Model Reduction and Neural Networks

Derniers papiers

• From Path Signatures to Sequential Modeling: Incremental Signature Contributions for Offline RL

  Ziyi Zhao, Qingchuan Li, Yuxuan Xu · 13 février 2026

  Path signatures embed trajectories into tensor algebra and constitute a universal, non-parametric representation of paths; however, in the standard form, they collapse temporal structure into a single global object, which limits their suitability for decision-making problems that require step-wise r…

• Toward Adaptive Non-Intrusive Reduced-Order Models: Design and Challenges

  Amirpasha Hedayat, Alberto Padovan, Karthik Duraisamy · 13 février 2026

  Projection-based Reduced Order Models (ROMs) are often deployed as static surrogates, which limits their practical utility once a system leaves the training manifold. We formalize and study adaptive non-intrusive ROMs that update both the latent subspace and the reduced dynamics online. Building on …

• Learning to Control: The iUzawa-Net for Nonsmooth Optimal Control of Linear PDEs

  Yongcun Song, Xiaoming Yuan, Hangrui Yue, Tianyou Zeng · 13 février 2026

  We propose an optimization-informed deep neural network approach, named iUzawa-Net, aiming for the first solver that enables real-time solutions for a class of nonsmooth optimal control problems of linear partial differential equations (PDEs). The iUzawa-Net unrolls an inexact Uzawa method for saddl…

• GHOST: Unmasking Phantom States in Mamba2 via Grouped Hidden-state Output-aware Selection & Truncation

  Michael Menezes, Anastasios Kyrillidis · 13 février 2026

  While Mamba2's expanded state dimension enhances temporal modeling, it incurs substantial inference overhead that saturates bandwidth during autoregressive generation. Standard pruning methods fail to address this bottleneck: unstructured sparsity leaves activations dense, magnitude-based selection …

• Neuro-Symbolic Multitasking: A Unified Framework for Discovering Generalizable Solutions to PDE Families

  Yipeng Huang, Dejun Xu, Zexin Lin, Zhenzhong Wang, Min Jiang · 13 février 2026

  Solving Partial Differential Equations (PDEs) is fundamental to numerous scientific and engineering disciplines. A common challenge arises from solving the PDE families, which are characterized by sharing an identical mathematical structure but varying in specific parameters. Traditional numerical m…

• Free Lunch for Stabilizing Rectified Flow Inversion

  Chenru Wang, Beier Zhu, Chi Zhang · 13 février 2026

  Rectified-Flow (RF)-based generative models have recently emerged as strong alternatives to traditional diffusion models, demonstrating state-of-the-art performance across various tasks. By learning a continuous velocity field that transforms simple noise into complex data, RF-based models not only …

• Latent Generative Solvers for Generalizable Long-Term Physics Simulation

  Zituo Chen, Haixu Wu, Sili Deng · 13 février 2026

  We study long-horizon surrogate simulation across heterogeneous PDE systems. We introduce Latent Generative Solvers (LGS), a two-stage framework that (i) maps diverse PDE states into a shared latent physics space with a pretrained VAE, and (ii) learns probabilistic latent dynamics with a Transformer…

• Structured Hybrid Mechanistic Models for Robust Estimation of Time-Dependent Intervention Outcomes

  Tomer Meir, Ori Linial, Danny Eytan, Uri Shalit · 13 février 2026

  Estimating intervention effects in dynamical systems is crucial for outcome optimization. In medicine, such interventions arise in physiological regulation (e.g., cardiovascular system under fluid administration) and pharmacokinetics, among others. Propofol administration is an anesthetic interventi…

• Latent-Variable Learning of SPDEs via Wiener Chaos

  Sebastian Zeng, Andreas Petersson, Wolfgang Bock · 13 février 2026

  We study the problem of learning the law of linear stochastic partial differential equations (SPDEs) with additive Gaussian forcing from spatiotemporal observations. Most existing deep learning approaches either assume access to the driving noise or initial condition, or rely on deterministic surrog…

• The Observer Effect in World Models: Invasive Adaptation Corrupts Latent Physics

  Christian Intern\`o, Jumpei Yamaguchi, Loren Amdahl-Culleton, Markus Olhofer, David Klindt, Barbara Hammer · 13 février 2026

  Determining whether neural models internalize physical laws as world models, rather than exploiting statistical shortcuts, remains challenging, especially under out-of-distribution (OOD) shifts. Standard evaluations often test latent capability via downstream adaptation (e.g., fine-tuning or high-ca…

• Statistical Learning Analysis of Physics-Informed Neural Networks

  David A. Barajas-Solano · 12 février 2026

  We study the training and performance of physics-informed learning for initial and boundary value problems (IBVP) with physics-informed neural networks (PINNs) from a statistical learning perspective. Specifically, we restrict ourselves to parameterizations with hard initial and boundary condition c…

• SimuScene: Training and Benchmarking Code Generation to Simulate Physical Scenarios

  Yanan Wang, Renxi Wang, Yongxin Wang, Xuezhi Liang, Fajri Koto, Timothy Baldwin, Xiaodan Liang, Haonan Li · 12 février 2026

  Large language models (LLMs) have been extensively studied for tasks like math competitions, complex coding, and scientific reasoning, yet their ability to accurately represent and simulate physical scenarios via code remains underexplored. We propose SimuScene, the first systematic study that train…

• Spatiotemporal Field Generation Based on Hybrid Mamba-Transformer with Physics-informed Fine-tuning

  Peimian Du, Jiabin Liu, Xiaowei Jin, Wangmeng Zuo, Hui Li · 12 février 2026

  This research confronts the challenge of substantial physical equation discrepancies encountered in the generation of spatiotemporal physical fields through data-driven trained models. A spatiotemporal physical field generation model, named HMT-PF, is developed based on the hybrid Mamba-Transformer …

• Solving PDEs in One Shot via Fourier Features with Exact Analytical Derivatives

  Antonin Sulc · 12 février 2026

  Recent random feature methods for solving partial differential equations (PDEs) reduce computational cost compared to physics-informed neural networks (PINNs) but still rely on iterative optimization or expensive derivative computation. We observe that sinusoidal random Fourier features possess a cy…

• PEST: Physics-Enhanced Swin Transformer for 3D Turbulence Simulation

  Yilong Dai, Shengyu Chen, Xiaowei Jia, Peyman Givi, Runlong Yu · 12 février 2026

  Accurate simulation of turbulent flows is fundamental to scientific and engineering applications. Direct numerical simulation (DNS) offers the highest fidelity but is computationally prohibitive, while existing data-driven alternatives struggle with stable long-horizon rollouts, physical consistency…

• A Multimodal Conditional Mixture Model with Distribution-Level Physics Priors

  Jinkyo Han, Bahador Bahmani · 12 février 2026

  Many scientific and engineering systems exhibit intrinsically multimodal behavior arising from latent regime switching and non-unique physical mechanisms. In such settings, learning the full conditional distribution of admissible outcomes in a physically consistent and interpretable manner remains a…

• Direct Learning of Calibration-Aware Uncertainty for Neural PDE Surrogates

  Carlos Stein Brito · 12 février 2026

  Neural PDE surrogates are often deployed in data-limited or partially observed regimes where downstream decisions depend on calibrated uncertainty in addition to low prediction error. Existing approaches obtain uncertainty through ensemble replication, fixed stochastic noise such as dropout, or post…

• Unlocked Backpropagation using Wave Scattering

  Christian Pehle, Jean-Jacques Slotine · 12 février 2026

  Both the backpropagation algorithm in machine learning and the maximum principle in optimal control theory are posed as a two-point boundary problem, resulting in a "forward-backward" lock. We derive a reformulation of the maximum principle in optimal control theory as a hyperbolic initial value pro…

• On the Role of Consistency Between Physics and Data in Physics-Informed Neural Networks

  Nicol\'as Becerra-Zuniga, Lucas Lacasa, Eusebio Valero, Gonzalo Rubio · 12 février 2026

  Physics-informed neural networks (PINNs) have gained significant attention as a surrogate modeling strategy for partial differential equations (PDEs), particularly in regimes where labeled data are scarce and physical constraints can be leveraged to regularize the learning process. In practice, howe…

• Adaptive recurrent flow map operator learning for reaction diffusion dynamics

  Huseyin Tunc · 11 février 2026

  Reaction-diffusion (RD) equations underpin pattern formation across chemistry, biology, and physics, yet learning stable operators that forecast their long-term dynamics from data remains challenging. Neural-operator surrogates provide resolution-robust prediction, but autoregressive rollouts can dr…

• Empirical Stability Analysis of Kolmogorov-Arnold Networks in Hard-Constrained Recurrent Physics-Informed Discovery

  Enzo Nicolas Spotorno, Josafat Leal Filho, Antonio Augusto Medeiros Frohlich · 11 février 2026

  We investigate the integration of Kolmogorov-Arnold Networks (KANs) into hard-constrained recurrent physics-informed architectures (HRPINN) to evaluate the fidelity of learned residual manifolds in oscillatory systems. Motivated by the Kolmogorov-Arnold representation theorem and preliminary gray-bo…

• Supervised Metric Regularization Through Alternating Optimization for Multi-Regime Physics-Informed Neural Networks

  Enzo Nicolas Spotorno, Josafat Ribeiro Leal, Antonio Augusto Frohlich · 11 février 2026

  Standard Physics-Informed Neural Networks (PINNs) often face challenges when modeling parameterized dynamical systems with sharp regime transitions, such as bifurcations. In these scenarios, the continuous mapping from parameters to solutions can result in spectral bias or "mode collapse", where the…

• Solving PDEs With Deep Neural Nets under General Boundary Conditions

  Chenggong Zhang · 11 février 2026

  Partial Differential Equations (PDEs) are central to modeling complex systems across physical, biological, and engineering domains, yet traditional numerical methods often struggle with high-dimensional or complex problems. Physics-Informed Neural Networks (PINNs) have emerged as an efficient altern…

• Toeplitz Based Spectral Methods for Data-driven Dynamical Systems

  Vladimir R. Kostic, Karim Lounici, Massimiliano Pontil · 11 février 2026

  We introduce a Toeplitz-based framework for data-driven spectral estimation of linear evolution operators in dynamical systems. Focusing on transfer and Koopman operators from equilibrium trajectories without access to the underlying equations of motion, our method applies Toeplitz filters to the in…

• Learning to Discover Iterative Spectral Algorithms

  Zihang Liu, Oleg Balabanov, Yaoqing Yang, Michael W. Mahoney · 11 février 2026

  We introduce AutoSpec, a neural network framework for discovering iterative spectral algorithms for large-scale numerical linear algebra and numerical optimization. Our self-supervised models adapt to input operators using coarse spectral information (e.g., eigenvalue estimates and residual norms), …