Model Reduction and Neural Networks

Derniers papiers

• Attention mechanism for scalable mesh-based neural surrogates of free-surface fluids

  Federico Lanteri, Massimiliano Cremonesi · 23 juin 2026

  High-fidelity simulations of free-surface flows using Lagrangian methods such as the Particle Finite Element Method (PFEM) are computationally demanding due to continuous domain updates and repeated solution of the governing equations. This challenge is further amplified by non-Newtonian rheologies,…

• Adaptive Hard-Soft Physics-Informed Neural Networks for Robust Boundary-Constrained PDE Solving

  Duc Tien Nguyen, Trinh Minh Tuan, Nguyen Duc Manh, Vu Linh Nguyen, Dinh Gia Ninh · 23 juin 2026

  Physics-informed neural networks (PINNs) provide an effective way to solve partial differential equations (PDEs) by embedding physical principles into the learning process. However, the conventional PINN formulation, in which all constraints are imposed as soft penalty terms within a composite loss,…

• Patched Flow Matching: Generative Wall-Pressure Reconstruction Beyond Training-Domain Scales from Sparse Sensors

  Meet Hemant Parikh, Yi Liu, Jian-Xun Wang · 23 juin 2026

  Characterizing the complete wall-pressure spectrum in turbulent wall-bounded flows requires simultaneous access to the viscous-scale high-wavenumber content and the outer-layer low-wavenumber content -- a requirement that neither short-domain direct numerical simulation (DNS) nor sparse experimental…

• LSTM Variants for Chaotic Dynamical Systems: An Empirical Study on the Lorenz Attractor

  Ruslan Gokhman · 23 juin 2026

  Forecasting chaotic dynamical systems such as the Lorenz attractor is notoriously difficult: small numerical errors are amplified exponentially over long autoregressive rollouts. We study seven recurrent and convolutional architectures for the AI-DEEDS 2026 Chaotic Systems Challenge: a vanilla LSTM,…

• NewPINNs: Physics-Informing Neural Networks Using Conventional Solvers for Partial Differential Equations

  Satish Chandran, Maedeh Makki, Maziar Raissi, Adrien Grenier, Behzad Mohebbi · 23 juin 2026

  We introduce NewPINNs, a physics-informing learning framework that couples neural networks with conventional numerical solvers for solving differential equations. Rather than enforcing governing equations and boundary conditions through residual-based loss terms, NewPINNs integrates the solver direc…

• Spectrally Safe Neural Operator Warm-Starts for Large-Scale Newton Solvers

  Jaemin Oh, Youngkyu Lee, Jerome Darbon, George Em Karniadakis · 23 juin 2026

  Neural operators are increasingly used to warm-start Newton solvers for nonlinear PDEs, on the premise that a low test error places the initial guess inside the basin of attraction. We show that this premise is unreliable. An operator trained to the relative \(L^2\) error \(O(10^{-3})\) can still pr…

• Input-schema identifiability limits in physics-informed surrogates for mechanics-governed flow

  Daniel Cieslak, Andrzej Czyzewski · 23 juin 2026

  Physics-informed and data-driven surrogates are increasingly used to approximate mechanics-governed flow fields, but the target quantities assigned to such models are not always identifiable from the input variables available at prediction time. We introduce an input-schema identifiability certifica…

• Jacobian-Adaptive Weighting for Stability: Enhancing Long-term Rollout of Neural Partial Differential Equation Solvers via Spatially-Adaptive Regularization

  Fengxiang Nie, Yasuhiro Suzuki · 23 juin 2026

  Data-driven surrogate models can significantly accelerate the simulation of continuous dynamical systems, yet the step-wise accumulation of errors during autoregressive time-stepping often leads to spectral blow-up and unphysical divergence. Existing global regularization techniques can enforce cont…

• Inverse Problem for Partial Differential Equations with Jump Discontinuities in Coefficients by Two-stage Physics-Informed Deep Learning and Statistical Mixture Models

  Zhikun Zhang, Guanyu Pan, Xiangjun Wang, Yong Xu, Guangtao Zhang · 23 juin 2026

  This work proposes a two-stage physics-informed deep learning framework that combines neural-network-based sampling with statistical inference and constrained parameter refinement. In the first stage, a dual-network physics-informed architecture is used, where a main-network approximates the PDE sol…

• TF-SNO: Time-Frequency Gated Spectral Neural Operators for Learning Non-Stationary Partial Differential Equations

  Yitian Zhou, Chaoning Zhang, Zhenzhen Huang, Haoxuan Yu, Jiaquan Zhang, Yiran Li, Fan Mo, Kuien Liu, Jie Zou, Caiyan Qin, Yang Yang · 23 juin 2026

  Non-stationary partial differential equations (PDEs) arise throughout scientific computing, where the dominant frequency content and energy distribution can drift over time. While efficient in PDE solving, many spectral neural operators apply a shared spectral response across rollout stages, leading…

• Frequency-Domain Neural ODEs for Modeling Non-Linear Dynamical Systems

  Mohammed Ashraf, Ayman A. El-Badawy · 23 juin 2026

  Standard continuous-depth models, such as Neural Ordinary Differential Equations (NODEs), offer significant advantages in modeling physical systems by learning continuous vector fields rather than discrete temporal steps. However, when applied to complex dynamical systems, standard NODEs frequently …

• Topological Out-of-Domain Generalization in Dynamical Systems Reconstruction

  Georg Trede, Charlotte Ricarda Doll, Elias Weber, Daniel Durstewitz · 23 juin 2026

  Predicting the behavior of dynamical systems (DS) beyond the dynamical and parameter regimes observed in training is a pivotal and essentially unresolved problem in scientific ML. It is central to any good scientific theory, which we expect to be able to make predictions about regimes not covered by…

• SPADE: Structure-Prior Adaptive Decision Estimation

  Yifan Wang · 23 juin 2026

  Physical-structure priors such as conservation laws, Hamiltonian forms, and symmetries can improve scientific machine learning when correct, but can degrade predictions when misspecified. Existing methods usually enforce a chosen structure or tune a soft penalty, without a calibrated rule for decidi…

• Physics-Informed Neural Networks for Computing the Morse Index of the Critical Catenoid

  Miraj Samarakkody · 23 juin 2026

  The Morse index of a free boundary minimal surface is encoded in its Jacobi-Steklov spectrum, and we test how faithfully a physics-informed neural network (PINN) reproduces that spectrum on a problem whose answer is already known in closed form. The benchmark is the critical catenoid in the unit bal…

• LIG: Layer-wise Integrated Gradients for Within-Layer Flow Analysis in Transformers

  Eight Suzuki, Hideitsu Hino, Noboru Murata · 23 juin 2026

  Transformers achieve strong performance, but their internal computations remain opaque. We view each Transformer layer as a dynamic graph whose nodes are token representations and per-head attention outputs, with Multi-Head Attention (ATT) and MLP as module boundaries. On this graph we use LIG (Laye…

• Physics-Guided Dual-Stream Heterogeneous Graph Neural Network for Predicting Full-Field Structural Response of Stiffened Panels

  Yuecheng Cai, Jasmin Jelovica · 23 juin 2026

  Iterative design and optimization of large, complex structures require fast and accurate prediction of stress, displacement, and other fields. Finite element analysis (FEA) is computationally expensive for this task. Existing neural network surrogates often struggle with varying topologies and compl…

• ELADO: Elliptic PDE Assessment Datasets for Operator Learning

  Frank Ehebrecht, Toni Scharle, Martin Atzmueller · 23 juin 2026

  We introduce ELADO (Elliptic PDE Assessment Datasets for Operator Learning), a systematic benchmark suite constructed to show and quantify failure modes of neural operator architectures when learning solution operators of elliptic PDEs. While the benchmarks of existing datasets focus on average case…

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

  Yong Wang, Tao Zhou, Xuhui Meng · 19 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…

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

  Yunlong Li, Fei Wang · 19 juin 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…

• 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 juin 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…

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

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

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

  Ashim Dhor, Rasel Mondal, Pin Yu Chen · 19 juin 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…

• Modularity-Free Conflict-Averse Training for Generalized PINNs

  Heejo Kong, Beomchul Park, Sung-Jin Kim, Seong-Whan Lee · 19 juin 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…

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

  Hyeonbin Moon, Donghyuk Cho, Jecheon Yu, Jeong Whan Yoon, Seunghwa Ryu · 19 juin 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…

• 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 juin 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…