Model Reduction and Neural Networks

Derniers papiers

• Interpretability-Guided Layer Selection over Subspace Projection: SAEs as Stethoscopes, Not Scalpels, for Raw Task Vector Model Editing

  Li Lei, Madalina Ciobanu, Qingqing Mao, Ritankar Das · 28 mai 2026

  LLMs increasingly require surgical model editing to enhance domain-specific capabilities without incurring the computational cost or catastrophic forgetting associated with full fine-tuning. Sparse Autoencoders (SAEs) have emerged as a promising tool in this setting, in principle allowing for featur…

• Hybrid Neural World Models

  Pranav Lakshmanan, Paras Chopra · 28 mai 2026

  Neural surrogates promise large speedups over classical solvers for physical dynamics but fail silently at sharp dynamical events such as shocks, fronts, and contact. We present hybrid neural world models for physical dynamics: a recipe for training and deploying multi-horizon surrogates in physical…

• Neural Quantum Spectral Operator Learning for Solving Partial Differential Equations

  Chanyoung Kim, Myeonghwan Seong, Yujin Kim, Daniel K. Park, Youngjoon Hong · 28 mai 2026

  Partial differential equations (PDEs) are central to modeling physical and engineering systems, but repeatedly solving parametric PDEs remains computationally expensive. Operator learning enables fast surrogate inference, yet typically requires large input-output paired datasets generated by costly …

• Sparse POD Mode Selection and Manifold Dimensionality Reduction with Neural Networks

  Tomoki Koike, Prakash Mohan, Marc T. Henry de Frahan, Elizabeth Qian, Julie Bessac · 28 mai 2026

  High-performance computing enables simulation of high-dimensional physical systems, but downstream analyses such as inverse problems and control remain computationally expensive, motivating model order reduction (MOR) to construct efficient low-dimensional surrogates. Proper Orthogonal Decomposition…

• History-aware adaptive reduced-order models via incremental singular value decomposition

  Amirpasha Hedayat, Ali Mohaghegh, Laura Balzano, Cheng Huang, Karthik Duraisamy · 28 mai 2026

  Reduced-order models (ROMs) can accelerate high-dimensional dynamical simulations, but their accuracy often deteriorates when online dynamics leave the regime represented by offline training data. We develop a projection-based adaptive ROM framework based on incremental singular value decomposition …

• CFDTwin: An open-source GUI and Python toolkit for POD-NN surrogate modeling of ANSYS Fluent simulations

  Daniel Curl, Han Hu · 28 mai 2026

  High-fidelity computational fluid dynamics (CFD) is widely used for thermal-fluid design, but repeated CFD solves remain expensive for design optimization, uncertainty analysis, and digital-twin workflows. Recently, our team has demonstrated that a proper orthogonal decomposition and neural-network …

• Deep Learning-based Algebraic Reynolds Stress Closures for RANS Simulations of Turbulent Flows

  Daniel Dehtyriov, Jonathan F. MacArt, Justin Sirignano · 27 mai 2026

  Turbulence is ubiquitous in engineering and science, yet direct simulation is prohibitively expensive. The Reynolds-averaged Navier-Stokes (RANS) equations provide savings exceeding ten orders of magnitude but introduce unclosed terms (the closure problem). Offline-trained machine-learning (ML) clos…

• Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations

  Shuang Chen, Juncai He, Xue-Cheng Tai · 27 mai 2026

  We introduce an abstract neural flow framework for neural networks and neural operators. The framework contains two continuous-depth models, namely neural flows with composition and separation structures, and covers both finite-dimensional function approximation and infinite-dimensional operator app…

• A PAC-Bayesian View of Generalisation for Physics-Informed Machine Learning

  Thien V. Nguyen, Amaury Habrard, Benjamin Guedj · 27 mai 2026

  Physics-informed machine learning (PIML) integrates mechanistic knowledge, typically in the form of partial differential equations (PDE), into data-driven models. Despite strong empirical performance, its statistical generalisation properties remain poorly understood, particularly in the regression …

• Data-driven sparse identification of governing PDEs via knockoff filters and multi-criteria trade-offs

  Pongpisit Thanasutives, Naichang Ke, Yoshinobu Kawahara · 27 mai 2026

  We propose KO-PDE-IDENT, a data-driven framework for identifying parsimonious partial differential equations (PDEs) with false discovery rate (FDR) control. PDE discovery from noisy observations is often hindered by extreme multicollinearity among candidate terms, which causes typical sparse-regress…

• Two-Parameter Flows for Learning Population Dynamics of Physical Systems

  Paul Schwerdtner, Tobias Blickhan, Benjamin Peherstorfer · 27 mai 2026

  This work addresses the problem of learning the dynamics of high-dimensional probability densities over time using unlabeled samples, without assuming access to trajectory information. We introduce two-parameter flows that learn only sampling-time transports from a base distribution to each marginal…

• MTL-FNO: A Lightweight Multi-Task Fourier Neural Operator for Sparse Field Reconstruction

  Siyu Ye, Shihang Li, Zhiqiang Gong, Benrong Zhang, Weien Zhou, Yiyong Huang, Wen Yao · 27 mai 2026

  Efficient onboard multi-field sparse reconstruction is essential for the autonomous operation of aerospace vehicles. While existing deep learning models exhibit promise for single-field reconstruction, deploying multiple independent models leads to prohibitive model size growth and fails to exploit …

• Recursive Flow Matching

  Jiahe Huang, Sihan Xu, Sharvaree Vadgama, Rose Yu · 27 mai 2026

  Generative models have emerged as a powerful paradigm for solving physics systems and modeling complex spatiotemporal dynamics. However, achieving high physical accuracy without incurring high computational cost remains a fundamental challenge, as existing approaches face a critical speed-fidelity t…

• Semigroup Consistency as a Diagnostic for Learned Physics Simulators

  Lennon J. Shikhman · 27 mai 2026

  Learned physics simulators are often evaluated by one-step or short-horizon prediction error, but these metrics can miss failures in temporal composition and long-horizon rollout. For autonomous, state-complete systems, exact solution maps satisfy a semigroup law: direct evolution over $s+t$ should …

• Planning Neural Dynamics with Lie Group Embedding through Supervised Projective Manifold Learning

  Tianwei Wang, Bryan Chen, Qian Zuo, Qiyue Xia, Xin Li, Wei Pang · 27 mai 2026

  We propose Lie group embedded dynamical neural networks (LieEDNN) and the corresponding learning algorithms based on gradient descent and metric projection on smooth manifold, where we treat Lie group as an intrinsic representation for continuous symmetry of manifold geometry. Thereby we achieve lea…

• Deep-layer limit and stability analysis of the basic forward-backward-splitting induced network (II): learning problems

  Xuan Lin, Chunlin Wu · 27 mai 2026

  Deep unfolding neural networks derived from iterative optimization schemes and numerical ordinary/partial differential equations (ODEs/PDEs) have attracted much attention in data science over the last decade. Therein, numerous important network architectures were constructed from the basic forward-b…

• PIDM-DP: Physics-Informed Diffusion with Dormand-Prince Integration for Chaotic System Identification and State Reconstruction across Multiple Dynamical Regimes

  Shailendra Dabral · 27 mai 2026

  Reconstructing continuous state trajectories of chaotic dynamical systems from sparse, noisy observations remains a fundamental open problem in nonlinear science. We introduce the Physics-Informed Diffusion Model with Dormand-Prince Integration (PIDM-DP), which embeds a fully differentiable 5th-orde…

• Autoregression-Free Neural Operators for Time-Dependent PDEs

  Jiaquan Zhang, Caiyan Qin, Haoyu Bian, Libin Cai, Yi Lu, Chaoning Zhang, Wei Dong, Yuanfang Guo, Yang Yang, Hen Tao Shen · 26 mai 2026

  Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs). For time-dependent PDEs, existing methods typically perform long-horizon prediction through autoregressive rollout directly in high-dimensi…

• Iterative Refinement Neural Operators are Learned Fixed-Point Solvers: A Principled Approach to Spectral Bias Mitigation

  Xiaotian Liu, Shuyuan Shang, Xiaopeng Wang, Pu Ren, Yaoqing Yang · 26 mai 2026

  Neural operators serve as fast, data-driven surrogates for scientific modeling but typically rely on a monolithic, single-pass inference procedure that struggles to resolve high-frequency details, a limitation known as spectral bias. We introduce the Iterative Refinement Neural Operator (IRNO), whic…

• NPSolver: Neural Poisson Solver with Iterative Physics Supervision

  Bocheng Zeng, Rui Zhang, Runze Mao, Mengtao Yan, Xuan Bai, Yang Liu, Zhi X. Chen, Hao Sun · 26 mai 2026

  Efficiently solving Poisson equations on complex, irregular domains remains a fundamental challenge in scientific computing, as classical iterative solvers often suffer from prohibitive runtime due to ill-conditioned systems. While neural operators offer a fast alternative, they typically rely on la…

• High-fidelity Modeling of Full-scale Pressurized Water Reactor Flow Fields for Machine Learning Applications

  Logan A. Burnett, Hyungjun Kim, Hsien-Cheng Chou, Arsha Witoelar, Robert A. Brewster, Benoit Forget, Emilio Baglietto, Majdi I. Radaideh · 26 mai 2026

  This work presents a high-fidelity computational fluid dynamics (CFD) and data-driven modeling framework for assembly-level flow characterization in a four-loop pressurized water reactor (PWR). A full lower-plenum and core-inlet domain was constructed using publicly available geometry and operating …

• Leveraging Gauge Freedom for Learning Non-Gradient Population Dynamics of Stochastic Systems

  Jules Berman, Tobias Blickhan, Benjamin Peherstorfer · 26 mai 2026

  Existing work on population dynamics inference often focuses on flows arising from vector fields that are the gradients of scalar potentials. Among all admissible flows that are compatible with the population dynamics, gradient flows are optimal in a specific sense: they minimize kinetic energy. The…

• Fourier Feature Pyramids for Physics-Informed Neural Networks

  Brandon Zhao, Yixuan Wang, Jonathan T. Barron, Katherine L. Bouman, Dor Verbin, Pratul P. Srinivasan · 26 mai 2026

  We present an improved neural field architecture for solving partial differential equations (PDEs). Current physics-informed neural networks (PINNs) provide a flexible framework for solving PDEs, but they struggle to achieve highly accurate solutions and require computation that scales poorly with p…

• IV-Net: A neural network for elliptic PDEs with random and highly varying coefficients

  Shan Zhong, George Biros · 26 mai 2026

  We introduce a novel neural operator architecture designed to approximate solutions of linear elliptic partial differential equations with high-contrast, spatially varying coefficients. The network, termed the Iterated V-shaped Net (IV-Net), realizes a mapping from the input coefficients and rightha…

• Mitigating Gradient Pathology in PINNs through Aligned Constraint

  Yichen Luo, Peiyu Zhu, Dongxiao Hu, Jia Wang, Tailin Wu, Dapeng Lan, Yu Liu, Zhibo Pang · 26 mai 2026

  While Physics-Informed Neural Networks (PINNs) are powerful for solving Partial Differential Equations (PDEs), their training is often paralyzed by gradient pathology. The gradients from the PDE residuals and boundary constraints oppose each other, trapping the model in local minima. Current solutio…