Model Reduction and Neural Networks

Derniers papiers

• Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation

  Nicole Hao · 4 août 2026

  Neural operators have emerged as a powerful tool for learning mappings between infinite-dimensional function spaces. However, their approximation properties in Sobolev norms remain poorly quantified, even though these norms control both function values and derivatives and are the natural metrics for…

• Modeling Unknown Nonlocal PDE Systems via Flow Map Learning

  Zhongshu Xu, Ying Li, Yanzhi Zhang, Dongbin Xiu · 4 août 2026

  Nonlocal partial differential equations arise in many applications but are often difficult to model and learn because of the presence of nonlocal operators. We present a flow-map learning (FML) framework for modeling unknown nonlocal PDEs directly from solution data. Rather than learning or approxim…

• Convex Neural Energy Elements: Monolithic Finite-Element Assembly of Geometry-Parameterized Neural Operators with Stability and Error Guarantees

  Hongyue Jiang, Jianjiang Zhan, Chenzhuo Zhang, Fan Wang · 4 août 2026

  Extending the neural-operator element method from individually trained, fixed-geometry neural elements to a library of reusable, geometry-parameterized element types fails structurally: a field-predicting operator trained by value regression induces an energy whose assembled Hessian is indefinite, a…

• An Embedded RISC-V Evaluation of Kolmogorov--Arnold Networks in Hard-Constrained Recurrent Physics-Informed Models

  Enzo Nicolas Spotorno, Josafat Leal Filho · 4 août 2026

  Hard-constrained recurrent physics-informed networks (HRPINNs) embed known dynamics inside a recurrent numerical integrator and restrict a neural branch to learning only the residual dynamics that the first-principles model does not capture. Kolmogorov--Arnold Networks (KANs) have been proposed as p…

• Barron Space Representations for Elliptic PDEs with Homogeneous Boundary Conditions

  Ziang Chen, Liqiang Huang · 4 août 2026

  We study the complexity of approximating high-dimensional second-order elliptic PDEs with homogeneous boundary conditions on the unit hypercube using Barron spaces. Under suitable Barron assumptions on the coefficients and forcing term, we prove that the solutions can be approximated to any prescrib…

• LieStoNet: Learning Lie Symmetries from Spatiotemporal Data for Stochastic Dynamical Systems

  Shida Liu, Abhishek Gupta, Sumit Sinha, L. Mahadevan · 4 août 2026

  Symmetry is central to modern machine learning and physics: invariances and equivariances improve sample efficiency, robustness, and out-of-distribution generalization, while symmetry principles guide scientific modeling. Yet for stochastic dynamical systems the relevant continuous symmetries are ra…

• HyperODE: Zero-Shot Surrogate for Simulation and Inference of Dynamical Systems

  Ajitesh Srivastava · 4 août 2026

  Understanding and controlling complex dynamical systems often requires executing thousands of numerical simulations across vast parametric landscapes, which is time-consuming. Machine learning surrogates significantly accelerate simulation by predicting state trajectories across different initializa…

• Hybrid Lagrangian-Eulerian Model for Lagrangian Fluid Simulation

  Ruoyan Li, Wei Wang, Yizhou Sun · 4 août 2026

  Pure Lagrangian neural simulators offer geometric flexibility and exact advection, making them well-suited for modeling moving domains and free surfaces. However, the absence of a fixed global reference frame introduces two severe limitations: a spatial bottleneck, in which model capacity is wasted …

• CoSynFlow: Conformal Symplectic Neural Flows for Cross-System Prediction of Dissipative Hamiltonian Dynamics

  Baige Xu, Takaharu Yaguchi · 4 août 2026

  Learning solution operators for differential equations is a central problem in scientific machine learning. However, many neural operator methods optimize prediction accuracy without explicitly enforcing the geometric structure of the dynamics. Structure-preserving models such as SympNets and Symple…

• Feature Interaction Modeling for Physics-Informed Neural Networks and Neural Operators

  Quan Gu, Hongxia Liu · 3 août 2026

  This work embeds feature interaction modules derived from factorization machines (FMs) into physics-informed neural networks (PINNs) and neural operator learning, to enhance model expressiveness for solution manifolds of parameterized partial differential equations (PDEs). Motivated by the second-or…

• Freeze, Then Select: Structured Field Adapters and Stability-Validated Weak Selection for PDE Discovery from Sparse Observations

  Juncheng Zhong, Chenghuang Shen, Jianfeng Liu, Zhengdong Xiao, Longjiu Luo, Qianrong Wang, Wenjun Xu, Wenlian Lu · 3 août 2026

  PDE discovery from sparse observations requires reconstructing a continuous field and selecting the correct differential terms. Our analysis of optimization paths in coupled neural PDE discovery reveals three behaviors: the exact support can persist to the end of training, appear only transiently, o…

• In-situ Autoguidance: Eliciting Self-Correction in Diffusion Models

  Enhao Gu, Haolin Hou · 3 août 2026

  The generation of high-quality, diverse, and prompt-aligned images is a central goal in image-generating diffusion models. The popular classifier-free guidance (CFG) approach improves quality and alignment at the cost of reduced variation, creating an inherent entanglement of these effects. Recent w…

• DFSC: Error-Controlled Differentiable Mittag-Leffler Propagation for Fractional Scientific Machine Learning

  Ning Hu, Haitao Duan, Shuqun Li, Chuyang Hu · 3 août 2026

  Fractional scientific machine learning requires numerical operators that can be differentiated, batched, accelerated, and composed with neural networks. When the dominant linear fractional evolution is known through a Mittag-Leffler propagator, repeatedly reconstructing that response with a history …

• Dynamics-aware identification of governing equations from sparse and noisy data

  Pongpisit Thanasutives, Yoshinobu Kawahara · 3 août 2026

  Sparse identification of nonlinear dynamics (SINDy) and PDE functional identification (PDE-FIND) recover parsimonious ordinary and partial differential equations (ODEs and PDEs) from data. However, sparse and noisy temporal measurements can make derivative estimates unreliable. To address this probl…

• HERO: History-Enriched Rollout Training for Long-Horizon Autoregressive Neural Operators

  Jiaquan Zhang, Shuxu Chen, Haifan Meng, Yi Lu, Zhihan Lyu, Fan Mo, Wei Dong, Yang Yang, Chaoning Zhang · 3 août 2026

  Neural operators provide fast surrogates for time-dependent partial differential equations (PDEs) by applying a learned evolution operator recursively to its own predictions, but this autoregressive rollout feeds every prediction error back as input, so local errors accumulate. Existing rollout-trai…

• PIKS: Universal Physics-Informed Kernel Methods

  Joachim Bona-Pellissier, Giacomo Meanti, Matteo Santacesaria, Lorenzo Rosasco · 30 juillet 2026

  Physics-informed machine learning incorporates physical principles --often expressed via differential operators-- into data-driven models. While physics-informed neural networks (PINNs) dominate empirical applications, the complexity of neural network architectures and optimization landscapes hinder…

• EvoPINN: Agentic Discovery of Executable Algorithms for Physics-Informed Neural Networks

  Peng Yin, Kai Li, Yifan Zhang, Jian Cheng · 30 juillet 2026

  Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs), yet their performance heavily relies on the manual, trial-and-error engineering of neural representations, loss formulations, and optimization dynamics. While Large Languag…

• Score-Based Stabilization for Time-Dependent Problems

  Eshed Gal, Eldad Haber, Uri Ascher · 29 juillet 2026

  We propose a score-based stabilization framework for numerical simulation of partial differential equations, in which a learned score model defines a stabilization operator applied to provisional numerical updates. This operator augments standard time-stepping schemes by enforcing structure and phys…

• SpectONet: A Physics-Guided Spectral Deep Operator Network for Euler-Bernoulli Beam Dynamics

  Shivani Saini, Ramesh Kumar Vats, Arup Kumar Sahoo · 29 juillet 2026

  This paper proposes a novel physics-guided spectral deep operator network, termed SpectONet, for solving Euler-Bernoulli beam (EBB) vibration problems. The proposed framework integrates the operator-learning capability of DeepONet with physics-informed constraints and Chebyshev-Gauss-Lobatto (CGL) s…

• Wall Shear Stress Reconstruction from Concentration: Differentiable Physics and Physics-Informed Neural Networks

  Mahmoud Elhadidy, Siva Viknesh, Roshan M. D'Souza, Amirhossein Arzani · 29 juillet 2026

  Wall shear stress (WSS) governs near-wall transport dynamics and is a key hemodynamic indicator in cardiovascular flows, yet remains difficult to infer accurately due to the need for precise computation of near-wall velocity gradients. Passive scalar fields, such as concentration or temperature, are…

• Extreme Event Aware ($\eta$-) Learning

  Kai Chang, Themistoklis P. Sapsis · 29 juillet 2026

  Quantifying and predicting rare and extreme events is challenging because such events are infrequent, severe, and expensive to simulate. Existing data-driven methods often require multiple extremes in the training data or sampling process, leading to accurate predictions in quiescent regimes but hig…

• Physics-Informed Neural Operator for Warm-Starting Background-Decomposed and Preconditioned PSFD: Enabling Scalable 3-D EUV Mask Simulation

  Doyun Kim, Werner Gillijns · 29 juillet 2026

  We present a physics-informed neural operator (PINO) trained with pseudo-spectral frequency-domain (PSFD) equations for electromagnetic (EM) scattering problems in EUV lithography. The Fourier neural operator is factorized into a two-dimensional lateral ($xy$) branch and a one-dimensional axial ($z$…

• Physics-Informed Broad Learning System: An Efficient Backpropagation-Free Framework for Solving Partial Differential Equations

  Pinki Khatun, M. Sajid, Abhinav Jha, M. Tanveer · 29 juillet 2026

  Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding governing physical laws into deep neural networks. However, their reliance on computationally expensive gradient-based optimization and deep architectures often…

• Multi-Fidelity Learning with Shallow Recurrent Decoders for Multi-Physics Applications

  Stefano Riva, Carolina Introini, J. Nathan Kutz, Antonio Cammi · 29 juillet 2026

  In reactor physics, neutronics and multi-physics phenomena can be modelled at different fidelity levels. High-fidelity models based on the Boltzmann transport equation, multi-group diffusion, or computational fluid dynamics are computationally demanding, whereas simplified models, such as zero-dimen…

• Neural operator discovery from heterogeneous trajectories

  Zituo Chen, Qiaofeng Li, Jiaxin Hu, Sili Deng · 28 juillet 2026

  Neural operators provide data-driven mappings for modeling dynamical systems. Extending them to families of systems typically requires explicit conditioning variables such as physical parameters, geometries, or boundary conditions. In many real-world settings, these quantities are unobserved. Here, …