Model Reduction and Neural Networks

Derniers papiers

• Analytic Bijections for Smooth and Interpretable Normalizing Flows

  Mathis Gerdes, Miranda C. N. Cheng · 19 janvier 2026

  A key challenge in designing normalizing flows is finding expressive scalar bijections that remain invertible with tractable Jacobians. Existing approaches face trade-offs: affine transformations are smooth and analytically invertible but lack expressivity; monotonic splines offer local control but …

• Operator learning on domain boundary through combining fundamental solution-based artificial data and boundary integral techniques

  Haochen Wu, Heng Wu, Benzhuo Lu · 19 janvier 2026

  For linear partial differential equations with known fundamental solutions, this work introduces a novel operator learning framework that relies exclusively on domain boundary data, including solution values and normal derivatives, rather than full-domain sampling. By integrating the previously deve…

• Forcing and Diagnosing Failure Modes of Fourier Neural Operators Across Diverse PDE Families

  Lennon Shikhman · 19 janvier 2026

  Fourier Neural Operators (FNOs) have shown strong performance in learning solution maps of partial differential equations (PDEs), but their robustness under distribution shifts, long-horizon rollouts, and structural perturbations remains poorly understood. We present a systematic stress-testing fram…

• U-PINet: Physics-Informed Hierarchical Learning for Radar Cross Section Prediction via 3D Electromagnetic Scattering Reconstruction

  Rui Zhu, Yuexing Peng, George C. Alexandropoulos, Peng Wang, Wenbo Wang, Wei Xiang · 19 janvier 2026

  Conventional computational electromagnetics (CEM) solvers can deliver high fidelity radar cross section (RCS) signatures by first solving the induced surface currents on 3-dimensional (3D) targets and then evaluating the scattered fields via radiation integrals. However, their computational cost bec…

• GenDA: Generative Data Assimilation on Complex Urban Areas via Classifier-Free Diffusion Guidance

  Francisco Giral, \'Alvaro Manzano, Ignacio G\'omez, Ricardo Vinuesa, Soledad Le Clainche · 19 janvier 2026

  Urban wind flow reconstruction is essential for assessing air quality, heat dispersion, and pedestrian comfort, yet remains challenging when only sparse sensor data are available. We propose GenDA, a generative data assimilation framework that reconstructs high-resolution wind fields on unstructured…

• Comprehensive Robust Dynamic Mode Decomposition from Mode Extraction to Dimensional Reduction

  Yuki Nakamura, Shingo Takemoto, Shunsuke Ono · 19 janvier 2026

  We propose Comprehensive Robust Dynamic Mode Decomposition (CR-DMD), a novel framework that robustifies the entire DMD process - from mode extraction to dimensional reduction - against mixed noise. Although standard DMD widely used for uncovering spatio-temporal patterns and constructing low-dimensi…

• A Natural Primal-Dual Hybrid Gradient Method for Adversarial Neural Network Training on Solving Partial Differential Equations

  Shu Liu, Stanley Osher, Wuchen Li · 19 janvier 2026

  We propose a scalable preconditioned primal-dual hybrid gradient algorithm for solving partial differential equations (PDEs). We multiply the PDE with a dual test function to obtain an inf-sup problem whose loss functional involves lower-order differential operators. The Primal-Dual Hybrid Gradient …

• AC-PKAN: Attention-Enhanced and Chebyshev Polynomial-Based Physics-Informed Kolmogorov-Arnold Networks

  Hangwei Zhang, Zhimu Huang, Yan Wang · 19 janvier 2026

  Kolmogorov-Arnold Networks (KANs) have recently shown promise for solving partial differential equations (PDEs). Yet their original formulation is computationally and memory intensive, motivating the introduction of Chebyshev Type-I-based KANs (Chebyshev1KANs). Although Chebyshev1KANs have outperfor…

• The Curious Case of In-Training Compression of State Space Models

  Makram Chahine, Philipp Nazari, Daniela Rus, T. Konstantin Rusch · 19 janvier 2026

  State Space Models (SSMs), developed to tackle long sequence modeling tasks efficiently, offer both parallelizable training and fast inference. At their core are recurrent dynamical systems that maintain a hidden state, with update costs scaling with the state dimension. A key design challenge is st…

• Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs

  Lorenzo Tomada, Federico Pichi, Gianluigi Rozza · 19 janvier 2026

  Graph Neural Networks (GNNs) are emerging as powerful tools for nonlinear Model Order Reduction (MOR) of time-dependent parameterized Partial Differential Equations (PDEs). However, existing methodologies struggle to combine geometric inductive biases with interpretable latent behavior, overlooking …

• Continuous-Depth Transformers with Learned Control Dynamics

  Peter Jemley · 16 janvier 2026

  We present a hybrid transformer architecture that replaces discrete middle layers with a continuous-depth Neural Ordinary Differential Equation (ODE) block, enabling inference-time control over generation attributes via a learned steering signal. Unlike standard transformers that process representat…

• DInf-Grid: A Neural Differential Equation Solver with Differentiable Feature Grids

  Navami Kairanda, Shanthika Naik, Marc Habermann, Avinash Sharma, Christian Theobalt, Vladislav Golyanik · 16 janvier 2026

  We present a novel differentiable grid-based representation for efficiently solving differential equations (DEs). Widely used architectures for neural solvers, such as sinusoidal neural networks, are coordinate-based MLPs that are both computationally intensive and slow to train. Although grid-based…

• Data-driven stochastic reduced-order modeling of parametrized dynamical systems

  Andrew F. Ilersich, Kevin Course, Prasanth B. Nair · 16 janvier 2026

  Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle with stochastic dynamics and fail to quantify prediction un…

• A reduced-order derivative-informed neural operator for subsurface fluid-flow

  Jeongjin Park, Grant Bruer, Huseyin Tuna Erdinc, Abhinav Prakash Gahlot, Felix J. Herrmann · 16 janvier 2026

  Neural operators have emerged as cost-effective surrogates for expensive fluid-flow simulators, particularly in computationally intensive tasks such as permeability inversion from time-lapse seismic data, and uncertainty quantification. In these applications, the fidelity of the surrogate's gradient…

• Introduction to optimization methods for training SciML models

  Alena Kopani\v{c}\'akov\'a, Elisa Riccietti · 16 janvier 2026

  Optimization is central to both modern machine learning (ML) and scientific machine learning (SciML), yet the structure of the underlying optimization problems differs substantially across these domains. Classical ML typically relies on stochastic, sample-separable objectives that favor first-order …

• SPIKE: Sparse Koopman Regularization for Physics-Informed Neural Networks

  Jose Marie Antonio Minoza · 16 janvier 2026

  Physics-Informed Neural Networks (PINNs) provide a mesh-free approach for solving differential equations by embedding physical constraints into neural network training. However, PINNs tend to overfit within the training domain, leading to poor generalization when extrapolating beyond trained spatiot…

• Stable Differentiable Modal Synthesis for Learning Nonlinear Dynamics

  Victor Zheleznov, Stefan Bilbao, Alec Wright, Simon King · 16 janvier 2026

  Modal methods are a long-standing approach to physical modelling synthesis. Extensions to nonlinear problems are possible, including the case of a high-amplitude vibration of a string. A modal decomposition leads to a densely coupled nonlinear system of ordinary differential equations. Recent work i…

• Discrete Solution Operator Learning for Geometry-Dependent PDEs

  Jinshuai Bai, Haolin Li, Zahra Sharif Khodaei, M. H. Aliabadi, YuanTong Gu, Xi-Qiao Feng · 15 janvier 2026

  Neural operator learning accelerates PDE solution by approximating operators as mappings between continuous function spaces. Yet in many engineering settings, varying geometry induces discrete structural changes, including topological changes, abrupt changes in boundary conditions or boundary types,…

• Terminally constrained flow-based generative models from an optimal control perspective

  Weiguo Gao, Ming Li, Qianxiao Li · 15 janvier 2026

  We address the problem of sampling from terminally constrained distributions with pre-trained flow-based generative models through an optimal control formulation. Theoretically, we characterize the value function by a Hamilton-Jacobi-Bellman equation and derive the optimal feedback control as the mi…

• HGATSolver: A Heterogeneous Graph Attention Solver for Fluid-Structure Interaction

  Qin-Yi Zhang, Hong Wang, Siyao Liu, Haichuan Lin, Linying Cao, Xiao-Hu Zhou, Chen Chen, Shuangyi Wang, Zeng-Guang Hou · 15 janvier 2026

  Fluid-structure interaction (FSI) systems involve distinct physical domains, fluid and solid, governed by different partial differential equations and coupled at a dynamic interface. While learning-based solvers offer a promising alternative to costly numerical simulations, existing methods struggle…

• Kernel Limit for a Class of Recurrent Neural Networks Trained on Ergodic Data Sequences

  Samuel Chun-Hei Lam, Justin Sirignano, Konstantinos Spiliopoulos · 15 janvier 2026

  Mathematical methods are developed to characterize the asymptotics of recurrent neural networks (RNN) as the number of hidden units, data samples in the sequence, hidden state updates, and training steps simultaneously grow to infinity. In the case of an RNN with a simplified weight matrix, we prove…

• Soft Partition-based KAPI-ELM for Multi-Scale PDEs

  Vikas Dwivedi, Monica Sigovan, Bruno Sixou · 14 janvier 2026

  Physics-informed machine learning holds great promise for solving differential equations, yet existing methods struggle with highly oscillatory, multiscale, or singularly perturbed PDEs due to spectral bias, costly backpropagation, and manually tuned kernel or Fourier frequencies. This work introduc…

• Multi-Preconditioned LBFGS for Training Finite-Basis PINNs

  Marc Salvad\'o-Benasco, Aymane Kssim, Alexander Heinlein, Rolf Krause, Serge Gratton, Alena Kopani\v{c}\'akov\'a · 14 janvier 2026

  A multi-preconditioned LBFGS (MP-LBFGS) algorithm is introduced for training finite-basis physics-informed neural networks (FBPINNs). The algorithm is motivated by the nonlinear additive Schwarz method and exploits the domain-decomposition-inspired additive architecture of FBPINNs, in which local ne…

• Gradient-free online learning of subgrid-scale dynamics with neural emulators

  Hugo Frezat, Ronan Fablet, Guillaume Balarac, Julien Le Sommer · 14 janvier 2026

  In this paper, we propose a generic algorithm to train machine learning-based subgrid parametrizations online, i.e., with \textit{a posteriori} loss functions, but for non-differentiable numerical solvers. The proposed approach leverages a neural emulator to approximate the reduced state-space solve…

• A Mesh-Adaptive Hypergraph Neural Network for Unsteady Flow Around Oscillating and Rotating Structures

  Rui Gao, Zhi Cheng, Rajeev K. Jaiman · 14 janvier 2026

  Graph neural networks, recently introduced into the field of fluid flow surrogate modeling, have been successfully applied to model the temporal evolution of various fluid flow systems. Existing applications, however, are mostly restricted to cases where the domain is time-invariant. The present wor…