Model Reduction and Neural Networks

Derniers papiers

• Recursively Trained Diffusion Models: Limiting Collapse Distribution and Spectral Characterization

  Na\"il B. Khelifa, Richard E. Turner, Ramji Venkataramanan · 15 juin 2026

  Recursive training of generative models on their own outputs can lead to model collapse, a compounding drift away from the true data distribution. Existing theoretical works bound finite-round error accumulation in the context of diffusion models, but two questions remain open:~what distribution doe…

• Robin-Neumann Coupling of PINN and FEM Solvers: A Steklov-Poincar\'e View, with Application to Fluid-Structure Interaction with Contact

  Mikel Landajuela · 15 juin 2026

  Physics-informed neural networks (PINNs) are meshless and carry moving geometry and topology change through resampling of collocation points; the finite-element method (FEM) is the workhorse for boundary-fitted discretisations. Coupling the two across a shared interface promises the best of both, ye…

• Graph Diffusion Residuals for Control-Function Instrumental Variables

  Rui Wu, Zongyuan Chen, Hong Xie, Defu Lian, Enhong Chen · 15 juin 2026

  Control-function instrumental variable estimators need a first-stage residual, not merely a first-stage prediction. High-capacity first stages can interpolate treatment and leave too little residual information for the outcome equation. We study Adaptive Anisotropic Instrumental Heat Flow (A-IHF), a…

• CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field data

  Benjamin Alheit, Siddhant Kumar, Mathias Peirlinck · 15 juin 2026

  Constitutive artificial neural networks (CANNs) provide interpretable material model discovery, but have so far been used in stress-supervised settings based on apparent stress-strain data from homogeneous tests. Because each test samples only a narrow loading path and provides homogenized rather th…

• Zero-shot generalization of transformer neural operators to larger domains

  Armand de Villeroch\'e, Sibo Cheng, Vincent Le Guen, Marc Bocquet, Rem-Sophia Mouradi, Patrick Armand, Alban Farchi, Patrick Massin · 15 juin 2026

  Transformer-based neural operators have shown remarkable performance for approximating solution operators of partial differential equations on complex geometries. However, existing approaches implicitly assume a fixed domain size, which limits their ability to generalize at inference. In this work, …

• EqCollide: Equivariant and Collision-Aware Deformable Objects Neural Simulator

  Qianyi Chen, Tianrun Gao, Chenbo Jiang, Tailin Wu · 15 juin 2026

  Simulating collisions of deformable objects is a fundamental yet challenging task due to the complexity of modeling solid mechanics and multi-body interactions. Existing data-driven methods often suffer from lack of equivariance to physical symmetries, inadequate handling of collisions, and limited …

• A fully GPU-based workflow for building physics emulators of hypersonic flows

  Fabian Paischer, Dylan Rubini, Deniz A. Bezgin, Aaron B. Buhendwa, David Hauser, Florian Sestak, Johannes Brandstetter, Sebastian Kaltenbach, Nikolaus A. Adams · 15 juin 2026

  The ability to resolve complex physical phenomena with high fidelity and at low computational cost is central to addressing key challenges in modern engineering. A prime example lies in hypersonic flows, where the precise prediction of the full flowfield topology, in particular with respect to shock…

• A Unified Framework for Structured Flow Modeling: From Representation to Verification and Model Discovery

  Diego Casadei · 15 juin 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 physical, engineered, and data-driven systems. The objective of this work is to establish a unified pe…

• On Approximating the Dynamic Response of Synchronous Generators via Operator Learning: A Step Towards Building Deep Operator-based Power Grid Simulators

  Christian Moya, Amirhossein Mollaali, Guang Lin, Meng Yue · 12 juin 2026

  This paper develops an Operator Learning framework for approximating the dynamic response of synchronous generators. The framework can be used to (i) build a neural network-based generator model that interacts with a power grid simulator or (ii) shadow the true generator's transient response. First,…

• A Physics-Inspired Optimizer: Velocity Regularized Adam

  Pranav Vaidhyanathan, Lucas Schorling, Natalia Ares, Maike Osborne · 11 juin 2026

  We introduce Velocity-Regularized Adam (VRAdam), a physics-inspired optimizer for training deep neural networks that draws on ideas from quartic terms for kinetic energy with its stabilizing effects on various system dynamics. Previous algorithms, including the ubiquitous Adam, operate at the so-cal…

• Structure-Preserving Neural Surrogates with Tractable Uncertainty Quantification

  Handi Zhang, Adrienne M. Propp, Brooks Kinch, Houman Owhadi, Nathaniel Trask · 11 juin 2026

  Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation. In this work, we construct data-driven reduced-…

• Spectrally Regularized Latent Flow Matching for Turbulence Generation

  Khalid Rafiq, Aditya G. Nair · 11 juin 2026

  Latent diffusion and flow matching have emerged as leading approaches for synthetic turbulence generation, yet they systematically under-represent dissipation-range amplitudes. We introduce a latent flow matching framework with a spectrally regularized compression stage that directly targets this fa…

• Reliable Error Estimation for PINNs: Lower and Upper A Posteriori Bounds

  Ismail Huseynov, Arzu Ahmadova, Agamirza Bashirov · 11 juin 2026

  Physics-informed neural networks (PINNs) combine machine learning with physical laws to solve differential equations. While existing results provide rigorous \emph{a posteriori} upper bounds for PINN prediction errors, complete certification also requires complementary lower information in order to …

• SirenFNO: Efficient and Full Frequency Learning of Fourier Neural Operators

  Pengqing Shi, Jie Yin, Stephen Tierney, Junbin Gao · 11 juin 2026

  Fourier neural operators (FNOs) are effective and efficient surrogates for approximating solutions of PDEs and generalize across discretizations. However, owing to the reliance on frequency truncation to maintain learning efficiency of FNOs, empirical studies suggest that FNOs exhibit spectral bias …

• How Low Can You Go? Active Learning for Sparse Model Discovery in the Ultra-Low-Data Limit

  Ana Larra\~naga, Urban Fasel, Steven L. Brunton · 11 juin 2026

  Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering. While early approaches relied on empirical data and heuristics, modern data-driven methods offer greater flexibility and fewer assumptions. However, data acquisition in re…

• Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems

  Zhen Zhang, Alessandro Alla, George Em Karniadakis · 11 juin 2026

  Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-informed neural networks (PINNs) have emerged as a flexible alternative. Their relative performance remains difficult to asse…

• HAMNO: A Hierarchical Adaptive Multi-scale Neural Operator with Physics-Informed Learning for Dynamical Systems

  Mostafa Bamdad, Mohammad Sadegh Eshaghi, Timon Rabczuk · 11 juin 2026

  Neural operators provide a powerful framework for learning solution mappings of partial differential equations directly in function space. However, many existing architectures still struggle to represent nonlinear time-dependent systems that involve multi-scale structures, long-range interactions, a…

• Loss Landscape Diagnosis for Gradient-Based Gray-Scott System Inversion: Disentangling the Roles of PINN Components

  Yan Yang · 11 juin 2026

  Gradient-based inversion of reaction-diffusion systems is typically approached via surrogate models or physics-informed neural networks (PINNs), while the most direct route, backpropagation through the PDE's structure itself, has largely been avoided. We pursue this direct route as a diagnostic prob…

• Least-Action-Guided Diffusion for Physical Extrapolation

  Zhongxin Yang, Yuanwei Bin, Xiang I. A. Yang, Shiyi Chen · 11 juin 2026

  Reliable extrapolation remains a central challenge for generative models in computational physics, because models trained over finite ranges of time, parameters, or geometries may produce physically inconsistent predictions outside the training distribution. We introduce a least-action-principle-gui…

• Sparse probes and murky physics: a case study of interpretability challenges in a foundation model for continuum dynamics

  Katherine Rosenfeld, Maike Sonnewald · 11 juin 2026

  Generative AI emulators are increasingly used in scientific domains where we already have strong theory, benchmarks, and physical intuition. This raises a central evaluation and interpretability question: when a foundation-style model can reproduce known continuum dynamics, what internal mechanism s…

• Population-Aware Physics-Informed Neural Particle Flow for Bayesian Update

  Batu Candan, Simone Servadio · 10 juin 2026

  Physics-informed neural particle flow (PINPF) learns a deterministic transport field that moves particles from a prior distribution toward a Bayesian posterior while enforcing the governing probability-evolution equation. However, the standard PINPF velocity model processes particles independently a…

• A Constrained Natural-Language Interface for Variational Multi-Physics Finite Element Simulations in FEniCS

  Nilay Upadhyay, Wesley F. Reinhart · 10 juin 2026

  Large language models can reduce the manual effort required to set up finite element simulations, but they introduce reliability risks when generated solver code lies on the critical path. We present a constrained natural-language interface for multi-physics finite element analysis in which the LLM …

• Structure from Reasoning, Numbers from Search: On-Premise Open LLMs as Structural Priors for Coupled MIMO Controller Tuning

  Jiaxuan Chen, Haonan Li, Yang Shu · 10 juin 2026

  Tuning controllers for strongly coupled multi-input multi-output (MIMO) industrial processes is hard: decentralized classical auto-tuning ignores loop interaction, and local numerical optimization from natural initializations stalls in the resulting non-convex cost landscape. We ask whether on-premi…

• Divide-and-Conquer Modeling for the CTF-4-Science Lorenz Benchmark

  Shundong Li · 10 juin 2026

  This work presents a divide-and-conquer modeling strategy for the CTF-4-Science Lorenz benchmark, which evaluates chaotic-system prediction across twelve hidden scores and five scenario families: clean forecasting, noisy reconstruction, noisy-input forecasting, few-shot learning, and parametric gene…

• Uncertainty-aware Multi-fidelity Closure via Conditional Normalizing Flows

  Jice Zeng, Shady E. Ahmed, David Barajas-Solano, Panos Stinis · 10 juin 2026

  Reduced-order models (ROMs) provide an efficient surrogate for complex multiscale systems, but their predictive accuracy is often compromised by truncation errors and the inadequate representation of interactions between resolved and unresolved scales. The missing effect of truncated (unresolved) sc…