Model Reduction and Neural Networks

Derniers papiers

• Free-RBF-KAN: Kolmogorov-Arnold Networks with Adaptive Radial Basis Functions for Efficient Function Learning

  Shao-Ting Chiu, Siu Wun Cheung, Ulisses Braga-Neto, Chak Shing Lee, Rui Peng Li · 13 janvier 2026

  Kolmogorov-Arnold Networks (KANs) have shown strong potential for efficiently approximating complex nonlinear functions. However, the original KAN formulation relies on B-spline basis functions, which incur substantial computational overhead due to De Boor's algorithm. To address this limitation, re…

• Hard Constraint Projection in a Physics Informed Neural Network

  Miranda J. S. Horne (University of Leeds), Peter K. Jimack (University of Leeds), Amirul Khan (University of Leeds), He Wang (University College London) · 13 janvier 2026

  In this work, we embed hard constraints in a physics informed neural network (PINN) which predicts solutions to the 2D incompressible Navier Stokes equations. We extend the hard constraint method introduced by Chen et al. (arXiv:2012.06148) from a linear PDE to a strongly non-linear PDE. The PINN is…

• Dual-Level Models for Physics-Informed Multi-Step Time Series Forecasting

  Mahdi Nasiri, Johanna Kortelainen, Simo S\"arkk\"a · 13 janvier 2026

  This paper develops an approach for multi-step forecasting of dynamical systems by integrating probabilistic input forecasting with physics-informed output prediction. Accurate multi-step forecasting of time series systems is important for the automatic control and optimization of physical processes…

• Structure-preserving learning and prediction in optimal control of collective motion

  Sofiia Huraka, Vakhtang Putkaradze · 13 janvier 2026

  Wide-spread adoption of unmanned vehicle technologies requires the ability to predict the motion of the combined vehicle operation from observations. While the general prediction of such motion for an arbitrary control mechanism is difficult, for a particular choice of control, the dynamics reduces …

• Layerwise goal-oriented adaptivity for neural ODEs: an optimal control perspective

  Michael Hinterm\"uller, Michael Hinze, Denis Korolev · 13 janvier 2026

  In this work, we propose a novel layerwise adaptive construction method for neural network architectures. Our approach is based on a goal--oriented dual-weighted residual technique for the optimal control of neural differential equations. This leads to an ordinary differential equation constrained o…

• A Comparison of Parametric Dynamic Mode Decomposition Algorithms for Thermal-Hydraulics Applications

  Stefano Riva, Andrea Missaglia, Carolina Introini, In Cheol Bang, Antonio Cammi · 13 janvier 2026

  In recent years, algorithms aiming at learning models from available data have become quite popular due to two factors: 1) the significant developments in Artificial Intelligence techniques and 2) the availability of large amounts of data. Nevertheless, this topic has already been addressed by metho…

• Neural Operators for Biomedical Spherical Heterogeneity

  Hao Tang, Hao Chen, Hao Li, Chao Li · 13 janvier 2026

  Spherical deep learning has been widely applied to a broad range of real-world problems. Existing approaches often face challenges in balancing strong spherical geometric inductive biases with the need to model real-world heterogeneity. To solve this while retaining spherical geometry, we first intr…

• CompNO: A Novel Foundation Model approach for solving Partial Differential Equations

  Hamda Hmida, Hsiu-Wen Chang Joly, Youssef Mesri · 13 janvier 2026

  Partial differential equations (PDEs) govern a wide range of physical phenomena, but their numerical solution remains computationally demanding, especially when repeated simulations are required across many parameter settings. Recent Scientific Foundation Models (SFMs) aim to alleviate this cost by …

• StablePDENet: Enhancing Stability of Operator Learning for Solving Differential Equations

  Chutian Huang, Chang Ma, Kaibo Wang, Yang Xiang · 13 janvier 2026

  Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust self-supervised neural operator framework that enhances sta…

• An adjoint method for training data-driven reduced-order models

  Donglin Liu, Francisco Garc\'ia Atienza, Mengwu Guo · 13 janvier 2026

  Reduced-order modeling lies at the interface of numerical analysis and data-driven scientific computing, providing principled ways to compress high-fidelity simulations in science and engineering. We propose a training framework that couples a continuous-time form of operator inference with the adjo…

• Backward Reconstruction of the Chafee--Infante Equation via Physics-Informed WGAN-GP

  Joseph L. Shomberg · 13 janvier 2026

  We present a physics-informed Wasserstein GAN with gradient penalty (WGAN-GP) for solving the inverse Chafee--Infante problem on two-dimensional domains with Dirichlet boundary conditions. The objective is to reconstruct an unknown initial condition from a near-equilibrium state obtained after 100 e…

• Supervised and Unsupervised Neural Network Solver for First Order Hyperbolic Nonlinear PDEs

  Zakaria Baba, Alexandre M. Bayen, Alexi Canesse, Maria Laura Delle Monache, Martin Drieux, Zhe Fu, Nathan Lichtl\'e, Zihe Liu, Hossein Nick Zinat Matin, Benedetto Piccoli · 13 janvier 2026

  We present a neural network-based method for learning scalar hyperbolic conservation laws. Our method replaces the traditional numerical flux in finite volume schemes with a trainable neural network while preserving the conservative structure of the scheme. The model can be trained both in a supervi…

• Machine learning assisted state prediction of misspecified linear dynamical system via modal reduction

  Rohan Vitthal Thorat, Rajdip Nayek · 12 janvier 2026

  Accurate prediction of structural dynamics is imperative for preserving digital twin fidelity throughout operational lifetimes. Parametric models with fixed nominal parameters often omit critical physical effects due to simplifications in geometry, material behavior, damping, or boundary conditions,…

• Variance Reduction Methods Do Not Need to Compute Full Gradients: Improved Efficiency through Shuffling

  Daniil Medyakov, Gleb Molodtsov, Savelii Chezhegov, Alexey Rebrikov, Aleksandr Beznosikov · 12 janvier 2026

  Stochastic optimization algorithms are widely used for machine learning with large-scale data. However, their convergence often suffers from non-vanishing variance. Variance Reduction (VR) methods, such as SVRG and SARAH, address this issue but introduce a bottleneck by requiring periodic full gradi…

• GlueNN: gluing patchwise analytic solutions with neural networks

  Doyoung Kim, Donghee Lee, Hye-Sung Lee, Jiheon Lee, Jaeok Yi · 12 janvier 2026

  In many problems in physics and engineering, one encounters complicated differential equations with strongly scale-dependent terms for which exact analytical or numerical solutions are not available. A common strategy is to divide the domain into several regions (patches) and simplify the equation i…

• Bayesian BiLO: Bilevel Local Operator Learning for Efficient Uncertainty Quantification of Bayesian PDE Inverse Problems with Low-Rank Adaptation

  Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub · 12 janvier 2026

  Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while preserving physical structure, and provide the scalability and adaptability needed for emerging imaging technologies and clin…

• Learn to Evolve: Self-supervised Neural JKO Operator for Wasserstein Gradient Flow

  Xue Feng, Li Wang, Deanna Needell, Rongjie Lai · 12 janvier 2026

  The Jordan-Kinderlehrer-Otto (JKO) scheme provides a stable variational framework for computing Wasserstein gradient flows, but its practical use is often limited by the high computational cost of repeatedly solving the JKO subproblems. We propose a self-supervised approach for learning a JKO soluti…

• Structure-preserving Lift & Learn: Scientific machine learning for nonlinear conservative partial differential equations

  Harsh Sharma, Juan Diego Draxl Giannoni, Boris Kramer · 9 janvier 2026

  This work presents structure-preserving Lift & Learn, a scientific machine learning method that employs lifting variable transformations to learn structure-preserving reduced-order models for nonlinear partial differential equations (PDEs) with conservation laws. We propose a hybrid learning approac…

• Practical Aspects on Solving Differential Equations Using Deep Learning: A Primer

  Georgios Is. Detorakis · 9 janvier 2026

  Deep learning has become a popular tool across many scientific fields, including the study of differential equations, particularly partial differential equations. This work introduces the basic principles of deep learning and the Deep Galerkin method, which uses deep neural networks to solve differe…

• Green's-Function Spherical Neural Operators for Biological Heterogeneity

  Hao Tang, Hao Chen, Hao Li, Chao Li · 9 janvier 2026

  Spherical deep learning has been widely applied to a broad range of real-world problems. Existing approaches often face challenges in balancing strong spherical geometric inductive biases with the need to model real-world heterogeneity. To solve this while retaining spherical geometry, we first intr…

• Guiding diffusion models to reconstruct flow fields from sparse data

  Marc Amor\'os-Trepat, Luis Medrano-Navarro, Qiang Liu, Luca Guastoni, Nils Thuerey · 9 janvier 2026

  The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn complex patterns from data and to generalize across diverse …

• Convergence Rates for Learning Pseudo-Differential Operators

  Jiaheng Chen, Daniel Sanz-Alonso · 9 janvier 2026

  This paper establishes convergence rates for learning elliptic pseudo-differential operators, a fundamental operator class in partial differential equations and mathematical physics. In a wavelet-Galerkin framework, we formulate learning over this class as a structured infinite-dimensional regressio…

• PIVONet: A Physically-Informed Variational Neuro ODE Model for Efficient Advection-Diffusion Fluid Simulation

  Hei Shing Cheung, Qicheng Long, Zhiyue Lin · 8 janvier 2026

  We present PIVONet (Physically-Informed Variational ODE Neural Network), a unified framework that integrates Neural Ordinary Differential Equations (Neuro-ODEs) with Continuous Normalizing Flows (CNFs) for stochastic fluid simulation and visualization. First, we demonstrate that a physically informe…

• Discontinuous Galerkin finite element operator network for solving non-smooth PDEs

  Kapil Chawla, Youngjoon Hong, Jae Yong Lee, Sanghyun Lee · 8 janvier 2026

  We introduce Discontinuous Galerkin Finite Element Operator Network (DG--FEONet), a data-free operator learning framework that combines the strengths of the discontinuous Galerkin (DG) method with neural networks to solve parametric partial differential equations (PDEs) with discontinuous coefficien…

• Mitigating Label Noise using Prompt-Based Hyperbolic Meta-Learning in Open-Set Domain Generalization

  Kunyu Peng, Di Wen, M. Saquib Sarfraz, Yufan Chen, Junwei Zheng, David Schneider, Kailun Yang, Jiamin Wu, Alina Roitberg, Rainer Stiefelhagen · 8 janvier 2026

  Open-Set Domain Generalization (OSDG) is a challenging task requiring models to accurately predict familiar categories while minimizing confidence for unknown categories to effectively reject them in unseen domains. While the OSDG field has seen considerable advancements, the impact of label noise--…