Model Reduction and Neural Networks

Derniers papiers

• A Unified Framework for Structured Flow Modeling: From Continuous Fields to Data-Driven Representations

  Diego Casadei · 19 mai 2026

  Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of domains, including physical, engineered, and data-driven systems. This work provides a unified perspec…

• Long-horizon prediction of three-dimensional wall-bounded turbulence with CTA-Swin-UNet and resolvent analysis

  Bo Chen, Yitong Fan, Jie Yao, Weipeng Li · 19 mai 2026

  Long-horizon prediction of three-dimensional (3D) wall-bounded turbulence with machine-learning methods remains a challenging task, due to the rapid accumulation of autoregressive errors and the substantially computational cost. To address these challenges, we present a hybrid machine-learning frame…

• Geometry-Aware Attention Guidance for Diffusion Models via Modern Hopfield Dynamics

  Kwanyoung Kim · 19 mai 2026

  Classifier-Free Guidance (CFG) improves sample quality in diffusion models, but its dual-pass inference and reliance on null-condition training limit its use in few-step regimes. Attention-space guidance has emerged as a complementary paradigm that addresses this gap, yet why prior sparse-vs-dense a…

• Generative Adversarial Learning from Deterministic Processes

  Joris C. K\"uhl, Hanno Gottschalk · 19 mai 2026

  Physical AI is being successfully applied to data which does not follow the traditional paradigm of independent and identically distributed (i.i.d.) samples. In fact, physical AI is often trained on data which is not random at all, and is instead derived from chaotic dynamical systems like turbulenc…

• Geometric Dictionary Learning of Dynamical Systems with Optimal Transport

  Thibaut Germain, Sami Chemlal, R\'emi Flamary, Vladimir R. Kostic, Karim Lounici · 19 mai 2026

  Learning dynamical systems through operator-theoretic representations provides a powerful framework for analyzing complex dynamics, as spectral quantities such as eigenvalues and invariant structures encode characteristic time scales and long-term behavior. However, dynamical operators are typically…

• Wavelet Flow Matching for Multi-Scale Physics Emulation

  Gabriele Accarino, Juan Nathaniel, Carla Roesch, Pierre Gentine, Sara Shamekh, Duncan Watson-Parris, Viviana Acquaviva · 19 mai 2026

  Accurate emulation of multi-scale physical systems governed by PDEs demands models that remain stable over long autoregressive rollouts while preserving fine-scale structures. Deterministic emulators produce overly-smoothed predictions, while generative approaches better capture details but are cost…

• BlendedNet++: A dataset and benchmark for field-resolved aerodynamics and inverse design of blended wing body aircraft

  Nicholas Sung, Steven Spreizer, Mohamed Elrefaie, Matthew C. Jones, Faez Ahmed · 19 mai 2026

  The conceptual design of Blended Wing Body (BWB) aircraft is often constrained by the high computational cost of resolving complex aerodynamics over a high-dimensional design space. While deep learning offers a pathway to rapid aerodynamic prediction and inverse design, its adoption in aerospace eng…

• Identify Then Project: Contrastive Learning of Latent Dynamics from Partial Observations with Port-Hamiltonian Structure

  Peilun Li, Kaiyuan Tan, Daniel Moyer, Thomas Beckers · 19 mai 2026

  Identifying latent state representations and dynamics is essential when direct modeling in observation space is infeasible, particularly under partial and high-dimensional observations. In such settings, representation learning and physics-aware modeling are inherently coupled. We study this problem…

• Diffusion-Based Stochastic Operator Networks for Uncertainty Quantification in Stochastic Partial Differential Equations

  Phuoc-Toan Huynh, Richard Archibald, Feng Bao · 19 mai 2026

  We introduce a novel framework for uncertainty quantification of solution operators associated with stochastic partial differential equations (SPDEs). Although SPDEs play a central role in modeling complex physical systems under uncertainty, their practical use typically requires specifying the magn…

• Consistency of Learned Sparse Grid Quadrature Rules using NeuralODEs

  Hanno Gottschalk, Emil Partow, Tobias J. Riedlinger · 19 mai 2026

  We prove consistency of a recently proposed scheme that evaluates expected values by composing a learned transport map with Clenshaw--Curtis sparse-grid quadrature on a tractable product source. Our analysis hinges on the structural fact that composition of a $C^k_{\mathrm{mix}}$-regular function --…

• Physics-Aligned Canonical Equivariant Fourier Neural Operator under Symmetry-Induced Shifts

  Jiaxiao Xu, Changhong Mou, Yeyu Zhang, Fengxiang He · 19 mai 2026

  Neural operators approximate PDE solution maps, but they need not respect the symmetries of the governing equation. In out-of-distribution (OOD) regimes, a standard neural operator must often learn coordinate alignment and physical evolution within a single map, which can hurt generalization. We use…

• SNLP: Layer-Parallel Inference via Structured Newton Corrections

  Ligong Han, Kai Xu, Hao Wang, Akash Srivastava · 19 mai 2026

  Autoregressive language models execute Transformer layers sequentially, creating a latency bottleneck that is not removed by conventional tensor or pipeline parallelism. We study whether this layerwise dependency can be relaxed by treating the hidden-state trace across layers as the solution of a no…

• pyforce-1.0.0: Python Framework for data-driven model Order Reduction of multi-physiCs problEms

  Stefano Riva, Yantao Luo, Carolina Introini, Antonio Cammi · 19 mai 2026

  pyforce is a Python package implementing Data-Driven Reduced Order Modelling techniques for applications to multi-physics problems, mainly set in the Nuclear Engineering world. The package is part of the ROSE (Reduced Order modelling with data-driven techniques for multi-phySics problEms): mathemati…

• A Critical Assessment of PINNs and Operator Learning for Geotechnical Engineering

  Krishna Kumar · 19 mai 2026

  Scientific machine learning (SciML) offers neural-network alternatives to numerical workflows in geotechnical engineering. This paper benchmarks multi-layer perceptrons (MLPs), physics-informed neural networks (PINNs), deep operator networks (DeepONet), and graph network simulators (GNS) against fin…

• SAFE-SVD: Sensitivity-Aware Fidelity-Enforcing SVD for Physics Foundation Models

  Chengjie Hong, Feixiang He, Yiheng Zeng, Lulu Kang, He Wang · 19 mai 2026

  We propose a new method for compressing physics foundation models (PFMs) which is a new trend in AI for Science. While model compression is essential for reducing memory use and accelerating inference in large foundation models, it remains under-explored for PFMs, where preserving physical fidelity …

• Multi-Fidelity Flow Matching: Cascaded Refinement of PDE Solutions

  Sipeng Chen, Junliang Liu, Hewei Tang, Shibo Li · 18 mai 2026

  The source distribution in conditional flow matching is a design parameter that can be calibrated to data, not a default isotropic prior. We exploit this in Multi-Fidelity Flow Matching (MFFM), a cascade refinement framework for parametric PDE solutions: the source is calibrated to the empirical low…

• When and Why Adversarial Training Improves PINNs: A Neural Tangent Kernel Perspective

  Yuan-dong Cao, Chi Chiu SO, Jun-Min Wang, He Wang · 18 mai 2026

  Physics-informed neural networks (PINNs) are powerful surrogates for differential equations but are notoriously difficult to train due to spectral bias, stiffness, and poor accuracy on high-frequency or multiscale solutions. Adversarial training based on generative adversarial networks (GANs) has re…

• Hypothesis-driven construction of mesoscopic dynamics

  Zhuoyuan Li, Aiqing Zhu, Qianxiao Li · 18 mai 2026

  Traditional scientific modeling typically begins with fixed, instance-wise effective equations and then carries out equation-specific analysis and computation, a procedure that becomes exceptionally challenging in complex applications such as multiscale systems. We propose an alternative paradigm by…

• Lagrangian Flow Matching: A Least-Action Framework for Principled Path Design

  Shukai Du, Junzhe Zhang, Yiming Li · 18 mai 2026

  Flow matching trains a neural velocity field by regression against a target velocity associated with a prescribed probability path connecting a simple initial distribution to the data distribution. A central design choice is the path itself. Existing constructions, including rectified and optimal-tr…

• Tadpole: Autoencoders as Foundation Models for 3D PDEs with Online Learning

  Qiang Liu, Felix Koehler, Benjamin Holzschuh, Nils Thuerey · 18 mai 2026

  We introduce Tadpole, a novel foundation model for three-dimensional partial differential equations (PDEs) that addresses key challenges in transferability, scalability to high dimensionality, and multi-functionality. Tadpole is pre-trained as an autoencoder on synthetic 3D PDE data generated by an …

• AOT-POT: Adaptive Operator Transformation for Large-Scale PDE Pre-training

  Qitan Lv, Hong Wang, Zhongkai Hao, Wen Wu, Xuenan Xu, Bowen Zhou, Feng Wu, Chao Zhang · 18 mai 2026

  Pre-training neural operators on diverse partial differential equation (PDE) datasets has emerged as a promising direction for building general-purpose surrogate models in scientific machine learning. However, the inherent complexity and structural diversity of PDE solution operators make multi-PDE …

• A numerical study into neural network surrogate model performance for uncertainty propagation

  Noah Wade, Kirubel Teferra · 18 mai 2026

  Neural network surrogate models have emerged as a promising approach to model solution fields for a wide variety of boundary value problems encountered in physical modeling. Stochastic problems represent an area of particularly high interest because of the potential to significantly reduce the repea…

• Universal Approximation of Nonlinear Operators and Their Derivatives

  Filippo de Feo · 18 mai 2026

  Derivative-Informed Operator Learning (DIOL), i.e. learning a (nonlinear) operator and its derivatives, is an open research frontier at the foundations of the influential field of Operator Learning (OL). In particular, Universal Approximation Theorems (UATs) of nonlinear operators and their derivati…

• Breakeven complexity: A new perspective on neural partial differential equation solvers

  Yijing Zhang, Nicholas Roberts, Tanya Marwah, Mikhail Khodak · 18 mai 2026

  Neural surrogate solvers of partial differential equations (PDEs) promise dramatic speedups over numerical methods, especially in scenarios requiring many solves. However, current accuracy-based evaluations do not fully consider two central issues: (1) neural solvers incur substantial up-front costs…

• Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems

  Yeang Makara, Yusuke Tanaka, Takashi Matsubara, Takaharu Yaguchi · 18 mai 2026

  The modeling and simulation of infinite-dimensional Hamiltonian systems are central problems in mathematical physics and engineering, however they pose significant computational and structural challenges for standard data-driven architectures. In this work, we introduce the Symplectic Neural Operato…