Model Reduction and Neural Networks

Últimos artículos

• Reliability-Aware Hard--Soft Physics-Informed Neural Networks for Robust Learning of Challenging Partial Differential Equations

  Duc Tien Nguyen, Hang Tran, Trinh Minh Tuan, Nguyen Duc Manh, Dinh Gia Ninh · 23 de julio de 2026

  Physics-informed neural networks (PINNs) provide a mesh-free framework for solving partial differential equations, but their training is often affected by loss imbalance, optimization stiffness, and difficulty in capturing localized or multi-mode solution structures. Hard-soft PINNs (HSPINN) allevia…

• PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs

  Amirhossein Sadr, Nima Soltani, Vahideh Moghtadaiee, Aida Pakniyat, Dara Rahmati, Saeid Gorgin · 23 de julio de 2026

  Physics-informed learning of partial differential equations (PDEs) has been dominated by multilayer perceptrons (MLPs), whose spectral bias and dense parameterization limit both accuracy and interpretability. Kolmogorov Arnold Networks (KANs) mitigate these limitations because their learnable spline…

• Label-Free Finite-Volume-Residual Training of Attention Graph Neural Networks for Coupled Thermo-Fluid Fields

  Tianyu Li, Zhiwei Cao, Qingang Zhang, Ruihang Wang, Binyang Song, Yonggang Wen · 23 de julio de 2026

  Neural surrogates are widely used in scientific machine learning for fast prediction of three-dimensional (3D) thermo-fluid fields. However, generating training data using conventional numerical solvers often incurs substantial computational and storage costs. We propose to train an attention graph …

• Interval and fuzzy physics-augmented neural networks (iPANN and fPANN) for uncertainty quantification and propagation in constitutive modeling

  Somesh Pratap Singh, Govinda Anantha Padmanabha, Jingye Tan, Steven Yang, Reese E. Jones, D. Thomas Seidl, Nikolaos Bouklas · 23 de julio de 2026

  Constitutive modeling under uncertainty remains a central challenge for reliable mechanics simulations, particularly when the available stress-deformation data are sparse, noisy, or heterogeneous. We propose interval and fuzzy physics-augmented neural networks (iPANNs and fPANNs) for uncertainty-awa…

• Scale-Aware Learning of Chaotic Dynamics on Unstructured Meshes via Binned Spectral Losses

  Kanad Sen, Romit Maulik · 23 de julio de 2026

  Surrogate modeling for high-dimensional nonlinear dynamical systems that exhibit chaos requires mechanisms that preserve not only pointwise accuracy but also the scale-dependent structure of physical fields. Bandwise spectral power losses, such as the binned spectral loss function, provide such supe…

• HypEMBER: Hypernetwork-based Ensemble for Robust Policy Learning of Parametrized Dynamical Systems

  Nicol\`o Botteghi, Gabriele Pascali, Urban Fasel, Andrea Manzoni · 23 de julio de 2026

  In this work we investigate reinforcement learning (RL) as a framework for the robust control of parametrized dynamical systems in presence of measurements and model uncertainties. High-dimensional state spaces, expensive numerical solvers, the partial knowledge of the governing equations, and the d…

• Boundary-Adapted PINNs for Elliptic Dirichlet Problems: $H^2(\Omega)$ A Priori Error Bounds with Application to Mean Escape Time Computation

  Nathanael Tepakbong, Jun Fan, Xiang Zhou, Ding-Xuan Zhou · 22 de julio de 2026

  Motivated by the numerical computation of the Mean Escape Time (MET) $\tau:\Omega\to\mathbb{R}$ of a stochastic process from a bounded domain $\Omega\subseteq\mathbb{R}^d$, we study elliptic Dirichlet boundary value problems (BVPs) using boundary-enforced Physics-Informed Neural Networks (PINNs), in…

• Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise

  Arthur Bizzi, Olga Fink · 22 de julio de 2026

  Neural stochastic differential equations (SDEs) have emerged as powerful tools for learning noisy or stochastic dynamics directly from data; however, existing approaches largely assume uncoupled and continuous noise, limiting their applicability to realistic stochastic drivers, and often scale poorl…

• Attractor Geometry Determines the Identifiability Limits of System Discovery

  Matteo Gallo, Fabio Anselmi, Paolo Lazzari · 22 de julio de 2026

  Symbolic discovery of governing equations from data is limited not only by algorithm design and data volume, but by the geometry of the attractor: what the long-run dynamics allow to be recovered. Using a within-system design on Lorenz-84, where one forcing parameter drives fixed-point, limit-cycle,…

• CircuitKIT : Circuit Discovery, Evaluation, and Application Toolkit for Mechanistic Interpretability

  Pratinav Seth, Hem Gosalia, Aditya Kasliwal, Vinay Kumar Sankarapu · 22 de julio de 2026

  Circuit analysis can support not only model explanation but also downstream interventions such as pruning, editing, steering, and selective fine-tuning. However, conducting such analyses currently requires stitching together separate implementations for discovery, evaluation, and intervention, as we…

• Real-time optimal control with shallow recurrent decoder networks

  Matteo Tomasetto, Francesco Braghin, J. Nathan Kutz, Andrea Manzoni · 22 de julio de 2026

  Controlling dynamical systems in real-time across multiple scenarios is critical to enabling adaptive control strategies, ensuring stability and efficiency. However, to tailor control actions in response to varying scenarios, traditional optimal control problems typically require several system simu…

• Spatio-Temporal Prediction of Unsteady Airfoil Aerodynamics Using Augmented Graph Neural Ordinary Differential Equations with Exogenous Controls

  Henrik Lange, Reik Thormann, Philipp Bekemeyer · 22 de julio de 2026

  Unsteady aerodynamic phenomena, such as gusts, turbulence, and fluid-structure interactions affect an aircraft during flight. For design, optimisation and certification, it is indispensable to quantify such unsteady aerodynamic effects. Industry-standard computational fluid dynamics methods, such as…

• Phasor Attention: Mean Root Square Normalization for Phase Manifold Preservation

  Sungwoo Goo, Hwi-yeol Yun, Sangkeun Jung · 21 de julio de 2026

  While Root Mean Square Normalization has become the de facto standard for accelerating modern sequence models, its reliance on the quadratic accumulation of independent scalars ($\sum x^2$) inherently triggers outlier-induced numerical instability, gradient starvation, and anisotropic phase distorti…

• Potential failures of physics-informed machine learning in traffic flow modeling: theoretical and experimental analysis

  Yuan-Zheng Lei, Yaobang Gong, Dianwei Chen, Yao Cheng, Xianfeng Terry Yang · 21 de julio de 2026

  This study investigates why physics-informed machine learning (PIML) can fail in macroscopic traffic flow modeling. We define failure as cases where a PIML model underperforms both purely data-driven and purely physics-based baselines by a given threshold. Unlike in other fields, physics residuals t…

• An Adjoint-Sensitivity Framework for Lost-in-the-Middle Phenomena in Causal Residual Transformers

  Cheng Huan, Hongwei Yuan · 21 de julio de 2026

  We develop an adjoint-sensitivity framework for positional influence in causal residual Transformers and separate unconditional analytic results from conditional boundary-shape conclusions. The principal unconditional theorem is the residual-to-depth-flow estimate for layer controls converging in $L…

• FlashPDE: A Drop-in Fused Triton Operator Library for Neural PDE Solvers

  Peiyu Zang, Bosen Xie, Ruoxiang Xu, Yongqiang Cai · 21 de julio de 2026

  Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differentiation memory overhead and inefficient execution of grid-based PDE operators. We present FlashPDE, a drop-in fused operat…

• Adaptive Mamba Neural Operators

  Zeyuan Song, Zheyu Jiang · 21 de julio de 2026

  Accurately solving partial differential equations (PDEs) on arbitrary geometries and a variety of meshes is an important task in science and engineering applications. In this paper, we propose Adaptive Mamba Neural Operators (AMO), which integrates reproducing kernels for state-space models (SSMs) r…

• Building a Neural Network from Scratch: Implementation, Evaluation, and Optimization

  Yuanzhe Jia · 21 de julio de 2026

  The widespread adoption of high-level deep learning libraries, while accelerating model development, has increasingly abstracted away the internal mechanics of neural networks, creating a gap between practical usage and fundamental understanding. To address this, the paper presents a self-contained …

• One-shot acceleration of transient PDE solvers via online-learned preconditioners

  Mikhail Khodak, Min Ki Jung, Brian Wynne, Edmond Chow, Egemen Kolemen · 21 de julio de 2026

  Data-driven acceleration of scientific computing workflows has been a high-profile aim of machine learning (ML) for science, with numerical simulation of transient partial differential equations (PDEs) being one of the main applications. The focus thus far has been on methods that require classical …

• fSRD: Fuzzy Spectral Region Decomposition -- Automated Multi Operator Koopman Representations via an Adaptive Spectral Learning Architecture

  Charles Bokor, Mark Cary, Denise Morrey, Fabrizio Bonatesta · 21 de julio de 2026

  Highly nonlinear chaotic dynamical systems remain difficult to model due to fundamental trade-offs between complexity, expressivity, and data efficiency. Modern machine learning methods achieve strong predictive performance but often rely on a-priori system knowledge or curated data with limited int…

• A Physics-Informed Neural Network with a Modified Lorentzian Activation for Nonlocal Gradient-Flow Equations in Dynamic Density Functional Theory

  Dimitrios Gourzoulidis, Soumaya Elkantassi, Serafim Kalliadasis · 20 de julio de 2026

  We develop a physics-informed neural network (PINN) framework for nonlocal partial differential equations arising in dynamic density functional theory (DDFT). Such equations are challenging for standard PINN methods because they involve nonlinearities, nonlocal interaction terms, and an underlying g…

• Discovering Generalizable Governing Equations for Graph Dynamical Systems with Interpretable Neural Networks

  Riccardo Cappi, Paolo Frazzetto, Nicol\`o Navarin, Alessandro Sperduti · 20 de julio de 2026

  The discovery of symbolic governing equations is a central goal in science; yet, it remains challenging particularly for graph dynamical systems, where the network topology further shapes the system behavior. While artificial intelligence offers powerful tools for modeling these dynamics, the field …

• Physics-enhanced reinforcement learning for real-time optimal control of dynamical systems

  Matteo Tomasetto, Nicol\`o Botteghi, Gabriele Bruni, Andrea Manzoni · 20 de julio de 2026

  Reinforcement learning (RL) has recently emerged as a promising feedback control strategy for nonlinear and complex dynamical systems. However, RL algorithms are sample inefficient and require a large number of interaction with the environment to synthesize optimal control strategies. Consequently, …

• Trainable Spline Representations for Physics-Informed Learning

  Giovanni Canali, Nicola Demo, Gianluigi Rozza · 20 de julio de 2026

  This work introduces Physics-Informed Splines (PI-Splines), a structured spline-based architecture for physics-informed learning. Instead of representing the solution of a differential equation with a neural network, PI-Splines directly parametrize the unknown field through a tensor-product B-spline…

• A Statistical Formulation Gap for Nonlinear Multiscale Physics-Informed Learning

  Ronald Katende · 20 de julio de 2026

  We prove a finite-sample formulation gap for physics-informed learning of nonlinear multiscale elliptic equations. For a uniformly monotone divergence-form class with coefficients oscillating at scale $\epsilon$, we derive a finite-width, finite-sample, and finite-iteration error bound for a boundar…