Model Reduction and Neural Networks

Derniers papiers

• Sparse-to-Field Reconstruction via Stochastic Neural Dynamic Mode Decomposition

  Yujin Kim, Sarah Dean · 26 novembre 2025

  Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD) provides a simple, data-driven approximation, but practical use is…

• Koopman operator-based discussion on partial observation in stochastic systems

  Jun Ohkubo · 26 novembre 2025

  It is sometimes difficult to achieve a complete observation for a full set of observables, and partial observations are necessary. For deterministic systems, the Mori-Zwanzig formalism provides a theoretical framework for handling partial observations. Recently, data-driven algorithms based on the K…

• Operator Learning at Machine Precision

  Aras Bacho, Aleksei G. Sorokin, Xianjin Yang, Th\'eo Bourdais, Edoardo Calvello, Matthieu Darcy, Alexander Hsu, Bamdad Hosseini, Houman Owhadi · 26 novembre 2025

  Neural operator learning methods have garnered significant attention in scientific computing for their ability to approximate infinite-dimensional operators. However, increasing their complexity often fails to substantially improve their accuracy, leaving them on par with much simpler approaches suc…

• Feature-Modulated UFNO for Improved Prediction of Multiphase Flow in Porous Media

  Alhasan Abdellatif, Hannah P. Menke, Ahmed H. Elsheikh, Florian Doster, Kamaljit Singh · 26 novembre 2025

  The UNet-enhanced Fourier Neural Operator (UFNO) extends the Fourier Neural Operator (FNO) by incorporating a parallel UNet pathway, enabling the retention of both high- and low-frequency components. While UFNO improves predictive accuracy over FNO, it inefficiently treats scalar inputs (e.g., tempe…

• Collapsing Taylor Mode Automatic Differentiation

  Felix Dangel, Tim Siebert, Marius Zeinhofer, Andrea Walther · 25 novembre 2025

  Computing partial differential equation (PDE) operators via nested backpropagation is expensive, yet popular, and severely restricts their utility for scientific machine learning. Recent advances, like the forward Laplacian and randomizing Taylor mode automatic differentiation (AD), propose forward …

• PINNsFailureRegion Localization and Refinement through White-box AdversarialAttack

  Shengzhu Shi, Yao Li, Zhichang Guo, Boying Wu, Yang Zhao · 25 novembre 2025

  Physics-informed neural networks (PINNs) have shown great promise in solving partial differential equations (PDEs). However, vanilla PINNs often face challenges when solving complex PDEs, especially those involving multi-scale behaviors or solutions with sharp or oscillatory characteristics. To prec…

• RRaPINNs: Residual Risk-Aware Physics Informed Neural Networks

  Ange-Cl\'ement Akazan, Issa Karambal, Jean Medard Ngnotchouye, Abebe Geletu Selassie. W · 25 novembre 2025

  Physics-informed neural networks (PINNs) typically minimize average residuals, which can conceal large, localized errors. We propose Residual Risk-Aware Physics-Informed Neural Networks PINNs (RRaPINNs), a single-network framework that optimizes tail-focused objectives using Conditional Value-at-Ris…

• Solution of Incompressible Flow Equations with Physics and Equality Constrained Artificial Neural Networks

  Qifeng Hu, Inanc Senocak · 25 novembre 2025

  We present a meshless method for the solution of incompressible Navier-Stokes equations in advection-dominated regimes using physics- and equality-constrained artificial neural networks combined with a conditionally adaptive augmented Lagrangian formulation. A single neural network parameterizes bot…

• SAOT: An Enhanced Locality-Aware Spectral Transformer for Solving PDEs

  Chenhong Zhou, Jie Chen, Zaifeng Yang · 25 novembre 2025

  Neural operators have shown great potential in solving a family of Partial Differential Equations (PDEs) by modeling the mappings between input and output functions. Fourier Neural Operator (FNO) implements global convolutions via parameterizing the integral operators in Fourier space. However, it o…

• MDBench: Benchmarking Data-Driven Methods for Model Discovery

  Amirmohammad Ziaei Bideh, Aleksandra Georgievska, Jonathan Gryak · 25 novembre 2025

  Model discovery aims to uncover governing differential equations of dynamical systems directly from experimental data. Benchmarking such methods is essential for tracking progress and understanding trade-offs in the field. While prior efforts have focused mostly on identifying single equations, typi…

• Predicting partially observable dynamical systems via diffusion models with a multiscale inference scheme

  Rudy Morel, Francesco Pio Ramunno, Jeff Shen, Alberto Bietti, Kyunghyun Cho, Miles Cranmer, Siavash Golkar, Olexandr Gugnin, Geraud Krawezik, Tanya Marwah, Michael McCabe, Lucas Meyer, Payel Mukhopadhyay, Ruben Ohana, Liam Parker, Helen Qu, Fran\c{c}ois Rozet, K. D. Leka, Fran\c{c}ois Lanusse, David Fouhey, Shirley Ho · 25 novembre 2025

  Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at a given time represents only a small fraction of what is nee…

• Adaptive Mesh-Quantization for Neural PDE Solvers

  Winfried van den Dool, Maksim Zhdanov, Yuki M. Asano, Max Welling · 25 novembre 2025

  Physical systems commonly exhibit spatially varying complexity, presenting a significant challenge for neural PDE solvers. While Graph Neural Networks can handle the irregular meshes required for complex geometries and boundary conditions, they still apply uniform computational effort across all nod…

• Reduced-Basis Deep Operator Learning for Parametric PDEs with Independently Varying Boundary and Source Data

  Yueqi Wang, Guang Lin · 25 novembre 2025

  Parametric PDEs power modern simulation, design, and digital-twin systems, yet their many-query workloads still hinge on repeatedly solving large finite-element systems. Existing operator-learning approaches accelerate this process but often rely on opaque learned trunks, require extensive labeled d…

• Active Learning with Selective Time-Step Acquisition for PDEs

  Yegon Kim, Hyunsu Kim, Gyeonghoon Ko, Juho Lee · 25 novembre 2025

  Accurately solving partial differential equations (PDEs) is critical to understanding complex scientific and engineering phenomena, yet traditional numerical solvers are computationally expensive. Surrogate models offer a more efficient alternative, but their development is hindered by the cost of g…

• KANO: Kolmogorov-Arnold Neural Operator

  Jin Lee, Ziming Liu, Xinling Yu, Yixuan Wang, Haewon Jeong, Murphy Yuezhen Niu, Zheng Zhang · 25 novembre 2025

  We introduce Kolmogorov--Arnold Neural Operator (KANO), a dual-domain neural operator jointly parameterized by both spectral and spatial bases with intrinsic symbolic interpretability. We theoretically demonstrate that KANO overcomes the pure-spectral bottleneck of Fourier Neural Operator (FNO): KAN…

• Diffusion Models are Molecular Dynamics Simulators

  Justin Diamond, Markus Lill · 25 novembre 2025

  We prove that a denoising diffusion sampler equipped with a sequential bias across the batch dimension is exactly an Euler-Maruyama integrator for overdamped Langevin dynamics. Each reverse denoising step, with its associated spring stiffness, can be interpreted as one step of a stochastic different…

• A joint optimization approach to identifying sparse dynamics using least squares kernel collocation

  Alexander W. Hsu, Ike W. Griss Salas, Jacob M. Stevens-Haas, J. Nathan Kutz, Aleksandr Aravkin, Bamdad Hosseini · 25 novembre 2025

  We develop an all-at-once modeling framework for learning systems of ordinary differential equations (ODE) from scarce, partial, and noisy observations of the states. The proposed methodology amounts to a combination of sparse recovery strategies for the ODE over a function library combined with tec…

• Learning Solution Operators for Partial Differential Equations via Monte Carlo-Type Approximation

  Salah Eddine Choutri, Prajwal Chauhan, Othmane Mazhar, Saif Eddin Jabari · 25 novembre 2025

  The Monte Carlo-type Neural Operator (MCNO) introduces a lightweight architecture for learning solution operators for parametric PDEs by directly approximating the kernel integral using a Monte Carlo approach. Unlike Fourier Neural Operators, MCNO makes no spectral or translation-invariance assumpti…

• Weighted Birkhoff Averages Accelerate Data-Driven Methods

  Maria Bou-Sakr-El-Tayar, Jason J. Bramburger, Matthew J. Colbrook · 25 novembre 2025

  Many data-driven algorithms in dynamical systems rely on ergodic averages that converge painfully slowly. One simple idea changes this: taper the ends. Weighted Birkhoff averages can converge much faster (sometimes superpolynomially, even exponentially) and can be incorporated seamlessly into existi…

• Enforcing governing equation constraints in neural PDE solvers via training-free projections

  Omer Rochman, Gilles Louppe · 24 novembre 2025

  Neural PDE solvers used for scientific simulation often violate governing equation constraints. While linear constraints can be projected cheaply, many constraints are nonlinear, complicating projection onto the feasible set. Dynamical PDEs are especially difficult because constraints induce long-ra…

• Towards fully differentiable neural ocean model with Veros

  Etienne Meunier, Said Ouala, Hugo Frezat, Julien Le Sommer, Ronan Fablet · 24 novembre 2025

  We present a differentiable extension of the VEROS ocean model, enabling automatic differentiation through its dynamical core. We describe the key modifications required to make the model fully compatible with JAX autodifferentiation framework and evaluate the numerical consistency of the resulting …

• Addressing A Posteriori Performance Degradation in Neural Network Subgrid Stress Models

  Andy Wu, Sanjiva K. Lele · 24 novembre 2025

  Neural network subgrid stress models often have a priori performance that is far better than the a posteriori performance, leading to neural network models that look very promising a priori completely failing in a posteriori Large Eddy Simulations (LES). This performance gap can be decreased by comb…

• Learning-Enhanced Observer for Linear Time-Invariant Systems with Parametric Uncertainty

  Hao Shu · 21 novembre 2025

  This work introduces a learning-enhanced observer (LEO) for linear time-invariant systems with uncertain dynamics. Rather than relying solely on nominal models, the proposed framework treats the system matrices as optimizable variables and refines them through gradient-based minimization of a steady…

• An Exterior-Embedding Neural Operator Framework for Preserving Conservation Laws

  Huanshuo Dong, Hong Wang, Hao Wu, Zhiwei Zhuang, Xuanze Yang, Ruiqi Shu, Yuan Gao, Xiaomeng Huang · 21 novembre 2025

  Neural operators have demonstrated considerable effectiveness in accelerating the solution of time-dependent partial differential equations (PDEs) by directly learning governing physical laws from data. However, for PDEs governed by conservation laws(e.g., conservation of mass, energy, or matter), e…

• Time dependent loss reweighting for flow matching and diffusion models is theoretically justified

  Lukas Billera, Hedwig Nora Nordlinder, Ben Murrell · 21 novembre 2025

  This brief note clarifies that, in Generator Matching (which subsumes a large family of flow matching and diffusion models over continuous, manifold, and discrete spaces), both the Bregman divergence loss and the linear parameterization of the generator can depend on both the current state $X_t$ and…