Model Reduction and Neural Networks

Derniers papiers

• Generalized Neural Operator for Parametric and Boundary-Value Problems

  Ruoyan Li, Yizhou Sun, Wei Wang · 27 juillet 2026

  Developing foundational neural simulators for Partial Differential Equations (PDEs) requires robust generalization across diverse physical parameters and boundary conditions. However, current deep learning approaches largely face a structural trade-off between condition-agnostic deployment and physi…

• Latent PDE mapping for efficient physics-informed learning across geometries with limited data

  Ingvild Askim Adde, Mary M. Maleckar, Gabriel Balaban · 27 juillet 2026

  In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data. Latent PDE mapping pulls back geometry-specific PDE residuals and boundary conditions to a predefined latent geome…

• Toward Goal-Agnostic Joint-Embedding Predictive Control of Partial Differential Equations

  Jonathan Gallagher, Roberto Guglielmi · 27 juillet 2026

  We present a goal-agnostic control framework for partial differential equations (PDEs) built around a joint-embedding predictive architecture (JEPA). The small 2D ViT encoder and action-conditioned latent dynamics are trained offline without a reward or downstream goal, frozen, and reused by a model…

• Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers

  Zhangyong Liang, Huanhuan Gao · 27 juillet 2026

  Energy natural gradient descent (ENGD) aligns parameter updates with the curvature of an underlying function-space energy, but existing formulations assume an unconstrained Euclidean parameter domain. We introduce \EMNGDfull{}, a manifold optimization framework for physics-informed and variational n…

• Multiplicity of Stable Attractors in Disordered Neural Models

  Raffaele Marino, Roberto Livi, Antonio Politi · 27 juillet 2026

  We show how large-deviation statistics allows one to obtain reliable estimates of the multiplicity of stable fixed-points in a model of neural ordinary differential equations previously employed in computational tasks. The result is obtained by developing a suitable perturbative method in the amplit…

• TwistedMerge: Certified Higher-Order Diagnostics and Abstention for Model Merging

  Ting Gong, Shitan Xu · 24 juillet 2026

  Model merging combines independently trained or fine-tuned models, but pairwise alignability does not imply globally consistent alignment. We formulate merging as a finite descent problem in which checkpoints are local objects, alignment maps are transitions, and cycle products are residuals. Twiste…

• A Graph Neural Network approach to zero-shot Digital Twins

  Alicia Tierz, Ic\'iar Alfaro, David Gonz\'alez, El\'ias Cueto · 24 juillet 2026

  Traditional Predictive Digital Twins often remain geometrically rigid, requiring extensive retraining or fine-tuning whenever the underlying physical domain or boundary conditions change. To overcome this limitation, we present a novel framework for \textit{Zero-Shot Digital Twins} that seamlessly c…

• HypNO: A Graph-Based Neural Operator with Physics-Informed Message Passing for Hyperbolic Conservation Laws

  Dimitrije \v{Z}drale, Cassie An Jeng, Katie Wang, Sonia Vanier, Alexandre Bayen, Hossein Nick Zinat Matin · 24 juillet 2026

  We introduce HypNO, a graph-based neural operator for scalar hyperbolic conservation laws. HypNO operates directly on a space-time graph of finite-volume cells and uses adjacency-factored, physics-informed message passing to respect upwinding and entropy admissibility near shocks. We benchmark the a…

• 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 juillet 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 …

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

  Kanad Sen, Romit Maulik · 23 juillet 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…

• 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 juillet 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…

• 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 juillet 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…

• 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 juillet 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…

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

  Nicol\`o Botteghi, Gabriele Pascali, Urban Fasel, Andrea Manzoni · 23 juillet 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…

• Real-time optimal control with shallow recurrent decoder networks

  Matteo Tomasetto, Francesco Braghin, J. Nathan Kutz, Andrea Manzoni · 22 juillet 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…

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

  Arthur Bizzi, Olga Fink · 22 juillet 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…

• 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 juillet 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…

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

  Henrik Lange, Reik Thormann, Philipp Bekemeyer · 22 juillet 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…

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

  Pratinav Seth, Hem Gosalia, Aditya Kasliwal, Vinay Kumar Sankarapu · 22 juillet 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…

• Attractor Geometry Determines the Identifiability Limits of System Discovery

  Matteo Gallo, Fabio Anselmi, Paolo Lazzari · 22 juillet 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,…

• 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 juillet 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 juillet 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 juillet 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 juillet 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…

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

  Sungwoo Goo, Hwi-yeol Yun, Sangkeun Jung · 21 juillet 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…