Model Reduction and Neural Networks

Derniers papiers

• Variational Continual Test-Time Adaptation

  Fan Lyu, Kaile Du, Yuyang Li, Hanyu Zhao, Fuyuan Hu, Zhang Zhang, Guangcan Liu, Liang Wang · 18 décembre 2025

  Continual Test-Time Adaptation (CTTA) task investigates effective domain adaptation under the scenario of continuous domain shifts during testing time. Due to the utilization of solely unlabeled samples, there exists significant uncertainty in model updates, leading CTTA to encounter severe error ac…

• Flow matching Operators for Residual-Augmented Probabilistic Learning of Partial Differential Equations

  Sahil Bhola, Karthik Duraisamy · 18 décembre 2025

  Learning probabilistic surrogates for partial differential equations remains challenging in data-scarce regimes: neural operators require large amounts of high-fidelity data, while generative approaches typically sacrifice resolution invariance. We formulate flow matching in an infinite-dimensional …

• SigMA: Path Signatures and Multi-head Attention for Learning Parameters in fBm-driven SDEs

  Xianglin Wu, Chiheb Ben Hammouda, Cornelis W. Oosterlee · 18 décembre 2025

  Stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm) are increasingly used to model systems with rough dynamics and long-range dependence, such as those arising in quantitative finance and reliability engineering. However, these processes are non-Markovian and lack a s…

• Boundary condition enforcement with PINNs: a comparative study and verification on 3D geometries

  Conor Rowan, Kai Hampleman, Kurt Maute, Alireza Doostan · 18 décembre 2025

  Since their advent nearly a decade ago, physics-informed neural networks (PINNs) have been studied extensively as a novel technique for solving forward and inverse problems in physics and engineering. The neural network discretization of the solution field is naturally adaptive and avoids meshing th…

• Soft Geometric Inductive Bias for Object Centric Dynamics

  Hampus Linander, Conor Heins, Alexander Tschantz, Marco Perin, Christopher Buckley · 18 décembre 2025

  Equivariance is a powerful prior for learning physical dynamics, yet exact group equivariance can degrade performance if the symmetries are broken. We propose object-centric world models built with geometric algebra neural networks, providing a soft geometric inductive bias. Our models are evaluated…

• Neural Modular Physics for Elastic Simulation

  Yifei Li, Haixu Wu, Zeyi Xu, Tuur Stuyck, Wojciech Matusik · 18 décembre 2025

  Learning-based methods have made significant progress in physics simulation, typically approximating dynamics with a monolithic end-to-end optimized neural network. Although these models offer an effective way to simulation, they may lose essential features compared to traditional numerical simulato…

• PIP$^2$ Net: Physics-informed Partition Penalty Deep Operator Network

  Hongjin Mi, Huiqiang Lun, Changhong Mou, Yeyu Zhang · 18 décembre 2025

  Operator learning has become a powerful tool for accelerating the solution of parameterized partial differential equations (PDEs), enabling rapid prediction of full spatiotemporal fields for new initial conditions or forcing functions. Existing architectures such as DeepONet and the Fourier Neural O…

• Derivative-Informed Fourier Neural Operator: Universal Approximation and Applications to PDE-Constrained Optimization

  Boyuan Yao, Dingcheng Luo, Lianghao Cao, Nikola Kovachki, Thomas O'Leary-Roseberry, Omar Ghattas · 17 décembre 2025

  We present approximation theories and efficient training methods for derivative-informed Fourier neural operators (DIFNOs) with applications to PDE-constrained optimization. A DIFNO is an FNO trained by minimizing its prediction error jointly on output and Fr\'echet derivative samples of a high-fide…

• SuperWing: a comprehensive transonic wing dataset for data-driven aerodynamic design

  Yunjia Yang, Weishao Tang, Mengxin Liu, Nils Thuerey, Yufei Zhang, Haixin Chen · 17 décembre 2025

  Machine-learning surrogate models have shown promise in accelerating aerodynamic design, yet progress toward generalizable predictors for three-dimensional wings has been limited by the scarcity and restricted diversity of existing datasets. Here, we present SuperWing, a comprehensive open dataset o…

• Physics-Informed Machine Learning for Two-Phase Moving-Interface and Stefan Problems

  Che-Chia Chang, Te-Sheng Lin, Ming-Chih Lai · 17 décembre 2025

  The Stefan problem is a classical free-boundary problem that models phase-change processes and poses computational challenges due to its moving interface and nonlinear temperature-phase coupling. In this work, we develop a physics-informed neural network framework for solving two-phase Stefan proble…

• Hybrid Iterative Solvers with Geometry-Aware Neural Preconditioners for Parametric PDEs

  Youngkyu Lee, Francesc Levrero Florencio, Jay Pathak, George Em Karniadakis · 17 décembre 2025

  The convergence behavior of classical iterative solvers for parametric partial differential equations (PDEs) is often highly sensitive to the domain and specific discretization of PDEs. Previously, we introduced hybrid solvers by combining the classical solvers with neural operators for a specific g…

• Probabilistic Predictions of Process-Induced Deformation in Carbon/Epoxy Composites Using a Deep Operator Network

  Elham Kiyani, Amit Makarand Deshpande, Madhura Limaye, Zhiwei Gao, Sai Aditya Pradeep, Srikanth Pilla, Gang Li, Zhen Li, George Em Karniadakis · 17 décembre 2025

  Fiber reinforcement and polymer matrix respond differently to manufacturing conditions due to mismatch in coefficient of thermal expansion and matrix shrinkage during curing of thermosets. These heterogeneities generate residual stresses over multiple length scales, whose partial release leads to pr…

• From STLS to Projection-based Dictionary Selection in Sparse Regression for System Identification

  Hangjun Cho, Fabio V. G. Amaral, Andrei A. Klishin, Cassio M. Oishi, Steven L. Brunton · 17 décembre 2025

  In this work, we revisit dictionary-based sparse regression, in particular, Sequential Threshold Least Squares (STLS), and propose a score-guided library selection to provide practical guidance for data-driven modeling, with emphasis on SINDy-type algorithms. STLS is an algorithm to solve the $\ell_…

• Variational Physics-Informed Ansatz for Reconstructing Hidden Interaction Networks from Steady States

  Kaiming Luo · 17 décembre 2025

  The interaction structure of a complex dynamical system governs its collective behavior, yet existing reconstruction methods struggle with nonlinear, heterogeneous, and higher-order couplings, especially when only steady states are observable. We propose a Variational Physics-Informed Ansatz (VPIA) …

• PIS: A Generalized Physical Inversion Solver for Arbitrary Sparse Observations via Set-Conditioned Diffusion

  Weijie Yang, Xun Zhang · 17 décembre 2025

  Estimation of PDE-constrained physical parameters from limited indirect measurements is inherently ill-posed, particularly when observations are sparse, irregular, and constrained by real-world sensor placement. This challenge is ubiquitous in fields such as fluid mechanics, seismic inversion, and s…

• Physically consistent model learning for reaction-diffusion systems

  Erion Morina, Martin Holler · 17 décembre 2025

  This paper addresses the problem of learning reaction-diffusion (RD) systems from data while ensuring physical consistency and well-posedness of the learned models. Building on a regularization-based framework for structured model learning, we focus on learning parameterized reaction terms and inves…

• Multi-Trajectory Physics-Informed Neural Networks for HJB Equations with Hard-Zero Terminal Inventory: Optimal Execution on Synthetic & SPY Data

  Anthime Valin · 16 décembre 2025

  We study optimal trade execution with a hard-zero terminal inventory constraint, modeled via Hamilton-Jacobi-Bellman (HJB) equations. Vanilla PINNs often under-enforce this constraint and produce unstable controls. We propose a Multi-Trajectory PINN (MT-PINN) that adds a rollout-based trajectory los…

• Multi-fidelity aerodynamic data fusion by autoencoder transfer learning

  Javier Nieto-Centenero, Esther Andr\'es, Rodrigo Castellanos · 16 décembre 2025

  Accurate aerodynamic prediction often relies on high-fidelity simulations; however, their prohibitive computational costs severely limit their applicability in data-driven modeling. This limitation motivates the development of multi-fidelity strategies that leverage inexpensive low-fidelity informat…

• Unified Control for Inference-Time Guidance of Denoising Diffusion Models

  Maurya Goyal, Anuj Singh, Hadi Jamali-Rad · 16 décembre 2025

  Aligning diffusion model outputs with downstream objectives is essential for improving task-specific performance. Broadly, inference-time training-free approaches for aligning diffusion models can be categorized into two main strategies: sampling-based methods, which explore multiple candidate outpu…

• Data-driven modelling of autonomous and forced dynamical systems

  Robert Szalai · 16 décembre 2025

  The paper demonstrates that invariant foliations are accurate, data-efficient and practical tools for data-driven modelling of physical systems. Invariant foliations can be fitted to data that either fill the phase space or cluster about an invariant manifold. Invariant foliations can be fitted to a…

• Flow-matching Operators for Residual-Augmented Probabilistic Learning of Partial Differential Equations

  Sahil Bhola, Karthik Duraisamy · 16 décembre 2025

  Learning probabilistic surrogates for PDEs remains challenging in data-scarce regimes: neural operators require large amounts of high-fidelity data, while generative approaches typically sacrifice resolution invariance. We formulate flow matching in an infinite-dimensional function space to learn a …

• KD-PINN: Knowledge-Distilled PINNs for ultra-low-latency real-time neural PDE solvers

  Karim Bounja, Lahcen Laayouni, Abdeljalil Sakat · 16 décembre 2025

  This work introduces Knowledge-Distilled Physics-Informed Neural Networks (KD-PINN), a framework that transfers the predictive accuracy of a high-capacity teacher model to a compact student through a continuous adaptation of the Kullback-Leibler divergence. To confirm its generality for various dyna…

• Rethinking Physics-Informed Regression Beyond Training Loops and Bespoke Architectures

  Lorenzo Sabug Jr., Eric Kerrigan · 16 décembre 2025

  We revisit the problem of physics-informed regression, and propose a method that directly computes the state at the prediction point, simultaneously with the derivative and curvature information of the existing samples. We frame each prediction as a constrained optimisation problem, leveraging multi…

• Adaptive Sampling for Hydrodynamic Stability

  Anshima Singh, David J. Silvester · 16 décembre 2025

  An adaptive sampling approach for efficient detection of bifurcation boundaries in parametrized fluid flow problems is presented herein. The study extends the machine-learning approach of Silvester (Machine Learning for Hydrodynamic Stability, arXiv:2407.09572), where a classifier network was traine…

• Neural equilibria for long-term prediction of nonlinear conservation laws

  J. Antonio Lara Benitez, Kareem Hegazy, Junyi Guo, Ivan Dokmani\'c, Michael W. Mahoney, Maarten V. de Hoop · 16 décembre 2025

  We introduce Neural Discrete Equilibrium (NeurDE), a machine learning framework for stable and accurate long-term forecasting of nonlinear conservation laws. NeurDE leverages a kinetic lifting that decomposes the dynamics into a fixed linear transport component and a local nonlinear relaxation to eq…