Model Reduction and Neural Networks

Derniers papiers

• LLM-driven design of physics-constrained constitutive models: two agents are better than one

  Marius Tacke, Matthias Busch, Kian Abdolazizi, Jonas Eichinger, Kevin Linka, Roland Aydin, Christian Cyron · 25 mai 2026

  Developing constitutive models that capture how materials deform under load traditionally requires years of specialized expertise in continuum mechanics, machine learning, and scientific programming. Large language models (LLMs) have recently been shown to lower this barrier by generating constituti…

• Spectral-inspired Operator Learning with Limited Data and Unknown Physics

  Han Wan, Rui Zhang, Hao Sun · 25 mai 2026

  Learning PDE dynamics from limited data with unknown physics is challenging. Existing neural PDE solvers either require large datasets or rely on known physics (e.g., PDE residuals or handcrafted stencils), leading to limited applicability. To address these challenges, we propose Spectral-Inspired N…

• Operator Learning for Reconstructing Flow Fields from Sparse Measurements: a Language Model Approach

  Qian Zhang, George Em Karniadakis · 25 mai 2026

  Reconstructing flow fields from sparse measurements is a fundamental problem in fluid mechanics with broad implications for modeling, control, and design. In this work, we propose a novel operator learning framework that leverages the architecture of language models to perform flow reconstruction in…

• Coupling-Robust Accuracy in Multiphysics Physics Informed Neural Networks via Kronecker-Preconditioned Optimization

  Youngjae Park, Jaemin Kim, Junghwa Hong · 25 mai 2026

  Physics-informed neural networks (PINNs) for coupled multiphysics systems suffer systematic accuracy degradation as inter-equation coupling strengthens. We provide a theoretical explanation for this phenomenon through neural tangent kernel (NTK) analysis: for linearly coupled systems, we prove that …

• ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models

  Chengze Li, Lingwei Wei, Li Sun, Hongbo Lv, Jie Yang, Hongrong Zhang, Kening Zheng, Wei-Chieh Huang, Enze Ma, Philip S. Yu · 25 mai 2026

  Partial differential equation (PDE) foundation models are pretrained networks that forecast how physical fields like velocity and pressure evolve from a single reusable solver. On unfamiliar flows their predictions drift step by step, errors concentrate in a few regions, yet retraining destabilizes …

• Cross-attention-based bipartite graph neural network for coupled nodal and elemental field prediction in large-deformation sheet material forming

  Yingxue Zhao, Haoran Li, Haosu Zhou, Tobias Pfaff, Nan Li · 25 mai 2026

  Finite element simulations of large-deformation sheet material forming involve node-element coupling between nodal kinematics and element-level deformation measures. Machine-learning surrogates can accelerate such simulations, but most graph-based models use node-centred representations. This repres…

• Learning partially observed systems with neural Hamiltonian ordinary differential equations

  Sunniva Meltzer, S{\o}lve Eidnes, Alexander Johannes Stasik · 25 mai 2026

  When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially observed settings, where some state variables are completel…

• Optimization of randomized neural networks for transfer operator approximation

  Mohammad Tabish, Stefan Klus · 25 mai 2026

  RaNNDy is a randomized neural network architecture for the data-driven approximation of transfer operators associated with complex dynamical systems. The weights and biases of the hidden layers of the network are randomly initialized and kept fixed, only the output layer is trained. This has several…

• RePCM: Region-Specific and Phenotype-Adaptive Bi-Ventricular Cardiac Motion Synthesis

  Xuan Yang, Xiaohan Yuan, Hao Li, Lingyu Chen, Yanan Liu, Lei Li · 22 mai 2026

  Cardiac motion over a cardiac cycle is crucial for quantifying regional function and is strongly affected by cardiovascular diseases. Since temporally dense mesh sequences are difficult to obtain in practice, we focus on leveraging the more accessible end-diastolic frame to infer a full-cycle sequen…

• Fast Reconstruction of Exact Maxwell Dynamics from Sparse Data

  Dan DeGenaro, Xin Li, Obed Amo, Michael Pokojovy, Sarah Adel Bargal, Markus Lange-Hegermann, Bogdan Rai\c{t}\u{a} · 21 mai 2026

  We introduce FLASH-MAX, a shallow, exact-by-construction neural network architecture for predicting homogeneous electromagnetic fields from sparse pointwise observations. Each hidden neuron represents a separate exact solution to Maxwell's equations, so that the network satisfies the governing equat…

• Data-Efficient Neural Operator Training via Physics-Based Active Learning

  Alicja Polanska, Lorenzo Zanisi, Vignesh Gopakumar, Stanislas Pamela · 21 mai 2026

  Solving partial differential equations with neural operators significantly reduces computational costs but remains bottlenecked by high training data requirements. Active learning offers a natural framework to mitigate this by selectively acquiring the most informative samples in an iterative manner…

• Learning First Integrals via Backward-Generated Data and Guided Reinforcement Learning

  Jingfeng Zhong, Zhengxiang Liu, Zhijie Wang, Shuai Li · 21 mai 2026

  The discovery of first integrals is of fundamental scientific importance for understanding conservation laws in dynamical systems. However, existing symbolic computation tools and Large Language Models (LLMs) remain limited on this task because high-quality training data are scarce and successful so…

• Deep Learning Surrogates for Emulating Stochastic Climate Tipping Dynamics

  Adeline Hillier, Jennifer Sleeman, Jay Brett, Caroline Tang, Jenelle Millison, Anand Gnanadesikan · 21 mai 2026

  This work explores a dynamics-informed Temporal Fusion Transformer (TFT) as a data-driven surrogate for computationally intensive Earth system simulations. Focusing on multivariate time series describing global ocean transport, we demonstrate the surrogate's ability to forecast tip events across tho…

• Time-Dependent PDE-Constrained Optimization via Weak-Form Latent Dynamics

  April Tran, Terry Haut, David Bortz, Youngsoo Choi · 21 mai 2026

  Optimization problems constrained by high-dimensional, time-dependent partial differential equations require repeated forward and sensitivity solves, making high-fidelity optimization computationally prohibitive in many-query design and control settings. We present a weak-form latent-space reduced-o…

• Learning to Think in Physics: Breaking Shortcut Learning in Scientific Diffusion via Representation Alignment

  Haozhe Jia, Pengyu Yin, Wenshuo Chen, Shaofeng Liang, Lei Wang, Bowen Tian, Xiucheng Wang, Nanqian Jia, Yutao Yue · 21 mai 2026

  Physics-informed diffusion models typically enforce PDE constraints only on final outputs, leaving intermediate representations unconstrained and prone to shortcut learning under shifted boundary conditions. We introduce **REPA-P**, a teacher-free, architecture-agnostic framework that aligns interme…

• Physics-informed convolutional neural networks for fluid flow through porous media

  Rafa{\l} Topolnicki, Pawe{\l} D{\l}otko, Maciej Matyka · 21 mai 2026

  Accurate simulation of fluid flow in porous media is challenging due to complex pore-space geometries and the computational cost of solving the Navier-Stokes equations. This difficulty is particularly important when repeated simulations are required, as standard numerical solvers may converge slowly…

• Point Cloud Sequence Encoding for Material-conditioned Graph Network Simulators

  Philipp Dahlinger, Bal\'azs Gyenes, Niklas Freymuth, Luca Geminiani, Tobias W\"urth, Johannes Mitsch, Nadja Klein, Luise K\"arger, Gerhard Neumann · 21 mai 2026

  Graph Network Simulators (GNSs) have emerged as powerful surrogates for complex physics-based simulation, offering inherent differentiability and orders-of-magnitude speedups over traditional solvers. However, GNSs typically assume access to the underlying material parameters, such as stiffness or v…

• AirfoilGen: A valid-by-construction and performance-aware latent diffusion model for airfoil generation

  Zhijie Yang, Min Tang, Qiang Zou · 21 mai 2026

  Airfoil shape design is a fundamental task in aerospace engineering, with a direct impact on flight stability and fuel consumption. Deep learning has recently emerged as a promising tool for this task, but existing deep generative approaches remain limited in both geometric validity and physical con…

• Conflict-Aware Additive Guidance for Flow Models under Compositional Rewards

  Xuehui Yu, Fucheng Cai, Meiyi Wang, Xiaopeng Fan, Harold Soh · 21 mai 2026

  Inference-time guided sampling steers state-of-the-art diffusion and flow models without fine-tuning by interpreting the generation process as a controllable trajectory. This provides a simple and flexible way to inject external constraints (e.g., cost functions or pre-trained verifiers) for control…

• The impact of observation density on Bayesian inversion of latent dynamics in shock-dominated flows

  Bipin Tiwari, Muhammad Abid, Omer San · 20 mai 2026

  Inferring unknown initial states in shock-dominated compressible flows from sparse and noisy measurements is a challenging ill-posed inverse problem due to nonlinear wave interactions and limited sensing. In this work, we develop a non-intrusive reduced-order modeling framework for efficient Bayesia…

• Symmetry in the Wild: The Role of Equivariance in Neural Fluid Surrogates

  Patryk Rygiel, Julian Suk, Kak Khee Yeung, Christoph Brune, Jelmer M. Wolterink · 20 mai 2026

  Neural surrogates enable orders-of-magnitude acceleration of computational fluid dynamics (CFD) simulations, with the potential to transform engineering and healthcare workflows. Neural surrogate use in real-world applications requires addressing scalability to large, high-resolution surface and vol…

• Multi-Headed Transformer Architectures as Time-dependent Wasserstein Gradient Flows

  Alex Massucco, Leonardo Del Grande, Marcello Carioni, Christoff Brune, Carola-Bibiane Sch\"onlieb · 20 mai 2026

  In recent years, transformer architectures have revolutionized the field of language processing, opening the door to previously unforeseen possibilities. However, from a theoretical point of view, the mathematical models proposed in the literature often lack direct contact with the actual architectu…

• From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models

  Jianan Yang, Yiran Wang, Shuai Li, Fujun Cao, Xuefei Yan, Junmin Liu · 20 mai 2026

  Physics-informed neural networks (PINNs) offer a mesh-free framework for solving partial differential equations (PDEs), yet training often suffers from gradient pathologies, spectral bias, and poor convergence, especially for problems with strong nonlinearity, sharp gradients, or multiscale features…

• Learning When to Adapt

  Ali Zindari, Xiaowen Jiang, Rotem Mulayoff, Sebastian U. Stich · 20 mai 2026

  Low-rank adaptation (LoRA) is a widely used parameter-efficient fine-tuning method, yet its learned correction is static: the same low-rank update is applied to every input. This input-agnostic approach creates an inevitable compromise between adapting to the fine-tuning distribution and preserving …

• NORi: An ML-Augmented Ocean Boundary Layer Parameterization

  Xin Kai Lee, Ali Ramadhan, Andre Souza, Gregory LeClaire Wagner, Simone Silvestri, John Marshall, Raffaele Ferrari · 20 mai 2026

  NORi is a machine learning (ML) parameterization of ocean boundary layer turbulence that is physics-based and augmented with neural networks. NORi stands for neural ordinary differential equations (NODEs) Richardson number (Ri) closure. The physical parameterization is controlled by a Richardson num…