Model Reduction and Neural Networks

Derniers papiers

• LNN-PINN: A Unified Physics-Only Training Framework with Liquid Residual Blocks

  Ze Tao, Hanxuan Wang, Fujun Liu · 7 avril 2026

  Physics-informed neural networks (PINNs) have attracted considerable attention for their ability to integrate partial differential equation priors into deep learning frameworks; however, they often exhibit limited predictive accuracy when applied to complex problems. To address this issue, we propos…

• General Explicit Network (GEN): A novel deep learning architecture for solving partial differential equations

  Genwei Ma, Ting Luo, Ping Yang, Xing Zhao · 7 avril 2026

  Machine learning, especially physics-informed neural networks (PINNs) and their neural network variants, has been widely used to solve problems involving partial differential equations (PDEs). The successful deployment of such methods beyond academic research remains limited. For example, PINN metho…

• Learning Sampled-data Control for Swarms via MeanFlow

  Anqi Dong, Yongxin Chen, Karl H. Johansson, Johan Karlsson · 7 avril 2026

  Steering large-scale swarms with only limited control updates is often needed due to communication or computational constraints, yet most learning-based approaches do not account for this and instead model instantaneous velocity fields. As a result, the natural object for decision making is a finite…

• Simple yet Effective: Low-Rank Spatial Attention for Neural Operators

  Zherui Yang, Haiyang Xin, Tao Du, Ligang Liu · 7 avril 2026

  Neural operators have emerged as data-driven surrogates for solving partial differential equations (PDEs), and their success hinges on efficiently modeling the long-range, global coupling among spatial points induced by the underlying physics. In many PDE regimes, the induced global interaction kern…

• A Robust SINDy Autoencoder for Noisy Dynamical System Identification

  Kairui Ding · 7 avril 2026

  Sparse identification of nonlinear dynamics (SINDy) has been widely used to discover the governing equations of a dynamical system from data. It uses sparse regression techniques to identify parsimonious models of unknown systems from a library of candidate functions. Therefore, it relies on the ass…

• PINNs in PDE Constrained Optimal Control Problems: Direct vs Indirect Methods

  Zhen Zhang, Shanqing Liu, Alessandro Alla, Jerome Darbon, George Em Karniadakis · 7 avril 2026

  We study physics-informed neural networks (PINNs) as numerical tools for the optimal control of semilinear partial differential equations. We first recall the classical direct and indirect viewpoints for optimal control of PDEs, and then present two PINN formulations: a direct formulation based on m…

• Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements

  Xuyang Li, Mahdi Masmoudi, Rami Gharbi, Nizar Lajnef, Vishnu Naresh Boddeti · 7 avril 2026

  Parameterized partial differential equations (PDEs) underpin the mathematical modeling of complex systems in diverse domains, including engineering, healthcare, and physics. A central challenge in using PDEs for real-world applications is to accurately infer the parameters, particularly when the par…

• On Data-Driven Koopman Representations of Nonlinear Delay Differential Equations

  Santosh Mohan Rajkumar, Dibyasri Barman, Kumar Vikram Singh, Debdipta Goswami · 6 avril 2026

  This work establishes a rigorous bridge between infinite-dimensional delay dynamics and finite-dimensional Koopman learning, with explicit and interpretable error guarantees. While Koopman analysis is well-developed for ordinary differential equations (ODEs) and partially for partial differential eq…

• Learning Contractive Integral Operators with Fredholm Integral Neural Operators

  Kyriakos C. Georgiou, Constantinos Siettos, Athanasios N. Yannacopoulos · 6 avril 2026

  We generalize the framework of Fredholm Neural Networks, to learn non-expansive integral operators arising in Fredholm Integral Equations (FIEs) of the second kind in arbitrary dimensions. We first present the proposed Fredholm Integral Neural Operators (FREDINOs), for FIEs and prove that they are u…

• PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems

  Tiantian Sun, Jian Zu · 6 avril 2026

  Physics-informed neural networks and Physics-informed DeepONet excel in solving partial differential equations; however, they often fail to converge for singularly perturbed problems. To address this, we propose two novel frameworks, Prandtl-Van Dyke neural network(PVD-Net) and its operator learning…

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

  Jun Sur Richard Park, Auroni Huque Hashim, Siu Wun Cheung, Youngsoo Choi, Yeonjong Shin · 6 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…

• Mitigating Data Scarcity in Spaceflight Applications for Offline Reinforcement Learning Using Physics-Informed Deep Generative Models

  Alex E. Ballentine, Nachiket U. Bapat, Raghvendra V. Cowlagi · 6 avril 2026

  The deployment of reinforcement learning (RL)-based controllers on physical systems is often limited by poor generalization to real-world scenarios, known as the simulation-to-reality (sim-to-real) gap. This gap is particularly challenging in spaceflight, where real-world training data are scarce du…

• Rethinking Forward Processes for Score-Based Data Assimilation in High Dimensions

  Eunbi Yoon, Donghan Kim, Dae Wook Kim · 6 avril 2026

  Data assimilation is the process of estimating the time-evolving state of a dynamical system by integrating model predictions and noisy observations. It is commonly formulated as Bayesian filtering, but classical filters often struggle with accuracy or computational feasibility in high dimensions. R…

• Complex-Valued GNNs for Distributed Basis-Invariant Control of Planar Systems

  Samuel Honor, Mohamed Abdelnaby, Kevin Leahy · 6 avril 2026

  Graph neural networks (GNNs) are a well-regarded tool for learned control of networked dynamical systems due to their ability to be deployed in a distributed manner. However, current distributed GNN architectures assume that all nodes in the network collect geometric observations in compatible bases…

• A Numerical Method for Coupling Parameterized Physics-Informed Neural Networks and FDM for Advanced Thermal-Hydraulic System Simulation

  Jeesuk Shin, Donggyun Seo, Sihyeong Yu, Joongoo Jeon · 6 avril 2026

  Severe accident analysis using system-level codes such as MELCOR is indispensable for nuclear safety assessment, yet the computational cost of repeated simulations poses a significant bottleneck for parametric studies and uncertainty quantification. Existing surrogate models accelerate these analyse…

• Information theory for dimensionality reduction in dynamical systems

  Matthew S. Schmitt, Maciej Koch-Janusz, Michel Fruchart, Daniel S. Seara, Michael Rust, Vincenzo Vitelli · 3 avril 2026

  The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and fast irrelevant variables, but such a separation of scales is…

• Experimental Design for Missing Physics

  Arno Strouwen, Sebasti\'an Miclu\c{t}a-C\^ampeanu · 3 avril 2026

  For most process systems, knowledge of the model structure is incomplete. This missing physics must then be learned from experimental data. Recently, a combination of universal differential equations and symbolic regression has become a popular tool to discover these missing physics. Universal diffe…

• UQ-SHRED: uncertainty quantification of shallow recurrent decoder networks for sparse sensing via engression

  Mars Liyao Gao, Yuxuan Bao, Amy S. Rude, Xinwei Shen, J. Nathan Kutz · 3 avril 2026

  Reconstructing high-dimensional spatiotemporal fields from sparse sensor measurements is critical in a wide range of scientific applications. The SHallow REcurrent Decoder (SHRED) architecture is a recent state-of-the-art architecture that reconstructs high-quality spatial domain from hyper-sparse s…

• Bias Inheritance in Neural-Symbolic Discovery of Constitutive Closures Under Function-Class Mismatch

  Hanbing Liang, Ze Tao, Fujun Liu · 3 avril 2026

  We investigate the data-driven discovery of constitutive closures in nonlinear reaction-diffusion systems with known governing PDE structures. Our objective is to robustly recover diffusion and reaction laws from spatiotemporal observations while avoiding the common pitfall where low residuals or sh…

• Interpretable Diagnostics and Adaptive Data Assimilation for Neural ODEs via Discrete Empirical Interpolation

  Hojin Kim, Romit Maulik · 3 avril 2026

  We present a framework that leverages the Discrete Empirical Interpolation Method (DEIM) for interpretable deep learning and dynamical system analysis. Although DEIM efficiently approximates nonlinear terms in projection-based reduced-order models (POD-ROM), its fixed interpolation points are repurp…

• Physics Informed Reinforcement Learning with Gibbs Priors for Topology Control in Power Grids

  Pantelis Dogoulis, Maxime Cordy · 3 avril 2026

  Topology control for power grid operation is a challenging sequential decision making problem because the action space grows combinatorially with the size of the grid and action evaluation through simulation is computationally expensive. We propose a physics-informed Reinforcement Learning framework…

• A Simultaneous Approach for Training Neural Differential-Algebraic Systems of Equations

  Laurens R. Lueg, Victor Alves, Daniel Schicksnus, John R. Kitchin, Carl D. Laird, Lorenz T. Biegler · 3 avril 2026

  Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has produced highly influential methods, such as neural ordinary d…

• Graph Neural Operator Towards Edge Deployability and Portability for Sparse-to-Dense, Real-Time Virtual Sensing on Irregular Grids

  William Howes, Jason Yoo, Kazuma Kobayashi, Subhankar Sarkar, Farid Ahmed, Souvik Chakraborty, Syed Bahauddin Alam · 3 avril 2026

  Accurate sensing of spatially distributed physical fields typically requires dense instrumentation, which is often infeasible in real-world systems due to cost, accessibility, and environmental constraints. Physics-based solvers address this through direct numerical integration of governing equation…

• A Residual Guided strategy with Generative Adversarial Networks in training Physics-Informed Transformer Networks

  Ziyang Zhang, Feifan Zhang, Weidong Tang, Lei Shi, Tailai Chen · 3 avril 2026

  Nonlinear partial differential equations (PDEs) are pivotal in modeling complex physical systems, yet traditional Physics-Informed Neural Networks (PINNs) often struggle with unresolved residuals in critical spatiotemporal regions and violations of temporal causality. To address these limitations, w…

• PI-JEPA: Label-Free Surrogate Pretraining for Coupled Multiphysics Simulation via Operator-Split Latent Prediction

  Brandon Yee, Pairie Koh · 3 avril 2026

  Reservoir simulation workflows face a fundamental data asymmetry: input parameter fields (geostatistical permeability realizations, porosity distributions) are free to generate in arbitrary quantities, yet existing neural operator surrogates require large corpora of expensive labeled simulation traj…