Model Reduction and Neural Networks

Derniers papiers

• PGOT: A Physics-Geometry Operator Transformer for Complex PDEs

  Zhuo Zhang, Xi Yang, Yuan Zhao, Canqun Yang · 30 décembre 2025

  While Transformers have demonstrated remarkable potential in modeling Partial Differential Equations (PDEs), modeling large-scale unstructured meshes with complex geometries remains a significant challenge. Existing efficient architectures often employ feature dimensionality reduction strategies, wh…

• From geometry to dynamics: Learning overdamped Langevin dynamics from sparse observations with geometric constraints

  Dimitra Maoutsa · 30 décembre 2025

  How can we learn the laws underlying the dynamics of stochastic systems when their trajectories are sampled sparsely in time? Existing methods either require temporally resolved high-frequency observations, or rely on geometric arguments that apply only to conservative systems, limiting the range of…

• Random Controlled Differential Equations

  Francesco Piatti, Thomas Cass, William F. Turner · 30 décembre 2025

  We introduce a training-efficient framework for time-series learning that combines random features with controlled differential equations (CDEs). In this approach, large randomly parameterized CDEs act as continuous-time reservoirs, mapping input paths to rich representations. Only a linear readout …

• Uncertainty-Aware Flow Field Reconstruction Using SVGP Kolmogorov-Arnold Networks

  Y. Sungtaek Ju · 30 décembre 2025

  Reconstructing time-resolved flow fields from temporally sparse velocimetry measurements is critical for characterizing many complex thermal-fluid systems. We introduce a machine learning framework for uncertainty-aware flow reconstruction using sparse variational Gaussian processes in the Kolmogoro…

• Differentiable Inverse Modeling with Physics-Constrained Latent Diffusion for Heterogeneous Subsurface Parameter Fields

  Zihan Lin, QiZhi He · 30 décembre 2025

  We present a latent diffusion-based differentiable inversion method (LD-DIM) for PDE-constrained inverse problems involving high-dimensional spatially distributed coefficients. LD-DIM couples a pretrained latent diffusion prior with an end-to-end differentiable numerical solver to reconstruct unknow…

• Adaptive Probability Flow Residual Minimization for High-Dimensional Fokker-Planck Equations

  Xiaolong Wu, Qifeng Liao · 30 décembre 2025

  Solving high-dimensional Fokker-Planck (FP) equations is a challenge in computational physics and stochastic dynamics, due to the curse of dimensionality (CoD) and the bottleneck of evaluating second-order diffusion terms. Existing deep learning approaches, such as Physics-Informed Neural Networks, …

• Neural Measures for learning distributions of Random PDEs

  Georgios Arampatzis, Stylianos Katsarakis, Charalambos Makridakis · 30 décembre 2025

  The integration of Scientific Machine Learning (SciML) techniques with uncertainty quantification (UQ) represents a rapidly evolving frontier in computational science. This work advances Physics-Informed Neural Networks (PINNs) by incorporating probabilistic frameworks to effectively model uncertain…

• M\"untz-Sz\'asz Networks: Neural Architectures with Learnable Power-Law Bases

  Gnankan Landry Regis N'guessan · 30 décembre 2025

  Standard neural network architectures employ fixed activation functions (ReLU, tanh, sigmoid) that are poorly suited for approximating functions with singular or fractional power behavior, a structure that arises ubiquitously in physics, including boundary layers, fracture mechanics, and corner sing…

• M\"untz-Sz\'asz Networks: Neural Architectures with Learnable Power-Law Bases

  Gnankan Landry Regis N'guessan · 30 décembre 2025

  Standard neural network architectures employ fixed activation functions (ReLU, tanh, sigmoid) that are poorly suited for approximating functions with singular or fractional power behavior, a structure that arises ubiquitously in physics, including boundary layers, fracture mechanics, and corner sing…

• PI-MFM: Physics-informed multimodal foundation model for solving partial differential equations

  Min Zhu, Jingmin Sun, Zecheng Zhang, Hayden Schaeffer, Lu Lu · 30 décembre 2025

  Partial differential equations (PDEs) govern a wide range of physical systems, and recent multimodal foundation models have shown promise for learning PDE solution operators across diverse equation families. However, existing multi-operator learning approaches are data-hungry and neglect physics dur…

• DBAW-PIKAN: Dynamic Balance Adaptive Weight Kolmogorov-Arnold Neural Network for Solving Partial Differential Equations

  Guokan Chen, Yao Xiao · 30 décembre 2025

  Physics-informed neural networks (PINNs) have led to significant advancements in scientific computing by integrating fundamental physical principles with advanced data-driven techniques. However, when dealing with problems characterized by multi-scale or high-frequency features, PINNs encounter pers…

• Physics-Informed Neural Networks for Device and Circuit Modeling: A Case Study of NeuroSPICE

  Chien-Ting Tung, Chenming Hu · 30 décembre 2025

  We present NeuroSPICE, a physics-informed neural network (PINN) framework for device and circuit simulation. Unlike conventional SPICE, which relies on time-discretized numerical solvers, NeuroSPICE leverages PINNs to solve circuit differential-algebraic equations (DAEs) by minimizing the residual o…

• Spectral Analysis of Hard-Constraint PINNs: The Spatial Modulation Mechanism of Boundary Functions

  Yuchen Xie, Honghang Chi, Haopeng Quan, Yahui Wang, Wei Wang, Yu Ma · 30 décembre 2025

  Physics-Informed Neural Networks with hard constraints (HC-PINNs) are increasingly favored for their ability to strictly enforce boundary conditions via a trial function ansatz $\tilde{u} = A + B \cdot N$, yet the theoretical mechanisms governing their training dynamics have remained unexplored. U…

• PhysicsCorrect: A Training-Free Approach for Stable Neural PDE Simulations

  Xinquan Huang, Paris Perdikaris · 29 décembre 2025

  Neural networks have emerged as powerful surrogates for solving partial differential equations (PDEs), offering significant computational speedups over traditional methods. However, these models suffer from a critical limitation: error accumulation during long-term rollouts, where small inaccuracies…

• Convolutional autoencoders for the reconstruction of three-dimensional interfacial multiphase flows

  Murray Cutforth, Shahab Mirjalili · 29 décembre 2025

  We present a systematic investigation of convolutional autoencoders for the reduced-order representation of three-dimensional interfacial multiphase flows. Focusing on the reconstruction of phase indicators, we examine how the choice of interface representation, including sharp, diffuse, and level-s…

• Sparse Hyperparametric Itakura-Saito Nonnegative Matrix Factorization via Bi-Level Optimization

  Laura Selicato, Flavia Esposito, Andersen Ang, Nicoletta Del Buono, Rafal Zdunek · 29 décembre 2025

  The selection of penalty hyperparameters is a critical aspect in Nonnegative Matrix Factorization (NMF), since these values control the trade-off between reconstruction accuracy and adherence to desired constraints. In this work, we focus on an NMF problem involving the Itakura-Saito (IS) divergence…

• kooplearn: A Scikit-Learn Compatible Library of Algorithms for Evolution Operator Learning

  Giacomo Turri, Gr\'egoire Pacreau, Giacomo Meanti, Timoth\'ee Devergne, Daniel Ordonez, Erfan Mirzaei, Bruno Belucci, Karim Lounici, Vladimir Kostic, Massimiliano Pontil, Pietro Novelli · 29 décembre 2025

  kooplearn is a machine-learning library that implements linear, kernel, and deep-learning estimators of dynamical operators and their spectral decompositions. kooplearn can model both discrete-time evolution operators (Koopman/Transfer) and continuous-time infinitesimal generators. By learning these…

• MAD-NG: Meta-Auto-Decoder Neural Galerkin Method for Solving Parametric Partial Differential Equations

  Qiuqi Li, Yiting Liu, Jin Zhao, Wencan Zhu · 29 décembre 2025

  Parametric partial differential equations (PDEs) are fundamental for modeling a wide range of physical and engineering systems influenced by uncertain or varying parameters. Traditional neural network-based solvers, such as Physics-Informed Neural Networks (PINNs) and Deep Galerkin Methods, often fa…

• A Frobenius-Optimal Projection for Enforcing Linear Conservation in Learned Dynamical Models

  John M. Mango, Ronald Katende · 29 décembre 2025

  We consider the problem of restoring linear conservation laws in data-driven linear dynamical models. Given a learned operator $\widehat{A}$ and a full-rank constraint matrix $C$ encoding one or more invariants, we show that the matrix closest to $\widehat{A}$ in the Frobenius norm and satisfying $C…

• A Multi-fidelity Double-Delta Wing Dataset and Empirical Scaling Laws for GNN-based Aerodynamic Field Surrogate

  Yiren Shen, Juan J. Alonso · 25 décembre 2025

  Data-driven surrogate models are increasingly adopted to accelerate vehicle design. However, open-source multi-fidelity datasets and empirical guidelines linking dataset size to model performance remain limited. This study investigates the relationship between training data size and prediction accur…

• GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformer

  Corey Adams, Rishikesh Ranade, Ram Cherukuri, Sanjay Choudhry · 25 décembre 2025

  We present GeoTransolver, a Multiscale Geometry-Aware Physics Attention Transformer for CAE that replaces standard attention with GALE, coupling physics-aware self-attention on learned state slices with cross-attention to a shared geometry/global/boundary-condition context computed from multi-scale …

• Improving Matrix Exponential for Generative AI Flows: A Taylor-Based Approach Beyond Paterson--Stockmeyer

  Jorge Sastre, Daniel Faronbi, Jos\'e Miguel Alonso, Peter Traver, Javier Ib\'a\~nez, Nuria Lloret · 25 décembre 2025

  The matrix exponential is a fundamental operator in scientific computing and system simulation, with applications ranging from control theory and quantum mechanics to modern generative machine learning. While Pad\'e approximants combined with scaling and squaring have long served as the standard, re…

• Analytic and Variational Stability of Deep Learning Systems

  Ronald Katende · 25 décembre 2025

  We propose a unified analytic and variational framework for studying stability in deep learning systems viewed as coupled representation-parameter dynamics. The central object is the Learning Stability Profile, which tracks the infinitesimal response of representations, parameters, and update mechan…

• Variationally correct operator learning: Reduced basis neural operator with a posteriori error estimation

  Yuan Qiu, Wolfgang Dahmen, Peng Chen · 25 décembre 2025

  Minimizing PDE-residual losses is a common strategy to promote physical consistency in neural operators. However, standard formulations often lack variational correctness, meaning that small residuals do not guarantee small solution errors due to the use of non-compliant norms or ad hoc penalty term…

• mLaSDI: Multi-stage latent space dynamics identification

  William Anderson, Seung Whan Chung, Robert Stephany, Youngsoo Choi · 24 décembre 2025

  Accurately solving partial differential equations (PDEs) is essential across many scientific disciplines. However, high-fidelity solvers can be computationally prohibitive, motivating the development of reduced-order models (ROMs). Recently, Latent Space Dynamics Identification (LaSDI) was proposed …