Model Reduction and Neural Networks

Derniers papiers

• Variational (Energy-Based) Spectral Learning: A Machine Learning Framework for Solving Partial Differential Equations

  M. M. Hammad · 7 janvier 2026

  We introduce variational spectral learning (VSL), a machine learning framework for solving partial differential equations (PDEs) that operates directly in the coefficient space of spectral expansions. VSL offers a principled bridge between variational PDE theory, spectral discretization, and contemp…

• Flow Matching and Diffusion Models via PointNet for Generating Fluid Fields on Irregular Geometries

  Ali Kashefi · 7 janvier 2026

  We present two novel generative geometric deep learning frameworks, termed Flow Matching PointNet and Diffusion PointNet, for predicting fluid flow variables on irregular geometries by incorporating PointNet into flow matching and diffusion models, respectively. In these frameworks, a reverse genera…

• U-PINet: Physics-Informed Hierarchical Learning for Accurate and Fast 3D RCS Prediction

  Rui Zhu, Yuexing Peng, Peng Wang, George C. Alexandropoulos, Wenbo Wang, Wei Xiang · 7 janvier 2026

  Accurate radar cross section (RCS) computation is a fundamental task in radar engineering and electromagnetic (EM) scattering analysis, underpinning target signature characterization, detection, and recognition. Conventional computational electromagnetics (CEM) solvers provide high-fidelity RCS pred…

• Latent Space Element Method

  Seung Whan Chung, Youngsoo Choi, Christopher Miller, H. Keo Springer, Kyle T. Sullivan · 6 janvier 2026

  How can we build surrogate solvers that train on small domains but scale to larger ones without intrusive access to PDE operators? Inspired by the Data-Driven Finite Element Method (DD-FEM) framework for modular data-driven solvers, we propose the Latent Space Element Method (LSEM), an element-based…

• M\"untz-Sz\'asz Networks: Neural Architectures with Learnable Power-Law Bases

  Gnankan Landry Regis N'guessan · 6 janvier 2026

  Standard neural network architectures employ fixed activation functions (ReLU, tanh, sigmoid) that are poorly suited for approximating functions with singular or fractional power behavior, a structure that arises ubiquitously in physics, including boundary layers, fracture mechanics, and corner sing…

• M\"untz-Sz\'asz Networks: Neural Architectures with Learnable Power-Law Bases

  Gnankan Landry Regis N'guessan · 6 janvier 2026

  Standard neural network architectures employ fixed activation functions (ReLU, tanh, sigmoid) that are poorly suited for approximating functions with singular or fractional power behavior, a structure that arises ubiquitously in physics, including boundary layers, fracture mechanics, and corner sing…

• Efficient temporal prediction of compressible flows in irregular domains using Fourier neural operators

  Yifan Nie, Qiaoxin Li · 6 janvier 2026

  This paper investigates the temporal evolution of high-speed compressible fluids in irregular flow fields using the Fourier Neural Operator (FNO). We reconstruct the irregular flow field point set into sequential format compatible with FNO input requirements, and then embed temporal bundling techniq…

• Expanding the Chaos: Neural Operator for Stochastic (Partial) Differential Equations

  Dai Shi, Lequan Lin, Andi Han, Luke Thompson, Jos\'e Miguel Hern\'andez-Lobato, Zhiyong Wang, Junbin Gao · 6 janvier 2026

  Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental tools for modeling stochastic dynamics across the natural sciences and modern machine learning. Developing deep learning models for approximating their solution operators promises not only …

• Identifying recurrent flows in high-dimensional dissipative chaos from low-dimensional embeddings

  Pierre Beck, Tobias M. Schneider · 6 janvier 2026

  Unstable periodic orbits (UPOs) are the non-chaotic, dynamical building blocks of spatio-temporal chaos, motivating a first-principles based theory for turbulence ever since the discovery of deterministic chaos. Despite their key role in the ergodic theory approach to fluid turbulence, identifying U…

• A-PINN: Auxiliary Physics-informed Neural Networks for Structural Vibration Analysis in Continuous Euler-Bernoulli Beam

  Shivani Saini, Ramesh Kumar Vats, Arup Kumar Sahoo · 6 janvier 2026

  Recent advancements in physics-informed neural networks (PINNs) and their variants have garnered substantial focus from researchers due to their effectiveness in solving both forward and inverse problems governed by differential equations. In this research, a modified Auxiliary physics-informed neur…

• Car Drag Coefficient Prediction from 3D Point Clouds Using a Slice-Based Surrogate Model

  Utkarsh Singh, Absaar Ali, Adarsh Roy · 6 janvier 2026

  The automotive industry's pursuit of enhanced fuel economy and performance necessitates efficient aerodynamic design. However, traditional evaluation methods such as computational fluid dynamics (CFD) and wind tunnel testing are resource intensive, hindering rapid iteration in the early design stage…

• Intrinsic-Metric Physics-Informed Neural Networks (IM-PINN) for Reaction-Diffusion Dynamics on Complex Riemannian Manifolds

  Julian Evan Chrisnanto, Salsabila Rahma Alia, Nurfauzi Fadillah, Yulison Herry Chrisnanto · 6 janvier 2026

  Simulating nonlinear reaction-diffusion dynamics on complex, non-Euclidean manifolds remains a fundamental challenge in computational morphogenesis, constrained by high-fidelity mesh generation costs and symplectic drift in discrete time-stepping schemes. This study introduces the Intrinsic-Metric P…

• Sparse FEONet: A Low-Cost, Memory-Efficient Operator Network via Finite-Element Local Sparsity for Parametric PDEs

  Seungchan Ko, Jiyeon Kim, Dongwook Shin · 5 janvier 2026

  In this paper, we study the finite element operator network (FEONet), an operator-learning method for parametric problems, originally introduced in J. Y. Lee, S. Ko, and Y. Hong, Finite Element Operator Network for Solving Elliptic-Type Parametric PDEs, SIAM J. Sci. Comput., 47(2), C501-C528, 2025. …

• Homogenization with Guaranteed Bounds via Primal-Dual Physically Informed Neural Networks

  Liya Gaynutdinova, Martin Do\v{s}k\'a\v{r}, Ond\v{r}ej Roko\v{s}, Ivana Pultarov\'a · 5 janvier 2026

  Physics-informed neural networks (PINNs) have shown promise in solving partial differential equations (PDEs) relevant to multiscale modeling, but they often fail when applied to materials with discontinuous coefficients, such as media with piecewise constant properties. This paper introduces a dual …

• Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunities

  Jian Cheng Wong, Abhishek Gupta, Chin Chun Ooi, Pao-Hsiung Chiu, Jiao Liu, Yew-Soon Ong · 5 janvier 2026

  Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically expressible laws of nature into their training loss function. By co…

• Neural Chains and Discrete Dynamical Systems

  Sauro Succi, Abhisek Ganguly, Santosh Ansumali · 5 janvier 2026

  We inspect the analogy between machine-learning (ML) applications based on the transformer architecture without self-attention, {\it neural chains} hereafter, and discrete dynamical systems associated with discretised versions of neural integral and partial differential equations (NIE, PDE). A compa…

• Active learning for data-driven reduced models of parametric differential systems with Bayesian operator inference

  Shane A. McQuarrie, Mengwu Guo, Anirban Chaudhuri · 5 janvier 2026

  This work develops an active learning framework to intelligently enrich data-driven reduced-order models (ROMs) of parametric dynamical systems, which can serve as the foundation of virtual assets in a digital twin. Data-driven ROMs are explainable, computationally efficient scientific machine learn…

• Solving nonlinear subsonic compressible flow in infinite domain via multi-stage neural networks

  Xuehui Qian, Hongkai Tao, Yongji Wang · 5 janvier 2026

  In aerodynamics, accurately modeling subsonic compressible flow over airfoils is critical for aircraft design. However, solving the governing nonlinear perturbation velocity potential equation presents computational challenges. Traditional approaches often rely on linearized equations or finite, tru…

• Deep learning methods for inverse problems using connections between proximal operators and Hamilton-Jacobi equations

  Oluwatosin Akande, Gabriel P. Langlois, Akwum Onwunta · 1 janvier 2026

  Inverse problems are important mathematical problems that seek to recover model parameters from noisy data. Since inverse problems are often ill-posed, they require regularization or incorporation of prior information about the underlying model or unknown variables. Proximal operators, ubiquitous in…

• Deep Learning in Geotechnical Engineering: A Critical Assessment of PINNs and Operator Learning

  Krishna Kumar · 1 janvier 2026

  Deep learning methods -- physics-informed neural networks (PINNs), deep operator networks (DeepONet), and graph network simulators (GNS) -- are increasingly proposed for geotechnical problems. This paper tests these methods against traditional solvers on canonical problems: wave propagation and beam…

• Soliton profiles: Classical Numerical Schemes vs. Neural Network - Based Solvers

  Chandler Haight, Svetlana Roudenko, Zhongming Wang · 1 janvier 2026

  We present a comparative study of classical numerical solvers, such as Petviashvili's method or finite difference with Newton iterations, and neural network-based methods for computing ground states or profiles of solitary-wave solutions to the one-dimensional dispersive PDEs that include the nonlin…

• Learning Temporally Consistent Turbulence Between Sparse Snapshots via Diffusion Models

  Mohammed Sardar, Ma{\l}gorzata J. Zimo\'n, Samuel Draycott, Alistair Revell, Alex Skillen · 1 janvier 2026

  We investigate the statistical accuracy of temporally interpolated spatiotemporal flow sequences between sparse, decorrelated snapshots of turbulent flow fields using conditional Denoising Diffusion Probabilistic Models (DDPMs). The developed method is presented as a proof-of-concept generative surr…

• Convergence of the generalization error for deep gradient flow methods for PDEs

  Chenguang Liu, Antonis Papapantoleon, Jasper Rou · 1 janvier 2026

  The aim of this article is to provide a firm mathematical foundation for the application of deep gradient flow methods (DGFMs) for the solution of (high-dimensional) partial differential equations (PDEs). We decompose the generalization error of DGFMs into an approximation and a training error. We f…

• Mathematical artificial data for operator learning

  Heng Wu, Benzhuo Lu · 1 janvier 2026

  Machine learning has emerged as a transformative tool for solving differential equations (DEs), yet prevailing methodologies remain constrained by dual limitations: data-driven methods demand costly labeled datasets while model-driven techniques face efficiency-accuracy trade-offs. We present the Ma…

• Lipschitz-Guided Design of Interpolation Schedules in Generative Models

  Yifan Chen, Eric Vanden-Eijnden, Jiawei Xu · 1 janvier 2026

  We study the design of interpolation schedules in the stochastic interpolants framework for flow and diffusion-based generative models. We show that while all scalar interpolation schedules achieve identical statistical efficiency under Kullback-Leibler divergence in path space after optimal diffusi…