Model Reduction and Neural Networks

Derniers papiers

• Continuous-Time Piecewise-Linear Recurrent Neural Networks

  Alena Br\"andle, Lukas Eisenmann, Florian G\"otz, Daniel Durstewitz · 18 février 2026

  In dynamical systems reconstruction (DSR) we aim to recover the dynamical system (DS) underlying observed time series. Specifically, we aim to learn a generative surrogate model which approximates the underlying, data-generating DS, and recreates its long-term properties (`climate statistics'). In s…

• Controlled oscillation modeling using port-Hamiltonian neural networks

  Maximino Linares, Guillaume Doras, Thomas H\'elie · 18 février 2026

  Learning dynamical systems through purely data-driven methods is challenging as they do not learn the underlying conservation laws that enable them to correctly generalize. Existing port-Hamiltonian neural network methods have recently been successfully applied for modeling mechanical systems. Howev…

• Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flows

  Ramansh Sharma, Matthew Lowery, Houman Owhadi, Varun Shankar · 18 février 2026

  We present a novel property-preserving kernel-based operator learning method for incompressible flows governed by the incompressible Navier-Stokes equations. Traditional numerical solvers incur significant computational costs to respect incompressibility. Operator learning offers efficient surrogate…

• Non-intrusive data-driven model order reduction for circuits based on Hammerstein architectures

  Joshua Hanson, Paul Kuberry, Biliana Paskaleva, Pavel Bochev · 18 février 2026

  We demonstrate that system identification techniques can provide a basis for effective, non-intrusive model order reduction (MOR) for common circuits that are key building blocks in microelectronics. Our approach is motivated by the practical operation of these circuits and utilizes a canonical Hamm…

• Randomness and signal propagation in physics-informed neural networks (PINNs): A neural PDE perspective

  Jean-Michel Tucny, Abhisek Ganguly, Santosh Ansumali, Sauro Succi · 18 février 2026

  Physics-informed neural networks (PINNs) often exhibit weight matrices that appear statistically random after training, yet their implications for signal propagation and stability remain unsatisfactorily understood, let alone the interpretability. In this work, we analyze the spectral and statistica…

• PolyNODE: Variable-dimension Neural ODEs on M-polyfolds

  Per {\AA}hag, Alexander Friedrich, Fredrik Ohlsson, Viktor Vigren N\"aslund · 18 février 2026

  Neural ordinary differential equations (NODEs) are geometric deep learning models based on dynamical systems and flows generated by vector fields on manifolds. Despite numerous successful applications, particularly within the flow matching paradigm, all existing NODE models are fundamentally constra…

• Symbolic recovery of PDEs from measurement data

  Erion Morina, Philipp Scholl, Martin Holler · 18 février 2026

  Models based on partial differential equations (PDEs) are powerful for describing a wide range of complex relationships in the natural sciences. Accurately identifying the PDE model, which represents the underlying physical law, is essential for a proper understanding of the problem. This reconstruc…

• Neural-POD: A Plug-and-Play Neural Operator Framework for Infinite-Dimensional Functional Nonlinear Proper Orthogonal Decomposition

  Changhong Mou, Binghang Lu, Guang Lin · 18 février 2026

  The rapid development of AI for Science is often hindered by the "discretization", where learned representations remain restricted to the specific grids or resolutions used during training. We propose the Neural Proper Orthogonal Decomposition (Neural-POD), a plug-and-play neural operator framework …

• Learning Data-Efficient and Generalizable Neural Operators via Fundamental Physics Knowledge

  Siying Ma, Mehrdad M. Zadeh, Mauricio Soroco, Wuyang Chen, Jiguo Cao, Vijay Ganesh · 18 février 2026

  Recent advances in scientific machine learning (SciML) have enabled neural operators (NOs) to serve as powerful surrogates for modeling the dynamic evolution of physical systems governed by partial differential equations (PDEs). While existing approaches focus primarily on learning simulations from …

• Morephy-Net: An Evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed Neural Operator Learning Networks

  Binghang Lu, Changhong Mou, Guang Lin · 18 février 2026

  We propose an evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed operator-learning Networks (Morephy-Net) to solve parametric partial differential equations (PDEs) in noisy data regimes, for both forward prediction and inverse identification. Existing physics-infor…

• Pseudo-differential-enhanced physics-informed neural networks

  Andrew Gracyk · 17 février 2026

  We present pseudo-differential enhanced physics-informed neural networks (PINNs), an extension of gradient enhancement but in Fourier space. Gradient enhancement of PINNs dictates that the PDE residual is taken to a higher differential order than prescribed by the PDE, added to the objective as an a…

• BEACONS: Bounded-Error, Algebraically-Composable Neural Solvers for Partial Differential Equations

  Jonathan Gorard, Ammar Hakim, James Juno · 17 février 2026

  The traditional limitations of neural networks in reliably generalizing beyond the convex hulls of their training data present a significant problem for computational physics, in which one often wishes to solve PDEs in regimes far beyond anything which can be experimentally or analytically validated…

• Ambient Physics: Training Neural PDE Solvers with Partial Observations

  Harris Abdul Majid, Giannis Daras, Francesco Tudisco, Steven McDonagh · 17 février 2026

  In many scientific settings, acquiring complete observations of PDE coefficients and solutions can be expensive, hazardous, or impossible. Recent diffusion-based methods can reconstruct fields given partial observations, but require complete observations for training. We introduce Ambient Physics, a…

• KoopGen: Koopman Generator Networks for Representing and Predicting Dynamical Systems with Continuous Spectra

  Liangyu Su, Jun Shu, Rui Liu, Deyu Meng, Zongben Xu · 17 février 2026

  Representing and predicting high-dimensional and spatiotemporally chaotic dynamical systems remains a fundamental challenge in dynamical systems and machine learning. Although data-driven models can achieve accurate short-term forecasts, they often lack stability, interpretability, and scalability i…

• Gradient Networks for Universal Magnetic Modeling of Synchronous Machines

  Junyi Li, Tim Foissner, Floran Martin, Antti Piippo, Marko Hinkkanen · 17 février 2026

  This paper presents a physics-informed neural network approach for dynamic modeling of saturable synchronous machines, including cases with spatial harmonics. We introduce an architecture that incorporates gradient networks directly into the fundamental machine equations, enabling accurate modeling …

• A Unified Physics-Informed Neural Network for Modeling Coupled Electro- and Elastodynamic Wave Propagation Using Three-Stage Loss Optimization

  Suhas Suresh Bharadwaj, Reuben Thomas Thovelil · 17 février 2026

  Physics-Informed Neural Networks present a novel approach in SciML that integrates physical laws in the form of partial differential equations directly into the NN through soft constraints in the loss function. This work studies the application of PINNs to solve a one dimensional coupled electro-ela…

• Geometry-Aware Physics-Informed PointNets for Modeling Flows Across Porous Structures

  Luigi Ciceri, Corrado Mio, Jianyi Lin, Gabriele Gianini · 17 février 2026

  Predicting flows that occur both through and around porous bodies is challenging due to coupled physics across fluid and porous regions and the need to generalize across diverse geometries and boundary conditions. We address this problem using two Physics Informed learning approaches: Physics Inform…

• Causally constrained reduced-order neural models of complex turbulent dynamical systems

  Fabrizio Falasca, Laure Zanna · 17 février 2026

  We introduce a flexible framework based on response theory and score matching to suppress spurious, noncausal dependencies in reduced-order neural emulators of turbulent systems, focusing on climate dynamics as a proof-of-concept. We showcase the approach using the stochastic Charney-DeVore model as…

• Are Statistical Methods Obsolete in the Era of Deep Learning? A Study of ODE Inverse Problems

  Skyler Wu, Shihao Yang, S. C. Kou · 17 février 2026

  In the era of AI, neural networks have become increasingly popular for modeling, inference, and prediction, largely due to their potential for universal approximation. With the proliferation of such deep learning models, a question arises: are leaner statistical methods still relevant? To shed insig…

• GenPANIS: A Latent-Variable Generative Framework for Forward and Inverse PDE Problems in Multiphase Media

  Matthaios Chatzopoulos, Phaedon-Stelios Koutsourelakis · 17 février 2026

  Inverse problems and inverse design in multiphase media, i.e., recovering or engineering microstructures to achieve target macroscopic responses, require operating on discrete-valued material fields, rendering the problem non-differentiable and incompatible with gradient-based methods. Existing appr…

• Parameter-Minimal Neural DE Solvers via Horner Polynomials

  T. Matuli\'c, D. Ser\v{s}i\'c · 17 février 2026

  We propose a parameter-minimal neural architecture for solving differential equations by restricting the hypothesis class to Horner-factorized polynomials, yielding an implicit, differentiable trial solution with only a small set of learnable coefficients. Initial conditions are enforced exactly by …

• DiffusionRollout: Uncertainty-Aware Rollout Planning in Long-Horizon PDE Solving

  Seungwoo Yoo, Juil Koo, Daehyeon Choi, Minhyuk Sung · 17 février 2026

  We propose DiffusionRollout, a novel selective rollout planning strategy for autoregressive diffusion models, aimed at mitigating error accumulation in long-horizon predictions of physical systems governed by partial differential equations (PDEs). Building on the recently validated probabilistic app…

• A Multiplicative Neural Network Architecture: Locality and Regularity of Approximation

  Hee-Sun Choi, Beom-Seok Han · 17 février 2026

  We introduce a multiplicative neural network architecture in which multiplicative interactions constitute the fundamental representation, rather than appearing as auxiliary components within an additive model. We establish a universal approximation theorem for this architecture and analyze its appro…

• Compressible Dynamics in Deep Overparameterized Low-Rank Learning & Adaptation

  Can Yaras, Peng Wang, Laura Balzano, Qing Qu · 16 février 2026

  While overparameterization in machine learning models offers great benefits in terms of optimization and generalization, it also leads to increased computational requirements as model sizes grow. In this work, we show that by leveraging the inherent low-dimensional structures of data and compressibl…

• A Machine Learning Approach to the Nirenberg Problem

  Gianfranco Cort\'es, Maria Esteban-Casadevall, Yueqing Feng, Jonas Henkel, Edward Hirst, Tancredi Schettini Gherardini, Alexander G. Stapleton · 16 février 2026

  This work introduces the Nirenberg Neural Network: a numerical approach to the Nirenberg problem of prescribing Gaussian curvature on $S^2$ for metrics that are pointwise conformal to the round metric. Our mesh-free physics-informed neural network (PINN) approach directly parametrises the conformal …