Model Reduction and Neural Networks

Derniers papiers

• A Greedy PDE Router for Blending Neural Operators and Classical Methods

  Sahana Rayan, Yash Patel, Ambuj Tewari · 8 mai 2026

  When solving PDEs, classical numerical solvers are often computationally expensive, while machine learning methods can suffer from spectral bias, failing to capture high-frequency components. Designing an optimal hybrid iterative solver--where, at each iteration, a solver is selected from an ensembl…

• Mean Mode Screaming: Mean--Variance Split Residuals for 1000-Layer Diffusion Transformers

  Pengqi Lu · 8 mai 2026

  Scaling Diffusion Transformers (DiTs) to hundreds of layers introduces a structural vulnerability: networks can enter a silent, mean-dominated collapse state that homogenizes token representations and suppresses centered variation. Through mechanistic auditing, we isolate the trigger event of this c…

• INEUS: Iterative Neural Solver for High-Dimensional PIDEs

  Jean-Loup Dupret, Davide Gallon, Patrick Cheridito · 8 mai 2026

  In this paper, we introduce INEUS, a meshfree iterative neural solver for partial integro-differential equations (PIDEs). The method replaces the explicit evaluation of nonlocal jump integrals with single-jump sampling and reformulates PIDE solving as a sequence of recursive regression problems. Lik…

• Data-Driven Variational Basis Learning Beyond Neural Networks: A Non-Neural Framework for Adaptive Basis Discovery

  Andrew Kiruluta · 8 mai 2026

  Classical representation systems such as Fourier series, wavelets, and fixed dictionaries provide analytically tractable basis expansions, but they are not intrinsically adapted to the empirical structure of modern high-dimensional data. Neural networks overcome this limitation by learning features …

• Towards Scalable One-Step Generative Modeling for Autoregressive Dynamical System Forecasting

  Tianyue Yang, Xiao Xue · 8 mai 2026

  Fast surrogate modeling for high-dimensional physical dynamics requires more than low short-term error: useful models must roll out efficiently while preserving the statistical structure of long trajectories. Neural operators provide inexpensive autoregressive forecasts but can drift in turbulent re…

• Physics-Informed Neural Networks with Learnable Loss Balancing and Transfer Learning

  Reza Pirayeshshirazinezhad · 8 mai 2026

  We propose a self-supervised physics-informed neural network (PINN) framework that adaptively balances physics-based and data-driven supervision for scientific machine learning under data scarcity. Unlike prior PINNs that rely on fixed or heuristic weighting of physics residuals and data loss, our a…

• Variational Smoothing and Inference for SDEs from Sparse Data with Dynamic Neural Flows

  Yu Wang, Arnab Ganguly · 8 mai 2026

  Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and parameters from sparse, noisy observations. Classical smoothing m…

• AeroJEPA: Learning Semantic Latent Representations for Scalable 3D Aerodynamic Field Modeling

  Francisco Giral, Abhijeet Vishwasrao, Andrea Arroyo Ramo, Mahmoud Golestanian, Federica Tonti, Adrian Lozano-Duran, Steven L. Brunton, Sergio Hoyas, Hector Gomez, Soledad Le Clainche, Ricardo Vinuesa · 8 mai 2026

  Aerodynamic surrogate models are increasingly used to replace repeated high-fidelity CFD evaluations in many-query design settings, but current approaches still face two important limitations: they often scale poorly to the very large fields arising in realistic 3D aerodynamics, and they rarely prod…

• ZNO: Stable Rational Neural Operators in the Z-Domain for Discrete-Time Dynamics

  Xianli Zhu, Jia Yin · 7 mai 2026

  We introduce the Z-Domain Neural Operator (ZNO), a causal neural operator whose layers are stable low-rank multiple-input multiple-output (MIMO) rational filters parameterized directly in the $z$-plane. ZNO addresses a limitation of existing operator learning methods, many of which are primarily tai…

• Geometry-Aware Neural Optimizer for Shape Optimization and Inversion

  Guoze Sun, Tianya Miao, Haoyang Huang, Huaguan Chen, Han Wan, Rui Zhang, Hao Sun · 7 mai 2026

  Geometry is central to PDE-governed systems, motivating shape optimization and inversion. Classical pipelines conduct costly forward simulation with geometry processing, requiring substantial expert effort. Neural surrogates accelerate forward analysis but do not close the loop because gradients fro…

• Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations

  Zhangyong Liang · 7 mai 2026

  We propose HIN-LRI, a hybrid framework that augments a classical numerical solver with a neural operator trained to correct the solver's structured truncation error. A base low-regularity integrator provides a consistent first-order approximation to nonlinear dispersive PDEs, while a lightweight neu…

• Differentiable Chemistry in PINNs for Solving Parameterized and Stiff Reaction Systems

  Milo\v{s} Babi\'c, Franz M. Rohrhofer, Stefan Posch · 7 mai 2026

  From neural ODEs to continuous-time machine learning, differentiable solvers allow physics, optimization, and simulation to become trainable components within deep learning systems. This has opened the path to a new generation of deep learning frameworks for scientific computing, with many promising…

• From Video-to-PDE: Data-Driven Discovery of Nonlinear Dye Plume Dynamics

  Cesar Acosta-Minoli, Sayantan Sarkar · 7 mai 2026

  Inferring continuum models directly from video is hampered by two facts: the recorded field is uncalibrated image intensity rather than a physical state, and direct numerical differentiation of noisy frames is unstable. We develop a video-to-PDE pipeline that converts grayscale recordings of an ink …

• Bilinear Mamba-Koopman Neural MPC for Varying Dynamics

  Matan Pagi, Zohar Sorek · 7 mai 2026

  Koopman-based neural MPC models generate time-varying dynamics from historical data, but preserve convexity by enforcing that the system operator is independent of the current control input. This conditional independence constraint limits adaptation to changing dynamics within a single MPC horizon, …

• Constrained Extreme Gradient Boosting for Adapting Reduced-Order Models

  Melika Baghi, Xiao Liu, Kamran Paynabar · 7 mai 2026

  High-fidelity simulations, such as computational fluid dynamics and finite element analysis, are essential for modeling complex engineering systems but are often prohibitively expensive for tasks including parametric studies, optimization, and real-time control. Projection-based reduced-order models…

• Model synthesis and identifiability analysis of stiff chemical reaction systems with inVAErt networks

  Sreejata Dey, Guoxiang Grayson Tong, Jonathan F. MacArt, Daniele E. Schiavazzi · 7 mai 2026

  We consider the problem of learning data-driven replicas for stiff systems of ordinary differential equations arising in chemical kinetics that can be evaluated with high computational efficiency. We first focus on training emulators for families of reaction equations under varying reaction rates, u…

• Deep Wave Network for Modeling Multi-Scale Physical Dynamics

  Alexander I. Khrabry, Edward A. Startsev, Andrew T. Powis, Igor D. Kaganovich · 7 mai 2026

  Performance of deep learning models is strongly governed by architectural capacity, with width and depth as primary controls. However, in physical-science applications, models are often compared at a single fixed size or by separating accuracy and computational cost, which can be misleading since ar…

• Simultaneous CNN Approximation on Manifolds with Applications to Boundary Value Problems

  Hanfei Zhou, Lei Shi · 7 mai 2026

  This paper develops convolutional neural network (CNN) methods for simultaneous approximation and elliptic boundary value problems on compact Riemannian manifolds. We establish simultaneous Sobolev approximation results for single- and multichannel CNNs, showing that manifold functions and their der…

• Replay-Based Continual Learning for Physics-Informed Neural Operators

  Yizheng Wang, Mohammad Sadegh Eshaghi, Xiaoying Zhuang, Timon Rabczuk, Yinghua Liu · 7 mai 2026

  Neural operators generally demonstrate strong predictive performance on in-distribution (ID) problems. However, a critical limitation of existing methods is their significant performance degradation when encountering out-of-distribution (OOD) data. To address this issue, this work introduces continu…

• FLUID: Continuous-Time Hyperconnected Sparse Transformer for Sink-Free Learning

  Waleed Razzaq, Yun-Bo Zhao · 7 mai 2026

  Continuous-time (CT) Transformers improve irregular and long-range modeling over CT-RNNs by exploiting inputs or outputs embeddings with continuous dynamics. However, the core scaled-dot-product-attention (SDPA) mechanism remains inherently discrete. We propose FLUID (Flexible Unified Information Dy…

• Neural-Guided Domain Restriction to Accelerate Pseudospectra Computation for Structured Non-normal Banded Matrices

  Amit Punia, Rakesh Kumar, Madan Lal · 7 mai 2026

  Computing pseudospectra of non-normal matrices is essential for understanding the stability and transient behavior of dynamical systems. Such analysis is critical in applications including fluid dynamics, control systems, and differential operators, where non-normality can lead to significant transi…

• Meta-Inverse Physics-Informed Neural Networks for High-Dimensional Ordinary Differential Equations

  Zhao Wei, Kenneth Hor Cheng Koh, Sheng Yuan Chin, James Chun Yip Chan, Chin Chun Ooi, Yew-Soon Ong · 6 mai 2026

  Solving inverse problems in dynamical systems governed by high-dimensional coupled ordinary differential equations (ODEs) is a ubiquitous challenge in scientific machine learning. In many real-world applications, researchers seek to uncover unknown parameters or model unknown dynamics even as the un…

• Amortized Variational Inference for Joint Posterior and Predictive Distributions in Bayesian Uncertainty Quantification

  Nan Feng, Xun Huan · 6 mai 2026

  Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior distribution of model parameters, and then propagating poste…

• Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks

  Diego Marcondes · 6 mai 2026

  The dual norm characterisation of weak solutions of second-order linear elliptic partial differential equations is mathematically natural but computationally intractable: evaluating the $H^{-1}$ norm of a residual requires a supremum over an infinite-dimensional function space. We prove that the $H^…

• PODiff: Latent Diffusion in Proper Orthogonal Decomposition Space for Scientific Super-Resolution

  Onkar Jadhav, Tim French, Matthew Rayson, Nicole L. Jones · 6 mai 2026

  Probabilistic super-resolution of high-dimensional spatial fields using diffusion models is often computationally prohibitive due to the cost of operating directly in pixel space. We propose PODiff, a structured conditional generative framework that performs diffusion in a fixed, variance-ordered Pr…