Model Reduction and Neural Networks

Derniers papiers

• Physics-guided surrogate learning enables zero-shot control of turbulent wings

  Yuning Wang, Pol Suarez, Mathis Bode, Ricardo Vinuesa · 13 avril 2026

  Turbulent boundary layers over aerodynamic surfaces are a major source of aircraft drag, yet their control remains challenging due to multiscale dynamics and spatial variability, particularly under adverse pressure gradients. Reinforcement learning has outperformed state-of-the-art strategies in can…

• Stochastic-Dimension Frozen Sampled Neural Network for High-Dimensional Gross-Pitaevskii Equations on Unbounded Domains

  Zhangyong Liang · 13 avril 2026

  In this paper, we propose a stochastic-dimension frozen sampled neural network (SD-FSNN) for solving a class of high-dimensional Gross-Pitaevskii equations (GPEs) on unbounded domains. SD-FSNN is unbiased across all dimensions, and its computational cost is independent of the dimension, avoiding the…

• Post-Hoc Guidance for Consistency Models by Joint Flow Distribution Learning

  Chia-Hong Hsu, Randall Balestriero · 13 avril 2026

  Classifier-free Guidance (CFG) lets practitioners trade-off fidelity against diversity in Diffusion Models (DMs). The practicality of CFG is however hindered by DMs sampling cost. On the other hand, Consistency Models (CMs) generate images in one or a few steps, but existing guidance methods require…

• Adjoint Matching through the Lens of the Stochastic Maximum Principle in Optimal Control

  Carles Domingo-Enrich, Jiequn Han · 13 avril 2026

  Reward fine-tuning of diffusion and flow models and sampling from tilted or Boltzmann distributions can both be formulated as stochastic optimal control (SOC) problems, where learning an optimal generative dynamics corresponds to optimizing a control under SDE constraints. In this work, we revisit a…

• FluidFlow: a flow-matching generative model for fluid dynamics surrogates on unstructured meshes

  David Ramos, Lucas Lacasa, Ferm\'in Guti\'errez, Eusebio Valero, Gonzalo Rubio · 13 avril 2026

  Computational fluid dynamics (CFD) provides high-fidelity simulations of fluid flows but remains computationally expensive for many-query applications. In recent years deep learning (DL) has been used to construct data-driven fluid-dynamic surrogate models. In this work we consider a different learn…

• Bias-Constrained Diffusion Schedules for PDE Emulations: Reconstruction Error Minimization and Efficient Unrolled Training

  Constantin Le Cle\"i, Nils Thuerey, Xiaoxiang Zhu · 13 avril 2026

  Conditional Diffusion Models are powerful surrogates for emulating complex spatiotemporal dynamics, yet they often fail to match the accuracy of deterministic neural emulators for high-precision tasks. In this work, we address two critical limitations of autoregressive PDE diffusion models: their su…

• Meta-Learned Basis Adaptation for Parametric Linear PDEs

  Vikas Dwivedi, Monica Sigovan, Bruno Sixou · 13 avril 2026

  We propose a hybrid physics-informed framework for solving families of parametric linear partial differential equations (PDEs) by combining a meta-learned predictor with a least-squares corrector. The predictor, termed \textbf{KAPI} (Kernel-Adaptive Physics-Informed meta-learner), is a shallow task-…

• Physics-Informed Neural Networks for Joint Source and Parameter Estimation in Advection-Diffusion Equations

  Brenda Anague, Bamdad Hosseini, Issa Karambal, Jean Medard Ngnotchouye · 10 avril 2026

  Recent studies have demonstrated the success of deep learning in solving forward and inverse problems in engineering and scientific computing domains, such as physics-informed neural networks (PINNs). Source inversion problems under sparse measurements for parabolic partial differential equations (P…

• Graph Neural ODE Digital Twins for Control-Oriented Reactor Thermal-Hydraulic Forecasting Under Partial Observability

  Akzhol Almukhametov, Doyeong Lim, Rui Hu, Yang Liu · 9 avril 2026

  Real-time supervisory control of advanced reactors requires accurate forecasting of plant-wide thermal-hydraulic states, including locations where physical sensors are unavailable. Meeting this need calls for surrogate models that combine predictive fidelity, millisecond-scale inference, and robustn…

• VertAX: a differentiable vertex model for learning epithelial tissue mechanics

  Alessandro Pasqui, Jim Martin Catacora Ocana, Anshuman Sinha, Matthieu Perez, Fabrice Delbary, Giorgio Gosti, Mattia Miotto, Domenico Caudo, Maxence Ernoult, Herv\'e Turlier · 9 avril 2026

  Epithelial tissues dynamically reshape through local mechanical interactions among cells, a process well captured by vertex models. Yet their many tunable parameters make inference and optimization challenging, motivating computational frameworks that flexibly model and learn tissue mechanics. We in…

• FlowAdam: Implicit Regularization via Geometry-Aware Soft Momentum Injection

  Devender Singh, Tarun Sheel · 9 avril 2026

  Adaptive moment methods such as Adam use a diagonal, coordinate-wise preconditioner based on exponential moving averages of squared gradients. This diagonal scaling is coordinate-system dependent and can struggle with dense or rotated parameter couplings, including those in matrix factorization, ten…

• MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systems

  Tianyue Yang, Xiao Xue · 9 avril 2026

  Neural operators have emerged as powerful surrogates for dynamical systems due to their grid-invariant properties and computational efficiency. However, the Fourier-based neural operator framework inherently truncates high-frequency components in spectral space, resulting in the loss of small-scale …

• Sparse-Aware Neural Networks for Nonlinear Functionals: Mitigating the Exponential Dependence on Dimension

  Jianfei Li, Shuo Huang, Han Feng, Ding-Xuan Zhou, Gitta Kutyniok · 9 avril 2026

  Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited interpretability. This work investigates how sparsity can help address thes…

• Amortized Filtering and Smoothing with Conditional Normalizing Flows

  Tiangang Cui, Xiaodong Feng, Chenlong Pei, Xiaoliang Wan, Tao Zhou · 9 avril 2026

  Bayesian filtering and smoothing for high-dimensional nonlinear dynamical systems are fundamental yet challenging problems in many areas of science and engineering. In this work, we propose AFSF, a unified amortized framework for filtering and smoothing with conditional normalizing flows. The core i…

• AE-ViT: Stable Long-Horizon Parametric Partial Differential Equations Modeling

  Iva Miku\v{s}, Boris Muha, Domagoj Vlah · 9 avril 2026

  Deep Learning Reduced Order Models (ROMs) are becoming increasingly popular as surrogate models for parametric partial differential equations (PDEs) due to their ability to handle high-dimensional data, approximate highly nonlinear mappings, and utilize GPUs. Existing approaches typically learn evol…

• A solver-in-the-loop framework for end-to-end differentiable coastal hydrodynamics

  Elsa Cardoso-Bihlo, Alex Bihlo · 9 avril 2026

  Numerical simulation of wave propagation and run-up is a cornerstone of coastal engineering and tsunami hazard assessment. However, applying these forward models to inverse problems, such as bathymetry estimation, source inversion, and structural optimization, remains notoriously difficult due to th…

• Multiscale Physics-Informed Neural Network for Complex Fluid Flows with Long-Range Dependencies

  Prashant Kumar, Rajesh Ranjan · 8 avril 2026

  Fluid flows are governed by the nonlinear Navier-Stokes equations, which can manifest multiscale dynamics even from predictable initial conditions. Predicting such phenomena remains a formidable challenge in scientific machine learning, particularly regarding convergence speed, data requirements, an…

• WGFINNs: Weak formulation-based GENERIC formalism informed neural networks

  Jun Sur Richard Park, Auroni Huque Hashim, Siu Wun Cheung, Youngsoo Choi, Yeonjong Shin · 8 avril 2026

  Data-driven discovery of governing equations from noisy observations remains a fundamental challenge in scientific machine learning. While GENERIC formalism informed neural networks (GFINNs) provide a principled framework that enforces the laws of thermodynamics by construction, their reliance on st…

• Generative Path-Law Jump-Diffusion: Sequential MMD-Gradient Flows and Generalisation Bounds in Marcus-Signature RKHS

  Daniel Bloch · 8 avril 2026

  This paper introduces a novel generative framework for synthesising forward-looking, c\`adl\`ag stochastic trajectories that are sequentially consistent with time-evolving path-law proxies, thereby incorporating anticipated structural breaks, regime shifts, and non-autonomous dynamics. By framing pa…

• LMI-Net: Linear Matrix Inequality--Constrained Neural Networks via Differentiable Projection Layers

  Sunbochen Tang, Andrea Goertzen, Navid Azizan · 8 avril 2026

  Linear matrix inequalities (LMIs) have played a central role in certifying stability, robustness, and forward invariance of dynamical systems. Despite rapid development in learning-based methods for control design and certificate synthesis, existing approaches often fail to preserve the hard matrix …

• FNO$^{\angle \theta}$: Extended Fourier neural operator for learning state and optimal control of distributed parameter systems

  Zhexian Li, Ketan Savla · 8 avril 2026

  We propose an extended Fourier neural operator (FNO) architecture for learning state and linear quadratic additive optimal control of systems governed by partial differential equations. Using the Ehrenpreis-Palamodov fundamental principle, we show that any state and optimal control of linear PDEs wi…

• Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Space

  Li Kunpeng, Wan Chenguang, Qu Zhisong, Lim Kyungtak, Virginie Grandgirard, Xavier Garbet, Yu Hua, Ong Yew Soon · 8 avril 2026

  High-fidelity modeling of turbulent flows requires capturing complex spatiotemporal dynamics and multi-scale intermittency, posing a fundamental challenge for traditional knowledge-based systems. While deep generative models, such as diffusion models and Flow Matching, have shown promising performan…

• A Theory-guided Weighted $L^2$ Loss for solving the BGK model via Physics-informed neural networks

  Gyounghun Ko, Sung-Jun Son, Seung Yeon Cho, Myeong-Su Lee · 8 avril 2026

  While Physics-Informed Neural Networks offer a promising framework for solving partial differential equations, the standard $L^2$ loss formulation is fundamentally insufficient when applied to the Bhatnagar-Gross-Krook (BGK) model. Specifically, simply minimizing the standard loss does not guarantee…

• Enhancing sample efficiency in reinforcement-learning-based flow control: replacing the critic with an adaptive reduced-order model

  Zesheng Yao, Zhen-Hua Wan, Canjun Yang, Qingchao Xia, Mengqi Zhang · 8 avril 2026

  Model-free deep reinforcement learning (DRL) methods suffer from poor sample efficiency. To overcome this limitation, this work introduces an adaptive reduced-order-model (ROM)-based reinforcement learning framework for active flow control. In contrast to conventional actor--critic architectures, th…

• Sparse Autoencoders as a Steering Basis for Phase Synchronization in Graph-Based CFD Surrogates

  Yeping Hu, Ruben Glatt, Shusen Liu · 8 avril 2026

  Graph-based surrogate models provide fast alternatives to high-fidelity CFD solvers, but their opaque latent spaces and limited controllability restrict use in safety-critical settings. A key failure mode in oscillatory flows is phase drift, where predictions remain qualitatively correct but gradual…