and the symmetry-quotiented learning dynamics of stochastic gradient descent, drawing on differential geometry, Lie group theory, and fluid mechanics. Specifically, after quotienting parameter symmetries and applying local-entropy c…

• P-K-GCN: Physics-augmented Koopman-enhanced Graph Convolutional Network for Deep Spatiotemporal Super-resolution

  Xizhuo (Cici), Zhang, Zekai Wang, Fei Liu, Bing Yao · 18 juin 2026

  High-fidelity simulation of spatiotemporal dynamics is computationally prohibitive, necessitating efficient super-resolution techniques to reconstruct high-resolution data from coarse-grained inputs. Traditional data-driven methods often lack physical constraints, and simple physics-informed learnin…

• Ghost Attractor Networks: Basin-Structured Dynamical Decoders for Closed-Loop Sequential Generation

  Tianyu Wang, Ying Wang, Zhihao Liu, Xi Vincent Wang, Lihui Wang · 18 juin 2026

  Sequential output generation with large-scale Transformer and diffusion decoders pays a memory cost that grows with sequence length, plus iterative per-step computation. Replacing them with small feed-forward decoders restores efficiency but produces unstructured latent representations that limit cl…

• OrthoReg: Orthogonal Regularization for Hybrid Symbolic-Neural Dynamical Systems

  Till Richter, Niki Kilbertus · 18 juin 2026

  Dynamical systems are fundamental to modeling the natural world, yet modeling them involves a persistent trade-off: manually prescribed mechanistic models are interpretable by design but often overly simplistic and misspecified; in contrast, flexible data-driven neural methods lack physical insight.…

• Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems

  Kuilin Qin, Lianfang Wang, Xu Sun, Jiwei Jia, Yu Wang, Yong Wang, Yuping Duan · 18 juin 2026

  Operator learning is an emerging interdisciplinary field that integrates machine learning with scientific computing. By mapping infinite-dimensional function spaces, this approach provides an efficient surrogate modeling framework for high-dimensional partial differential equations (PDEs). Compared …

• Acceleration of an algebraic multigrid pressure solver using graph neural networks

  Eric Chill\'on, Artur K. Lidtke, Nguyen Anh Khoa Doan, Bernat Font · 18 juin 2026

  Solving the pressure-Poisson equation remains the primary computational bottleneck in incompressible unstructured flow solvers primarily due to the inherent sensitivity of traditional linear solvers to mesh irregularities. This work introduces a data-driven algebraic multigrid (AMG) smoother that us…

• Hierarchical Attention via Domain Decomposition

  Stephan K\"ohler, Oliver Rheinbach · 18 juin 2026

  We propose a hierarchical attention mechanism based on two-level overlapping Schwarz domain decomposition. The method is motivated by the observation that two-level Schwarz domain decomposition methods combine local subdomain corrections with a coarse level that communicates global, long-range infor…

• A finite-element-inspired bipartite graph learned simulator for manufacturability assessment in large-deformation sheet forming

  Yingxue Zhao, Haoran Li, Haosu Zhou, Tobias Pfaff, Nan Li · 18 juin 2026

  Explicit dynamic finite element (FE) simulations are widely used for large deformation engineering analysis, but repeated simulations remain costly during design space exploration and optimisation. In explicit FE analysis, nodal kinematics and element level deformation measures evolve through couple…

• Surrogate Assisted Pedestrian Protection Design via a Foundation Model Orchestrated Workflow

  Osamu Ito, Akihiko Katagiri, Yoshikazu Nakagawa, Shin Saeki, Jun Shiraishi, Masato Sasaki · 17 juin 2026

  AI-driven engineering workflows face particular challenges in crash safety design: unlike aerodynamics, crash events involve highly nonlinear contact dynamics, material nonlinearity, and discrete state transitions that are difficult to capture with data-driven surrogate models. To the best of our kn…

• When Dynamics Models Read the Wrong Time Steps: Label-Free Event Credit Re-Anchoring for Robust Global Readouts

  Yifan Wang · 17 juin 2026

  Learned dynamics models often answer global physical questions, such as fault severity or impact stiffness, by pooling a per-step feature sequence into one readout vector. This sequence-to-global interface creates an under-studied temporal credit problem: with only trajectory-level supervision, a mo…

• A Convex Quasilinearization Method for Solving Nonlinear PDEs with Physics-Informed Neural Networks

  Gbenga T. Awojinrin, Abdul-Akeem Olawoyin, Rami M. Younis · 17 juin 2026

  We present a numerical method for the forward solution of nonlinear partial differential equations (PDEs) in which Bellman-Kalaba quasilinearization reduces the nonlinear problem to a sequence of linear subproblems, each discretized by collocation onto a trial space that is linear in its parameters …

• INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities

  Shayan Dodge (DESTeC, University of Pisa, Pisa, Italy), Alessandro Formisano (Department of Engineering, University of Campania Luigi Vanvitelli, Aversa, Italy), Sami Barmada (DESTeC, University of Pisa, Pisa, Italy) · 17 juin 2026

  We propose a new weak-form Physics-Informed Neural Network approach (named INI-VPINN). INI-VPINN naturally incorporates Neumann boundary and interface conditions into the variational formulation. It removes the need for additional loss terms or multiple subdomain networks. This framework employs com…

• Generalization Guarantees for Multi-Input Neural Operator Learning in Sobolev Spaces

  Yahong Yang, Zecheng Zhang, Wei Zhu, Wenjing Liao, Hao Liu · 17 juin 2026

  We develop approximation and generalization error estimates for multi-input neural operators, with the output error measured in Sobolev norms. In contrast to standard operator-learning settings with a single input function, our framework allows multiple input functions defined on possibly different …

• Operator Boosting Produces Pareto-Efficient PDE Surrogates

  Lennon J. Shikhman · 17 juin 2026

  Neural operators are widely used as surrogate solution maps for partial differential equations (PDEs), but full-size models can be costly to store, deploy, and evaluate in many-query scientific workflows. This work introduces Operator Boosting, a stagewise residual-learning framework for constructin…

• From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing

  Prashant K. Jha · 17 juin 2026

  This review examines neural operator architectures for learning solution operators of parametric partial differential equations (PDEs), with an emphasis on conceptual clarity and practical implementation. The work analyzes key models, including DeepONet, PCANet, and the Fourier Neural Operator, high…

• Finsler Geometry, Graph Neural Networks, and You

  T. Mitchell Roddenberry, Richard G. Baraniuk · 17 juin 2026

  Graph neural network architectures based on the graph Laplacian approximate the Laplace-Beltrami operator, thus limiting their application to isotropic operators. As a nonlinear alternative to the Laplace-Beltrami operator, we consider estimates of the Finsler Laplacian on point clouds sampled from …

• KFTD: Koopman-Fourier Time-Differentiable Network for Continuous Ocean Spatiotemporal Forecasting

  Qinghui Chen, Zekai Zhang, Hailong Liu, Jinglin Zhang, Cong Bai · 17 juin 2026

  Accurate oceanic forecasting is critical for climate monitoring and disaster early warning. However, ocean spatiotemporal forecasting encounters the double challenges of modeling complex dynamical systems and ensuring computational efficiency. We present Koopman Fourier Time-Differentiable (KFTD) Ne…

• Graphical conditional generative modeling for digital twin modeling

  Zongren Zou, Th\'eo Bourdais, Ricardo Baptista, Houman Owhadi · 16 juin 2026

  Digital twin modeling, including control and data assimilation under model uncertainty, often faces an open-ended fidelity problem: adding variables, data streams, and time scales can indefinitely increase model complexity, ultimately producing systems that are difficult to maintain, validate, inter…

• Dual-Network PINNs for Optimal Control: A Reproducible Benchmark on the Mass-Spring-Damper System

  Abdeladhim Tahimi, Rinaldo Vieira da Silva Junior · 16 juin 2026

  This work presents a transparent and reproducible benchmark study of a direct dual-network Physics-Informed Neural Network (PINN) formulation for the optimal control of a mass-spring-damper system. The classical linear-quadratic optimal control problem is solved by two independent classical methods …

• The Algebra of Units: From Buckingham's Pi-grec Theorem to Latent-Variable Learning

  Mauro Valorani · 16 juin 2026

  Engineers often measure many quantities-speed, pressure, temperature, length-expressed in different physical units. The Buckingham Pi-grec theorem states that these variables can always be combined into a smaller set of dimensionless numbers whose values fully determine the system's behaviour. Ide…

• RepNet: Tackling spectral bias in deep neural networks via parameter reparameterization

  Yong Wang, Tao Zhou, Xuhui Meng · 16 juin 2026

  Deep neural networks (DNNs) have achieved remarkable success in scientific computing, yet they often suffer from spectral bias in capturing oscillatory and multiscale behaviors. In this study, we investigate this limitation by examining the failure of shallow ReLU neural networks in fitting high-fre…

• Factorized Neural Operators Decompose Dynamic and Persistent Responses

  Hao Tang, Yuechen Duan, Jiongyu Zhu, Zimeng Feng, Hao Li, Chao Li · 16 juin 2026

  Physical systems often exhibit heterogeneous mechanisms, where rapidly evolving dynamics coexist with persistent structures. Capturing such multiscale physical behavior remains challenging for existing neural operators, which typically rely on single dominant inductive bias and therefore couple dist…

• Multi-Fidelity SINDy: Sparse Discovery of Nonlinear Dynamical Systems with Fidelity-Weighted Measurements

  Filippo Zacchei, Ana Larra\~naga, Attilio Frangi, Andrea Manzoni, Steven L. Brunton · 16 juin 2026

  Data from simulations and experiments are rarely noise-free and often exhibit heterogeneous levels of fidelity. Measurement uncertainty may vary across repeated observations, sensing devices, or even within a single experiment. This work addresses the problem of discovering nonlinear dynamical syste…

• MR-GVNO: A Geometry-Aware Variational Physics-Informed Neural Operator for Mindlin-Reissner Plates on Irregular Domains

  Siqi Wang, Daobo Sun, Yizheng Wang, Yilong Zhang, Yabin Jin, Xiaoying Zhuang, Timon Rabczuk · 16 juin 2026

  Plate and shell structures are widely used in engineering, making rapid response prediction under varying geometries, materials, and loads highly desirable. However, conventional finite element methods require repeated modeling and solution, resulting in high computational costs. This study proposes…