Model Reduction and Neural Networks

Derniers papiers

• One-Shot Transfer Learning for Nonlinear PDEs with Perturbative PINNs

  Samuel Auroy, Pavlos Protopapas · 17 novembre 2025

  We propose a framework for solving nonlinear partial differential equations (PDEs) by combining perturbation theory with one-shot transfer learning in Physics-Informed Neural Networks (PINNs). Nonlinear PDEs with polynomial terms are decomposed into a sequence of linear subproblems, which are effici…

• Bias-Restrained Prefix Representation Finetuning for Mathematical Reasoning

  Sirui Liang, Pengfei Cao, Jian Zhao, Cong Huang, Jun Zhao, Kang Liu · 17 novembre 2025

  Parameter-Efficient finetuning (PEFT) enhances model performance on downstream tasks by updating a minimal subset of parameters. Representation finetuning (ReFT) methods further improve efficiency by freezing model weights and optimizing internal representations with fewer parameters than PEFT, outp…

• PINGS-X: Physics-Informed Normalized Gaussian Splatting with Axes Alignment for Efficient Super-Resolution of 4D Flow MRI

  Sun Jo, Seok Young Hong, JinHyun Kim, Seungmin Kang, Ahjin Choi, Don-Gwan An, Simon Song, Je Hyeong Hong · 17 novembre 2025

  4D flow magnetic resonance imaging (MRI) is a reliable, non-invasive approach for estimating blood flow velocities, vital for cardiovascular diagnostics. Unlike conventional MRI focused on anatomical structures, 4D flow MRI requires high spatiotemporal resolution for early detection of critical cond…

• Towards Universal Neural Operators through Multiphysics Pretraining

  Mikhail Masliaev, Dmitry Gusarov, Ilya Markov, Alexander Hvatov · 17 novembre 2025

  Although neural operators are widely used in data-driven physical simulations, their training remains computationally expensive. Recent advances address this issue via downstream learning, where a model pretrained on simpler problems is fine-tuned on more complex ones. In this research, we investiga…

• Differentiation Strategies for Acoustic Inverse Problems: Admittance Estimation and Shape Optimization

  Nikolas Borrel-Jensen, Josiah Bjorgaard · 17 novembre 2025

  We demonstrate a practical differentiable programming approach for acoustic inverse problems through two applications: admittance estimation and shape optimization for resonance damping. First, we show that JAX-FEM's automatic differentiation (AD) enables direct gradient-based estimation of complex …

• Interpolation Conditions for Data Consistency and Prediction in Noisy Linear Systems

  Martina Vanelli, Nima Monshizadeh, Julien M. Hendrickx · 17 novembre 2025

  We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all trajectories consistent with the measured data and these pri…

• BubbleOKAN: A Physics-Informed Interpretable Neural Operator for High-Frequency Bubble Dynamics

  Yunhao Zhang, Sidharth S. Menon, Lin Cheng, Aswin Gnanaskandan, Ameya D. Jagtap · 17 novembre 2025

  In this work, we employ physics-informed neural operators to map pressure profiles from an input function space to the corresponding bubble radius responses. Our approach employs a two-step DeepONet architecture. To address the intrinsic spectral bias of deep learning models, our model incorporates …

• Differentiable Sparse Identification of Lagrangian Dynamics

  Zitong Zhang, Hao Sun · 17 novembre 2025

  Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise sensitivity in complex mechanical systems. The Lagrangian formalism…

• FlowPath: Learning Data-Driven Manifolds with Invertible Flows for Robust Irregularly-sampled Time Series Classification

  YongKyung Oh, Dong-Young Lim, Sungil Kim · 17 novembre 2025

  Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge. Neural controlled differential equations provide a principled framework for such tasks, yet their performance is highly sensitive to the choice of control path constructed from discrete…

• Symmetry aware Reynolds Averaged Navier Stokes turbulence models with equivariant neural networks

  Aaron Miller, Sahil Kommalapati, Robert Moser, Petros Koumoutsakos · 14 novembre 2025

  Accurate and generalizable Reynolds-averaged Navier-Stokes (RANS) models for turbulent flows rely on effective closures. We introduce tensor-based, symmetry aware closures using equivariant neural networks (ENNs) and present an algorithm for enforcing algebraic contraction relations among tensor com…

• PRDP: Progressively Refined Differentiable Physics

  Kanishk Bhatia, Felix Koehler, Nils Thuerey · 14 novembre 2025

  The physics solvers employed for neural network training are primarily iterative, and hence, differentiating through them introduces a severe computational burden as iterations grow large. Inspired by works in bilevel optimization, we show that full accuracy of the network is achievable through phys…

• Continuum Dropout for Neural Differential Equations

  Jonghun Lee, YongKyung Oh, Sungil Kim, Dong-Young Lim · 14 novembre 2025

  Neural Differential Equations (NDEs) excel at modeling continuous-time dynamics, effectively handling challenges such as irregular observations, missing values, and noise. Despite their advantages, NDEs face a fundamental challenge in adopting dropout, a cornerstone of deep learning regularization, …

• Spectral methods for Neural Integral Equations

  Emanuele Zappala · 14 novembre 2025

  Neural integral equations are deep learning models based on the theory of integral equations, where the model consists of an integral operator and the corresponding equation (of the second kind) which is learned through an optimization procedure. This approach allows to leverage the nonlocal propert…

• SVD-NO: Learning PDE Solution Operators with SVD Integral Kernels

  Noam Koren, Ralf J. J. Mackenbach, Ruud J. G. van Sloun, Kira Radinsky, Daniel Freedman · 14 novembre 2025

  Neural operators have emerged as a promising paradigm for learning solution operators of partial differential equa- tions (PDEs) directly from data. Existing methods, such as those based on Fourier or graph techniques, make strong as- sumptions about the structure of the kernel integral opera- tor, …

• Koopman Invariants as Drivers of Emergent Time-Series Clustering in Joint-Embedding Predictive Architectures

  Pablo Ruiz-Morales, Dries Vanoost, Davy Pissoort, Mathias Verbeke · 14 novembre 2025

  Joint-Embedding Predictive Architectures (JEPAs), a powerful class of self-supervised models, exhibit an unexplained ability to cluster time-series data by their underlying dynamical regimes. We propose a novel theoretical explanation for this phenomenon, hypothesizing that JEPA's predictive objecti…

• Generalizing PDE Emulation with Equation-Aware Neural Operators

  Qian-Ze Zhu, Paul Raccuglia, Michael P. Brenner · 14 novembre 2025

  Solving partial differential equations (PDEs) can be prohibitively expensive using traditional numerical methods. Deep learning-based surrogate models typically specialize in a single PDE with fixed parameters. We present a framework for equation-aware emulation that generalizes to unseen PDEs, cond…

• E-PINNs: Epistemic Physics-Informed Neural Networks

  Bruno Jacob, Ashish S. Nair, Amanda A. Howard, Jan Drgona, Panos Stinis · 14 novembre 2025

  Physics-informed neural networks (PINNs) have demonstrated promise as a framework for solving forward and inverse problems involving partial differential equations. Despite recent progress in the field, it remains challenging to quantify uncertainty in these networks. While techniques such as Bayesi…

• Group Averaging for Physics Applications: Accuracy Improvements at Zero Training Cost

  Valentino F. Foit, David W. Hogg, Soledad Villar · 14 novembre 2025

  Many machine learning tasks in the natural sciences are precisely equivariant to particular symmetries. Nonetheless, equivariant methods are often not employed, perhaps because training is perceived to be challenging, or the symmetry is expected to be learned, or equivariant implementations are seen…

• Physics-Informed Machine Learning for Characterizing System Stability

  Tomoki Koike, Elizabeth Qian · 13 novembre 2025

  In the design and operation of complex dynamical systems, it is essential to ensure that all state trajectories of the dynamical system converge to a desired equilibrium within a guaranteed stability region. Yet, for many practical systems -- especially in aerospace -- this region cannot be determin…

• Guaranteeing Conservation of Integrals with Projection in Physics-Informed Neural Networks

  Anthony Baez, Wang Zhang, Ziwen Ma, Lam Nguyen, Subhro Das, Luca Daniel · 13 novembre 2025

  We propose a novel projection method that guarantees the conservation of integral quantities in Physics-Informed Neural Networks (PINNs). While the soft constraint that PINNs use to enforce the structure of partial differential equations (PDEs) enables necessary flexibility during training, it also …

• Cross-Field Interface-Aware Neural Operators for Multiphase Flow Simulation

  ZhenZhong Wang, Xin Zhang, Jun Liao, Min Jiang · 13 novembre 2025

  Multiphase flow systems, with their complex dynamics, field discontinuities, and interphase interactions, pose significant computational challenges for traditional numerical solvers. While neural operators offer efficient alternatives, they often struggle to achieve high-resolution numerical accurac…

• A Neural-Operator Preconditioned Newton Method for Accelerated Nonlinear Solvers

  Youngkyu Lee, Shanqing Liu, Jerome Darbon, George Em Karniadakis · 13 novembre 2025

  We propose a novel neural preconditioned Newton (NP-Newton) method for solving parametric nonlinear systems of equations. To overcome the stagnation or instability of Newton iterations caused by unbalanced nonlinearities, we introduce a fixed-point neural operator (FPNO) that learns the direct mappi…

• When is a System Discoverable from Data? Discovery Requires Chaos

  Zakhar Shumaylov, Peter Zaika, Philipp Scholl, Gitta Kutyniok, Lior Horesh, Carola-Bibiane Sch\"onlieb · 13 novembre 2025

  The deep learning revolution has spurred a rise in advances of using AI in sciences. Within physical sciences the main focus has been on discovery of dynamical systems from observational data. Yet the reliability of learned surrogates and symbolic models is often undermined by the fundamental proble…

• A Finite Difference Approximation of Second Order Regularization of Neural-SDFs

  Haotian Yin, Aleksander Plocharski, Michal Jan Wlodarczyk, Przemyslaw Musialski · 13 novembre 2025

  We introduce a finite-difference framework for curvature regularization in neural signed distance field (SDF) learning. Existing approaches enforce curvature priors using full Hessian information obtained via second-order automatic differentiation, which is accurate but computationally expensive. Ot…

• Continuous Symmetry Discovery and Enforcement Using Infinitesimal Generators of Multi-parameter Group Actions

  Ben Shaw, Sasidhar Kunapuli, Abram Magner, Kevin R. Moon · 13 novembre 2025

  Symmetry-informed machine learning can exhibit advantages over machine learning which fails to account for symmetry. In the context of continuous symmetry detection, current state of the art experiments are largely limited to detecting affine transformations. Herein, we outline a computationally eff…