Model Reduction and Neural Networks

Derniers papiers

• Disentangled Representation Learning for Parametric Partial Differential Equations

  Ning Liu, Lu Zhang, Tian Gao, Yue Yu · 10 février 2026

  Neural operators (NOs) excel at learning mappings between function spaces, serving as efficient forward solution approximators for PDE-governed systems. However, as black-box solvers, they offer limited insight into the underlying physical mechanism, due to the lack of interpretable representations …

• Learning Nonlinear Systems In-Context: From Synthetic Data to Real-World Motor Control

  Tong Jian, Tianyu Dai, Tao Yu · 10 février 2026

  LLMs have shown strong in-context learning (ICL) abilities, but have not yet been extended to signal processing systems. Inspired by their design, we have proposed for the first time ICL using transformer models applicable to motor feedforward control, a critical task where classical PI and physics-…

• Is Flow Matching Just Trajectory Replay for Sequential Data?

  Soon Hoe Lim, Shizheng Lin, Michael W. Mahoney, N. Benjamin Erichson · 10 février 2026

  Flow matching (FM) is increasingly used for time-series generation, but it is not well understood whether it learns a general dynamical structure or simply performs an effective "trajectory replay". We study this question by deriving the velocity field targeted by the empirical FM objective on seque…

• Constructive conditional normalizing flows

  Borjan Geshkovski, Dom\`enec Ruiz-Balet · 10 février 2026

  Motivated by applications in conditional sampling, given a probability measure $\mu$ and a diffeomorphism $\phi$, we consider the problem of simultaneously approximating $\phi$ and the pushforward $\phi_{\#}\mu$ by means of the flow of a continuity equation whose velocity field is a perceptron neura…

• Curriculum-Learned Vanishing Stacked Residual PINNs for Hyperbolic PDE State Reconstruction

  Katayoun Eshkofti, Matthieu Barreau · 10 février 2026

  Modeling distributed dynamical systems governed by hyperbolic partial differential equations (PDEs) remains challenging due to discontinuities and shocks that hinder the convergence of traditional physics-informed neural networks (PINNs). The recently proposed vanishing stacked residual PINN (VSR-PI…

• MetaCluster: Enabling Deep Compression of Kolmogorov-Arnold Network

  Matthew Raffel, Adwaith Renjith, Lizhong Chen · 10 février 2026

  Kolmogorov-Arnold Networks (KANs) replace scalar weights with per-edge vectors of basis coefficients, thereby increasing expressivity and accuracy while also resulting in a multiplicative increase in parameters and memory. We propose MetaCluster, a framework that makes KANs highly compressible witho…

• Nansde-net: A neural sde framework for generating time series with memory

  Hiromu Ozai, Kei Nakagawa · 10 février 2026

  Modeling time series with long- or short-memory characteristics is a fundamental challenge in many scientific and engineering domains. While fractional Brownian motion has been widely used as a noise source to capture such memory effects, its incompatibility with It\^o calculus limits its applicabil…

• Learning-guided Kansa collocation for forward and inverse PDEs beyond linearity

  Zheyuan Hu, Weitao Chen, Cengiz \"Oztireli, Chenliang Zhou, Fangcheng Zhong · 10 février 2026

  Partial Differential Equations are precise in modelling the physical, biological and graphical phenomena. However, the numerical methods suffer from the curse of dimensionality, high computation costs and domain-specific discretization. We aim to explore pros and cons of different PDE solvers, and a…

• Approximating Matrix Functions with Deep Neural Networks and Transformers

  Rahul Padmanabhan, Simone Brugiapaglia · 10 février 2026

  Transformers have revolutionized natural language processing, but their use for numerical computation has received less attention. We study the approximation of matrix functions, which map scalar functions to matrices, using neural networks including transformers. We focus on functions mapping squar…

• FEM-Informed Hypergraph Neural Networks for Efficient Elastoplasticity

  Jianchuan Yang, Xi Chen, Jidong Zhao · 10 février 2026

  Graph neural networks (GNNs) naturally align with sparse operators and unstructured discretizations, making them a promising paradigm for physics-informed machine learning in computational mechanics. Motivated by discrete physics losses and Hierarchical Deep Learning Neural Network (HiDeNN) construc…

• Data Reconstruction: Identifiability and Optimization with Sample Splitting

  Yujie Shen, Zihan Wang, Jian Qian, Qi Lei · 10 février 2026

  Training data reconstruction from KKT conditions has shown striking empirical success, yet it remains unclear when the resulting KKT equations have unique solutions and, even in identifiable regimes, how to reliably recover solutions by optimization. This work hereby focuses on these two complementa…

• Causal Schr\"odinger Bridges: Constrained Optimal Transport on Structural Manifolds

  Rui Wu, Li YongJun · 10 février 2026

  Generative modeling typically seeks the path of least action via deterministic flows (ODE). While effective for in-distribution tasks, we argue that these deterministic paths become brittle under causal interventions, which often require transporting probability mass across low-density regions ("off…

• Neural MJD: Neural Non-Stationary Merton Jump Diffusion for Time Series Prediction

  Yuanpei Gao, Qi Yan, Yan Leng, Renjie Liao · 10 février 2026

  While deep learning methods have achieved strong performance in time series prediction, their black-box nature and inability to explicitly model underlying stochastic processes often limit their generalization to non-stationary data, especially in the presence of abrupt changes. In this work, we int…

• Initialization Schemes for Kolmogorov-Arnold Networks: An Empirical Study

  Spyros Rigas, Dhruv Verma, Georgios Alexandridis, Yixuan Wang · 10 février 2026

  Kolmogorov-Arnold Networks (KANs) are a recently introduced neural architecture that replace fixed nonlinearities with trainable activation functions, offering enhanced flexibility and interpretability. While KANs have been applied successfully across scientific and machine learning tasks, their ini…

• $\texttt{lrnnx}$: A library for Linear RNNs

  Karan Bania, Soham Kalburgi, Manit Tanwar, Dhruthi, Aditya Nagarsekar, Harshvardhan Mestha, Naman Chibber, Raj Deshmukh, Anish Sathyanarayanan, Aarush Rathore, Pratham Chheda · 10 février 2026

  Linear recurrent neural networks (LRNNs) provide a structured approach to sequence modeling that bridges classical linear dynamical systems and modern deep learning, offering both expressive power and theoretical guarantees on stability and trainability. In recent years, multiple LRNN-based architec…

• Time-Delayed Transformers for Data-Driven Modeling of Low-Dimensional Dynamics

  Albert Alcalde, Markus Widhalm, Emre Y{\i}lmaz · 10 février 2026

  We propose the time-delayed transformer (TD-TF), a simplified transformer architecture for data-driven modeling of unsteady spatio-temporal dynamics. TD-TF bridges linear operator-based methods and deep sequence models by showing that a single-layer, single-head transformer can be interpreted as a n…

• Rectified Flows for Fast Multiscale Fluid Flow Modeling

  Victor Armegioiu, Yannick Ramic, Siddhartha Mishra · 10 février 2026

  Statistical surrogate modeling of fluid flows is hard because dynamics are multiscale and highly sensitive to initial conditions. Conditional diffusion surrogates can be accurate, but usually need hundreds of stochastic sampling steps. We propose a rectified-flow surrogate that learns a time-depen…

• Rethinking Scientific Modeling: Toward Physically Consistent and Simulation-Executable Programmatic Generation

  Yongqing Jiang, Jianze Wang, Zhiqi Shen, Zhenghong Lin, Jiayuan Wang, Yijian Yang, Kaoshan Dai, Haoran Luo · 10 février 2026

  Structural modeling is a fundamental component of computational engineering science, in which even minor physical inconsistencies or specification violations may invalidate downstream simulations. The potential of large language models (LLMs) for automatic generation of modeling code has been demons…

• Featured Reproducing Kernel Banach Spaces for Learning and Neural Networks

  Isabel de la Higuera, Francisco Herrera, M. Victoria Velasco · 10 février 2026

  Reproducing kernel Hilbert spaces provide a foundational framework for kernel-based learning, where regularization and interpolation problems admit finite-dimensional solutions through classical representer theorems. Many modern learning models, however -- including fixed-architecture neural network…

• Interpretable Discovery of One-parameter Subgroups: A Modular Framework for Elliptical, Hyperbolic, and Parabolic Symmetries

  Pavan Karjol, Vivek V Kashyap, Rohan Kashyap, Prathosh A P · 10 février 2026

  We propose a modular, data-driven framework for jointly learning unknown functional mappings and discovering the underlying one-parameter symmetry subgroup governing the data. Unlike conventional geometric deep learning methods that assume known symmetries, our approach identifies the relevant conti…

• Discrete Adjoint Schr\"odinger Bridge Sampler

  Wei Guo, Yuchen Zhu, Xiaochen Du, Juno Nam, Yongxin Chen, Rafael G\'omez-Bombarelli, Guan-Horng Liu, Molei Tao, Jaemoo Choi · 10 février 2026

  Learning discrete neural samplers is challenging due to the lack of gradients and combinatorial complexity. While stochastic optimal control (SOC) and Schr\"odinger bridge (SB) provide principled solutions, efficient SOC solvers like adjoint matching (AM), which excel in continuous domains, remain u…

• Do physics-informed neural networks (PINNs) need to be deep? Shallow PINNs using the Levenberg-Marquardt algorithm

  Muhammad Luthfi Shahab, Imam Mukhlash, Hadi Susanto · 10 février 2026

  This work investigates the use of shallow physics-informed neural networks (PINNs) for solving forward and inverse problems of nonlinear partial differential equations (PDEs). By reformulating PINNs as nonlinear systems, the Levenberg-Marquardt (LM) algorithm is employed to efficiently optimize the …

• Radial M\"untz-Sz\'asz Networks: Neural Architectures with Learnable Power Bases for Multidimensional Singularities

  Gnankan Landry Regis N'guessan, Bum Jun Kim · 10 février 2026

  Radial singular fields, such as $1/r$, $\log r$, and crack-tip profiles, are difficult to model for coordinate-separable neural architectures. We show that any $C^2$ function that is both radial and additively separable must be quadratic, establishing a fundamental obstruction for coordinate-wise po…

• Lagged backward-compatible physics-informed neural networks for unsaturated soil consolidation analysis

  Dong Li (Department of Civil, Environmental, and Infrastructure Engineering, George Mason University, Fairfax, VA, USA), Shuai Huang (National Institute of Natural Hazards, Ministry of Emergency Management, Beijing, China), Yapeng Cao (State Key Laboratory of Cryospheric Science and Frozen Soil Engineering, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, China, Navier Laboratory, \'Ecole Nationale des Ponts et Chauss\'ees, Marne-la-Vall\'ee Cedex 2, France), Yujun Cui (Navier Laboratory, \'Ecole Nationale des Ponts et Chauss\'ees, Marne-la-Vall\'ee Cedex 2, France), Xiaobin Wei (School of Civil Engineering, Hebei University of Engineering, Handan, China), Hongtao Cao (College of Civil Engineering, Zhejiang University of Technology, Hangzhou, China) · 10 février 2026

  This study develops a Lagged Backward-Compatible Physics-Informed Neural Network (LBC-PINN) for simulating and inverting one-dimensional unsaturated soil consolidation under long-term loading. To address the challenges of coupled air and water pressure dissipation across multi-scale time domains, th…

• Schr\"odinger bridge problem via empirical risk minimization

  Denis Belomestny, Alexey Naumov, Nikita Puchkin, Denis Suchkov · 10 février 2026

  We study the Schr\"odinger bridge problem when the endpoint distributions are available only through samples. Classical computational approaches estimate Schr\"odinger potentials via Sinkhorn iterations on empirical measures and then construct a time-inhomogeneous drift by differentiating a kernel-s…