The paper presents a reinforcement‑learning framework that dynamically selects between full‑order models (FOMs) and reduced‑order models (ROMs) in hybrid domain decomposition simulations using the overlapping Schwarz alternating method (O‑SAM). Offline‑trained Deep Q‑networks choose subdomain‑local FOMs or pre‑trained Operator Inference ROMs based on a reward that balances accuracy, computational cost, and model‑switching frequency, and the learned policies are deployed on unseen problem instances without needing a reference FOM solution. Experiments on a 1D advection‑diffusion problem and a 3D elastic wave propagation benchmark show that the RL‑guided policies adaptively allocate high‑fidelity resolution as features propagate, outperforming static FOM/ROM assignments and demonstrating the feasibility of predictive online fidelity adaptation in Schwarz‑based hybrid simulations.
By Trishit Mondal, Irina Tezaur, Anthony Gruber
arXiv:2609.07814v1 Announce Type: new
Abstract: Physics-informed neural networks (PINNs) struggle on PDEs whose governing physics varies across the domain. We trace this to a structural property of s...
By Hanwen Wang, Paris Perdikaris
arXiv:2607. 11094v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs); however, their synchronous optimization treats residuals of different regions and constraints equally, which is inconsistent with the progressive "from source to response" physical information propagation path, degrading training stability and accuracy.
By Zhangyi Lian, Xinda Dong, Wenxuan Huo, Weifeng Huang, Gang Zhu, Qiang He
arXiv:2605. 08318v2 Announce Type: replace Abstract: We study the problem of \emph{architecture selection} for deep learning models trained to solve partial differential equations (PDEs), asking when transformer-based architectures with learned attention outperform Fourier-domain neural operators.
By Brandon Yee, Pairie Koh, Jack Rodriguez, Mihir Tekal
arXiv:2607. 02194v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have emerged as a promising route to solve partial differential equations, yet they have struggled to reach the precision of classical solvers.
By Joseph Webb, Sadok Jerad, Coralia Cartis
arXiv:2609.14841v1 Announce Type: new
Abstract: Scientific machine learning methods such as physics-informed neural networks (PINNs) increasingly rely on domain decomposition for better scalability w...
By Sidharth S. Menon, Irina Tezaur, Ameya D. Jagtap
arXiv:2605. 04853v2 Announce Type: replace Abstract: 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.
By Zhangyong Liang, Huanhuan Gao
LPINNs introduces a minimal modification to physics-informed neural networks (PINNs) by applying input‑dependent localization functions to the first hidden layer, creating receptive fields without domain partitioning. Across 13 localization families tested on a harmonic oscillator, a long‑interval heat equation, and a 4‑dimensional fourth‑order problem, three configurations—fixed Gaussian, inverse‑quadratic with learnable parameters, and fixed bump—significantly reduced solution error compared to the baseline. However, the benefit is not universal; many families performed worse, and only the inverse‑quadratic family consistently outperformed the baseline on all three equations.
By Lakshay Chawla, Hardik Jain
arXiv:2606. 08672v1 Announce Type: cross Abstract: Diffusion and flow generative models sample by integrating a learned ODE, but high quality still requires many sequential model evaluations.
By Sihyeon Kim, Seunghun Lee, Vikas Singh, Hyunwoo J. Kim
arXiv:2609.24947v1 Announce Type: new
Abstract: Neural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed n...
By S. Mohammad Mousavi, Teeratorn Kadeethum, Nikolaos Bouklas, Somdatta Goswami
The paper introduces a linearized Physics-Informed Neural Network (lPINN), a reduced‑order neural basis approach for solving forward and inverse differential equations. In an offline phase, lPINN learns continuous, differentiable neural basis functions from numerical solutions, which are then frozen for new problem instances; the online solution is obtained by minimizing the governing‑equation residual with additional constraints. Experiments on advection‑diffusion, Burgers', and nonlinear pendulum equations show that lPINN achieves lower solution and parameter errors than vanilla PINNs while reducing online inference times by up to three orders of magnitude, and its continuous representation generalizes to finer meshes without retraining.
By Wenhao Chen, Alexandre M. Tartakovsky
The paper investigates how different attention mechanisms affect the performance of DeepONet neural operators. Five variants—varying in cross‑attention, self‑attention, tokenization, and attention depth—are trained in both data‑driven and physics‑informed settings on one‑ and two‑dimensional PDE benchmarks. Results show that per‑sensor tokenization with cross‑attention consistently reduces error, while branch self‑attention helps only in complex spatial problems, and deeper cross‑attention yields diminishing returns with higher cost.
By Amar Alem Koric, Qibang Liu, Seid Koric