Model Reduction and Neural Networks

Latest papers

• Wall Shear Stress Reconstruction from Concentration: Differentiable Physics and Physics-Informed Neural Networks

  Mahmoud Elhadidy, Siva Viknesh, Roshan M. D'Souza, Amirhossein Arzani · 29 July 2026

  Wall shear stress (WSS) governs near-wall transport dynamics and is a key hemodynamic indicator in cardiovascular flows, yet remains difficult to infer accurately due to the need for precise computation of near-wall velocity gradients. Passive scalar fields, such as concentration or temperature, are…

• SpectONet: A Physics-Guided Spectral Deep Operator Network for Euler-Bernoulli Beam Dynamics

  Shivani Saini, Ramesh Kumar Vats, Arup Kumar Sahoo · 29 July 2026

  This paper proposes a novel physics-guided spectral deep operator network, termed SpectONet, for solving Euler-Bernoulli beam (EBB) vibration problems. The proposed framework integrates the operator-learning capability of DeepONet with physics-informed constraints and Chebyshev-Gauss-Lobatto (CGL) s…

• Multi-Fidelity Learning with Shallow Recurrent Decoders for Multi-Physics Applications

  Stefano Riva, Carolina Introini, J. Nathan Kutz, Antonio Cammi · 29 July 2026

  In reactor physics, neutronics and multi-physics phenomena can be modelled at different fidelity levels. High-fidelity models based on the Boltzmann transport equation, multi-group diffusion, or computational fluid dynamics are computationally demanding, whereas simplified models, such as zero-dimen…

• Score-Based Stabilization for Time-Dependent Problems

  Eshed Gal, Eldad Haber, Uri Ascher · 29 July 2026

  We propose a score-based stabilization framework for numerical simulation of partial differential equations, in which a learned score model defines a stabilization operator applied to provisional numerical updates. This operator augments standard time-stepping schemes by enforcing structure and phys…

• Extreme Event Aware ($\eta$-) Learning

  Kai Chang, Themistoklis P. Sapsis · 29 July 2026

  Quantifying and predicting rare and extreme events is challenging because such events are infrequent, severe, and expensive to simulate. Existing data-driven methods often require multiple extremes in the training data or sampling process, leading to accurate predictions in quiescent regimes but hig…

• Physics-Informed Neural Operator for Warm-Starting Background-Decomposed and Preconditioned PSFD: Enabling Scalable 3-D EUV Mask Simulation

  Doyun Kim, Werner Gillijns · 29 July 2026

  We present a physics-informed neural operator (PINO) trained with pseudo-spectral frequency-domain (PSFD) equations for electromagnetic (EM) scattering problems in EUV lithography. The Fourier neural operator is factorized into a two-dimensional lateral ($xy$) branch and a one-dimensional axial ($z$…

• Physics-Informed Broad Learning System: An Efficient Backpropagation-Free Framework for Solving Partial Differential Equations

  Pinki Khatun, M. Sajid, Abhinav Jha, M. Tanveer · 29 July 2026

  Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding governing physical laws into deep neural networks. However, their reliance on computationally expensive gradient-based optimization and deep architectures often…

• Neural operator discovery from heterogeneous trajectories

  Zituo Chen, Qiaofeng Li, Jiaxin Hu, Sili Deng · 28 July 2026

  Neural operators provide data-driven mappings for modeling dynamical systems. Extending them to families of systems typically requires explicit conditioning variables such as physical parameters, geometries, or boundary conditions. In many real-world settings, these quantities are unobserved. Here, …

• Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs

  Cheng Jing, Uvini Balasuriya Mudiyanselage, Abhishek Verma, Kallol Bera, Shahid Rauf, Kookjin Lee · 28 July 2026

  Parameterized and coupled partial differential equations (PDEs) are central to modeling phenomena in science and engineering, yet neural operator methods that address both aspects remain limited. We extend Fourier neural operators (FNOs) with minimal architectural modifications along two directions.…

• No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Study

  Georg Winkler, Martin Stoll · 28 July 2026

  A flow surrogate validated on a simple regime is often taken as evidence that the approach will carry to a richer one. We test this assumption on two transient flows under time-varying boundary conditions emulating the process startup: the three-dimensional slurry film in chemical-mechanical planari…

• On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement

  Baptiste Mathevon, Farah Cherfaoui, Amaury Habrard, Marc Sebban · 28 July 2026

  Partial differential equation (PDE) discovery aims to identify from data the governing law of a physical system. Constituting a cornerstone of scientific advancement, it has become during the past decade a major line of research in the rapidly evolving field of Physics-informed Machine Learning (PiM…

• Global Convergence of DGM and PINN Algorithms for Solving Nonlinear PDEs

  Justin Sirignano, Konstantinos Spiliopoulos, Samuel Cohen · 28 July 2026

  The Deep Galerkin Method (DGM) and Physics Informed Neural Networks (PINNs) have become widely-used methods for solving partial differential equations (PDEs) in the rapidly growing field of scientific machine learning. In these methods, a neural network is trained to approximate the PDE solution by …

• The balance between compactness and forecast accuracy of data-driven latent-space reduced-order models in controlled wake flows

  Alberto Solera-Rico, Patricia Garc\'ia-Caspue\~nas, Carlos Sanmiguel Vila, Stefano Discetti · 28 July 2026

  Model-based active flow control requires predictive models that are accurate, stable, and fast enough for real-time optimisation. In controlled wake flows, this is often achieved through Reduced-Order Models (ROMs) that first compress high-dimensional velocity snapshots into a latent space and then …

• Variational Boosting for Physics-Informed Neural Networks

  Pavlos Protopapas, Kaylee Vo · 28 July 2026

  Physics-Informed Neural Networks (PINNs) solve differential equations by minimizing the residual of a nonlinear operator over a neural parameterization of the solution. However, monolithic PINNs often suffer from ill-conditioning, spectral bias, and optimization instability. We introduce a variati…

• Physics Transformer: Tailoring Transformer for General PDE Prediction

  Guoze Sun, Rui Zhang, Jiankai Tang, Mengtao Yan, Runze Mao, Zhi X. Chen, Hao Sun · 28 July 2026

  Transformer architectures have attracted increasing attention for solving partial differential equations (PDEs), owing to their flexibility in handling irregular discretizations and their ability to capture long-range physical dependencies. However, unlike discrete language tokens or fixed-resolutio…

• Perturbative-NeuSA: A Structured Spectral Framework for Time-Dependent PDEs

  Xianli Zhu, Jia Yin · 28 July 2026

  Neural spectral PDE solvers often learn an entire unresolved vector field even when an inexpensive approximate model can already capture most of the trajectory. Here we introduce Perturbative-NeuSA, a residual formulation that decomposes the target solution into a low-fidelity background and a high-…

• Data-Driven Diffusion Processes on Differential Forms via the Projected Ambient Connection Laplacian

  Alvaro Almeida Gomez, Jorge Duque Franco · 28 July 2026

  We develop a data-driven approximation of the projected ambient connection Laplacian acting on differential forms over smooth Riemannian manifolds sampled by point clouds. The proposed construction extends the classical framework of diffusion maps and Vector Diffusion Maps from scalar functions and …

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

  Zhangyong Liang, Huanhuan Gao · 27 July 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…

• Generalized Neural Operator for Parametric and Boundary-Value Problems

  Ruoyan Li, Yizhou Sun, Wei Wang · 27 July 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 July 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 July 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…

• Multiplicity of Stable Attractors in Disordered Neural Models

  Raffaele Marino, Roberto Livi, Antonio Politi · 27 July 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 July 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…

• 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 July 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…

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

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