Model Reduction and Neural Networks

Derniers papiers

• Scalable Bayesian Inference for Nonlinear Conservation Laws

  Tim Weiland, Philipp Hennig · 1 juin 2026

  Nonlinear conservation laws are at the heart of many of the most important dynamical systems in science and engineering. In practical applications, such systems are often subject to various sources of uncertainty, e.g. due to sparse or noisy measurements. Inferring physical quantities and fields of …

• Learning Permutation-invariant Macroscopic Dynamics

  Zhichao Han, Mengyi Chen, Qianxiao Li · 1 juin 2026

  Accurately modeling the macroscopic dynamics of high-dimensional microscopic systems is of broad interest across the sciences. Many data-driven approaches learn a low-dimensional latent state through an autoencoder trained for pointwise input reconstruction. These methods typically assume a fixed or…

• Full-field prediction for engineering-scale three-dimensional aircraft with multigrid-hierarchical learning

  Yunfei Liu, Hao Wang, Yuhang Qi, Hao Yue, Dehong Meng, Wei Li, Rui Wang, Tiejun Li, Jie Liu, Junwu Hong, Xinhai Chen · 1 juin 2026

  High-fidelity computational fluid dynamics is essential for aerospace design, but engineering-scale simulations of practical three-dimensional aircraft remain computationally expensive. Learning-based flow-field initialization can improve efficiency by reducing the numerical distance between the ini…

• A holomorphic neural network framework for 3D boundary value problems governed by harmonic potentials

  Enrico Ballini, Allan Peter Engsig-Karup, Tito Andriollo · 1 juin 2026

  We present a neural-network-based framework for the solution of three-dimensional boundary value problems where the solution is expressible in terms of harmonic potentials. The approach leverages the Whittaker integral formula, which allows representing the solution through functions that are holomo…

• Reduced-order modeling of Hamiltonian dynamics based on symplectic neural networks

  Yongsheng Chen, Wei Guo, Qi Tang, Xinghui Zhong · 1 juin 2026

  We introduce a novel data-driven symplectic induced-order modeling (ROM) framework for high-dimensional Hamiltonian systems that unifies latent-space discovery and dynamics learning within a single, end-to-end neural architecture. The encoder-decoder is built from Henon neural networks (HenonNets) a…

• Multi-Scale Separable Fourier Neural Networks for Solving High-Frequency PDEs

  Qihong Yang, Qiaolin He · 1 juin 2026

  We propose a novel neural network architecture, termed Multi-Scale Separable Fourier Neural Networks (MS-SFNN), for the accurate and efficient solution of linear and nonlinear high-frequency partial differential equations (PDEs). MS-SFNN exploits a separable representation: given a $d$-dimensional i…

• Unfolding Generative Flows with Koopman Operators: Trajectory-Preserving Linearization

  Erkan Turan, Aristotelis Siozopoulos, Louis Martinez, Julien Gaubil, Emery Pierson, Maks Ovsjanikov · 1 juin 2026

  Continuous Normalizing Flows (CNFs) enable elegant generative modeling but remain bottlenecked by their iterative nature requiring costly sampling and lacking interpretability of the intermediate states. Recent approaches accelerate sampling by straightening trajectories or distilling endpoints, yet…

• PINNs Failure Modes are Overfitting

  Nigel T. Andersen, Takashi Matsubara · 1 juin 2026

  Physics-Informed Neural Networks (PINNs) are a common class of machine learning-based partial differential equation (PDE) solvers which train a network to represent a solution by minimizing a residual loss that encodes the PDE. Despite their successes, they are known to fail on certain simple equati…

• Circuit-Inspired High-Order Neural Networks with Unified Neural Dynamics Modeling for PDE Solving and Visual Perception

  Tongfei Chen, Jingying Yang, Linlin Yang, Juan Zhang, Jinhu L\"u, David Doermann, Chunyu Xie, Long He, Tian Wang, Guodong Guo, Baochang Zhang · 1 juin 2026

  Deep networks often rely on architectural heuristics to shape representation evolution, limiting their ability to model data governed by intrinsic dynamics. We present the Circuit-inspired High-Order Neural Network (CHONN), a modular framework that treats representation evolution as a latent potenti…

• Physics-Informed Coarsening for Multigrid Graph Neural Surrogates

  Amir Bazzi, David Cardinaux, Ramy Nemer, Jose Alaves, Arjun Kalkur Matpadi Raghavendra, Elie Hachem · 1 juin 2026

  Learning-based surrogates for partial differential equations have recently matched the accuracy of classical solvers while achieving orders-of-magnitude speedups, predominantly in fluid settings and structured geometries. In contrast, robust surrogates for deformable solids remain underexplored, des…

• Discovering Thermodynamically Admissible Dissipation Potentials via Grammar-Based Symbolic Regression

  Federico Califano, Jacopo Ciambella · 1 juin 2026

  Constitutive laws for inelastic materials must satisfy strict thermodynamic admissibility requirements, yet current data-driven approaches sacrifice interpretability, even when formal guarantees are provided by physics-encoded architectures. We propose a symbolic regression framework for the data-dr…

• Learning Transferable Predictability Representations

  Diyali Goswami, Auroop R. Ganguly · 1 juin 2026

  We study the problem of assigning a scalar score to a short trajectory window that reflects its position on an ordered continuum of predictability regimes, spanning structured deterministic dynamics to unstructured stochastic noise. Existing methods address deterministic-versus-stochastic discrimina…

• Free energy Estimation on Any State Space

  Jiajun He, Zijing Ou, Francisco Vargas, Yingzhen Li, Jos\'e Miguel Hern\'andez-Lobato, Carles Domingo-Enrich, Yuanqi Du · 1 juin 2026

  Free energy estimation is a fundamental yet challenging problem, from physics to statistics. Classical approaches rely on thermodynamic transformations, ranging from direct estimation, quasistatic integration, to finite-time averaging. Recent work [He and Du et al., 2025] learns neural transports to…

• The Dynamic-Probabilistic Consistency Gap in Chaotic Surrogate Modeling

  Andre Herz, Matthijs Pals, Daniel Durstewitz, Georgia Koppe · 1 juin 2026

  Dynamical systems reconstruction (DSR) aims to learn surrogate models that capture the dynamics underlying time-series data. Reliably deploying these surrogates requires uncertainty estimates consistent with the learned dynamics. We expose a dynamic-probabilistic consistency (DPC) gap: the pursuit o…

• VFEAgent: A Multimodal Agent Framework for End-to-End Automated Finite Element Analysis

  Jiachen Zhang (Peking University, China Agricultural University), Junyi Lao (Peking University), Chenghao Liu (Peking University), Siyuan Liu (Peking University), Shixin Wu (Peking University), Linsen Zhang (Peking University), Boyu Wang (Peking University), Songfang Huang (Peking University) · 29 mai 2026

  Finite Element Analysis (FEA) serves as the cornerstone of modern engineering design. However, its workflow is inherently complex and relies heavily on domain expertise. Although recent efforts have integrated Large Language Models (LLMs) into FEA, existing approaches face limitations in handling mu…

• Spectral Guidance for Flexible and Efficient Control of Diffusion Models

  Gabriel Moreira, Manuel Marques, Jo\~ao Paulo Costeira, Chenyan Xiong · 29 mai 2026

  We introduce Spectral Guidance, a framework for controlling diffusion models by leveraging the intrinsic geometry of the generative process. As data is progressively corrupted by noise, only a small number of features remain informative for control. We characterize them as the singular functions of …

• The Hamilton-Jacobi Theory of Deep Learning

  Jose Marie Antonio Mi\~noza, Erika Fille T. Legara, Christopher P. Monterola · 29 mai 2026

  In this paper, training a neural network is identified, exactly, as a search through Hamilton--Jacobi initial-value problems: each gradient step selects the initial data of a viscous Hamilton--Jacobi equation whose Hopf--Cole propagator best fits the observations; at inference, the input is the spat…

• Sequential Physics-Constrained Neural Operator Forward Modeling for the $\textit{Norne}$ Reservoir System

  Clement Etienam, Juntao Yang, Oleg Ovcharenko, Nick Luiken, Tsubasa Onishi, Nefeli Moridis, Issam Said · 29 mai 2026

  We develop a comprehensive mathematical and computational framework for sequential surrogate modeling of three-phase black-oil reservoir dynamics using neural operators, with particular emphasis on Fourier Neural Operators (FNO) and their physics-informed variant (PINO). The application focus is the…

• BuilDyn: Excitation-Driven Data Generation for Building Thermal Dynamics Modeling and Control

  Felix Koch, Thomas Krug, Fabian Raisch, Benjamin Sch\"afer, Benjamin Tischler · 29 mai 2026

  Machine learning (ML) is increasingly used for data-driven modeling of buildings to enable downstream tasks such as fault detection and diagnosis, and energy-efficient control. While recent work improves generalization across building characteristics, weather, and occupancy, generalization also depe…

• Inpainting physics: self-supervised learning for context-driven fluid simulation

  Jonas Weidner, Yeray Martin-Ruisanchez, Daniel Rueckert, Benedikt Wiestler, Julian Suk · 29 mai 2026

  Neural surrogate models for computational fluid dynamics (CFD) are typically trained as forward operators that map explicit problem specifications, such as geometry and boundary conditions, to solution fields. This ties the model to the conditioning variables seen during training and limits reuse un…

• Neural Operator-Based Surrogate Model for CFD:Helical Coil Steam Generator in Small Modular Reactor

  Minseo Lee, Seongmin Oh, Chaehyeon Song, Bumjin Cho, Shilaj Baral, Sangam Khanal, Minseop Song, Joongoo Jeon · 29 mai 2026

  Real-time thermal-hydraulic simulation is essential for digital twin (DT) technology that supports the safe and efficient operation of small modular reactors (SMRs). Computational fluid dynamics (CFD) provides high-fidelity flow analysis, but its computational cost prevents direct use in DT applicat…

• Faithful Embeddings of Irregular and Asynchronous Data for Online Log-NCDEs

  Benjamin Walker, Alexandre Bloch, Lingyi Yang, Sam Morley, Terry Lyons · 29 mai 2026

  Continuous-time models are a natural choice for irregular and asynchronous data. A central design choice is how to embed discrete observations into continuous time. Interpolation- and imputation-based embeddings reconstruct a continuous observation path, making the model sensitive to the choice of r…

• Adapting Automotive Aerodynamics Surrogates to New Vehicle Families via Transfer Learning

  Seunghwan Keum, Alok Warey · 29 mai 2026

  Deploying Scientific Machine Learning surrogates in industrial CFD workflows requires adapting pretrained models to new vehicle families without large datasets; yet whether geometric representations learned by a geometry encoder transfer to topologically distinct shapes remains unvalidated. We add…

• A Novel Tensor Product-Based Neural Network for Solving Partial Differential Equations

  Qihong Yang, Yangtao Deng, Qiaolin He, Shiquan Zhang · 29 mai 2026

  This paper presents the Tensor Product Network (TPNet), a novel neural architecture for efficient and accurate function approximation and PDE solving. The core of the proposal involves constructing the solution explicitly as a linear combination of basis functions integrated into the network, with c…

• Unveiling Multi-regime Patterns in SciML: Distinct Failure Modes and Regime-specific Optimization

  Yuxin Wang, Yuanzhe Hu, Xiaokun Zhong, Xiaopeng Wang, Haiquan Lu, Tianyu Pang, Michael W. Mahoney, Yujun Yan, Pu Ren, Yaoqing Yang · 29 mai 2026

  Neural networks trained under different hyperparameter settings can fall into distinct training "regimes," with consistent behavior within regimes and qualitative differences across regimes. In this paper, we study such multi-regime behavior in scientific machine learning (SciML) models through a re…