Model Reduction and Neural Networks

Latest papers

• A Hybrid GNN-FEM Framework for Phase-Field Fracture Simulation. Physics-Preserving Hybridization for Generalizable Surrogate Modeling

  Hyeonbin Moon, Yongjin Choi, Seunghwa Ryu · 19 June 2026

  Scientific machine learning (SciML) has emerged as a promising approach for accelerating simulations of complex physical systems, yet achieving physically consistent and generalizable predictions for nonlinear, history-dependent problems remains a central challenge. In this study, we propose a hybri…

• Structure-Oriented Randomized Neural Networks for Poisson-Nernst-Planck and Poisson-Nernst-Planck-Navier-Stokes Systems

  Yunlong Li, Fei Wang · 19 June 2026

  We develop a structure-oriented randomized neural network framework, termed SO-RaNN, for the Poisson-Nernst-Planck (PNP) system and the Poisson-Nernst-Planck-Navier-Stokes (PNP-NS) system. The decoupled linearized subproblems are solved iteratively by randomized neural networks in a space-time frame…

• Physics-Informed Discovery of Yield Functions in Plasticity via Convex Neural Representations

  Hyeonbin Moon, Donghyuk Cho, Jecheon Yu, Jeong Whan Yoon, Seunghwa Ryu · 19 June 2026

  Identifying anisotropic yield functions remains challenging since yielding is not directly observed in full-field mechanical measurements, directional calibration can require many loading directions, and selecting an appropriate analytical form is nontrivial. This study proposes a physics-informed f…

• Advances in Scientific Machine Learning for Coupled Fluid Flow and Transport

  Gabriel F. Barros, R\^omulo M. Silva, Alvaro L. G. A. Coutinho · 19 June 2026

  This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations. Such systems, found in applications like turbidity currents and thermal convection, feature…

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

  Yong Wang, Tao Zhou, Xuhui Meng · 19 June 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…

• Neural Architectures as Functional Priors in Physics-Informed Control Problems

  Sonia Rubio Herranz, Fernando Carlos L\'opez Hern\'andez, Antonio L\'opez Montes · 19 June 2026

  In this work we investigate the role of neural architectures as implicit functional priors in control problems governed by ordinary differential equations. Rather than focusing on highly complex problems, our objective is to investigate architecture-dependent effects in controlled dynamical systems …

• Evolutionary Two-Stage Hyperparameter Optimization Strategies for Physics-Informed Neural Networks

  Fedor Buzaev (HSE University), Dmitry Efremenko (HSE University), Egor Bugaev (HSE University), Andrei Ermakov (HSE University, AXXX), Denis Derkach (HSE University), Daria Pugacheva (HSE University, AXXX), Fedor Ratnikov (HSE University) · 19 June 2026

  Physics-Informed Neural Networks (PINNs) solve Partial Differential Equations (PDEs) by embedding physical laws into neural network training. However, their performance suffers from unstable convergence, training plateaus, and strong sensitivity to architectural and optimization hyperparameters due …

• Modularity-Free Conflict-Averse Training for Generalized PINNs

  Heejo Kong, Beomchul Park, Sung-Jin Kim, Seong-Whan Lee · 19 June 2026

  Physics-informed neural networks (PINNs) have become a powerful framework for solving PDEs by embedding physical laws into differentiable objectives. Despite their advances, training PINNs remains fragile: recent conflict-averse optimization schemes alleviate gradient interference between residual a…

• Quantum-classical physics-informed Kolmogorov-Arnold networks for PDEs

  Xiang Rao, Yuxuan Shen · 19 June 2026

  We develop QCPIKAN, the first quantum-classical physics-informed Kolmogorov-Arnold network designed to solve partial differential equations (PDEs). Built upon Chebyshev-polynomial KAN layers and parameterized quantum circuits, this hybrid framework embeds physical constraints into the training loss …

• Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System

  Zhiwen Yu, Derong Yang, Liujian Zhang, Kaixiang Yang, Peilin Zhan, Jianmin Lv, Jane You, C. L. Philip Chen · 19 June 2026

  Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems. While traditional numerical solvers are robust, they often incur prohibitive computational costs due to mesh dependencies, whereas recent Physics-Informed Neural Networks (PIN…

• ITNet: A Learnable Integral Transform That Subsumes Convolution, Attention, and Recurrence

  Ashim Dhor, Rasel Mondal, Pin Yu Chen · 19 June 2026

  Convolutional networks, recurrent networks, and transformers each encode different inductive biases -- locality, sequential memory, and content-dependent pairwise interaction -- and have remained mathematically distinct since their inception. We show that this fragmentation reflects not a fundamenta…

• Neural network surrogates with uncertainty quantification for inverse problems in partial differential equations

  Christian Jimenez-Beltran, Aretha L. Teckentrup, Antonio Vergari, Konstantinos C. Zygalakis · 19 June 2026

  Inverse problems for differential equations arise throughout science and engineering, where one seeks to infer unknown model parameters from noisy or incomplete observations. Traditional numerical methods for these problems are often computationally expensive, particularly in Bayesian settings where…

• Optimal scenario design for climate emulation

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

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

  Tianyu Wang, Ying Wang, Zhihao Liu, Xi Vincent Wang, Lihui Wang · 18 June 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…

• 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 June 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…

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

  Till Richter, Niki Kilbertus · 18 June 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.…

• 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 June 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…

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

  Taiki Miyagawa · 18 June 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…

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

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

• 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 June 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 …

• Hierarchical Attention via Domain Decomposition

  Stephan K\"ohler, Oliver Rheinbach · 18 June 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…

• Operator Boosting Produces Pareto-Efficient PDE Surrogates

  Lennon J. Shikhman · 17 June 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…

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

  Osamu Ito, Akihiko Katagiri, Yoshikazu Nakagawa, Shin Saeki, Jun Shiraishi, Masato Sasaki · 17 June 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 June 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…

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

  Qinghui Chen, Zekai Zhang, Hailong Liu, Jinglin Zhang, Cong Bai · 17 June 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…