arXiv Machine Learning

Trainable Spline Representations for Physics-Informed Learning

arXiv:2607. 15751v1 Announce Type: new Abstract: This work introduces Physics-Informed Splines (PI-Splines), a structured spline-based architecture for physics-informed learning.

arXiv AI

Jul 29

Physics-Informed Broad Learning System: An Efficient Backpropagation-Free Framework for Solving Partial Differential Equations

arXiv:2607. 25608v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding governing physical laws into deep neural networks.

By Pinki Khatun, M. Sajid, Abhinav Jha, M. Tanveer

rag benchmarks

arXiv Machine Learning

Jun 19

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System

arXiv:2606. 19754v1 Announce Type: new Abstract: Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems.

By Zhiwen Yu, Derong Yang, Liujian Zhang, Kaixiang Yang, Peilin Zhan, Jianmin Lv, Jane You, C. L. Philip Chen

arXiv Machine Learning

5d ago

Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations

arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).

By Heechang Kim, Qianying Cao, Hyomin Shin, Seungchul Lee, George Em Karniadakis, Minseok Choi

rag diffusion benchmarks

arXiv Machine Learning

Jun 19

Evolutionary Two-Stage Hyperparameter Optimization Strategies for Physics-Informed Neural Networks

arXiv:2606. 20442v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve Partial Differential Equations (PDEs) by embedding physical laws into neural network training.

By Fedor Buzaev (HSE University), Dmitry Efremenko (HSE University), Egor Bugaev (HSE University), Andrei Ermakov (HSE University, AXXX), Denis Derkach (HSE University), Daria Pugacheva (HSE University, AXXX), Fedor Ratnikov (HSE University)

rag

arXiv AI

Jun 4

Curvature-aware dynamic precision approach for physics-informed neural networks

arXiv:2606. 04736v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have become a promising framework for simulating partial differential equations (PDEs) by embedding physical laws directly into neural network training.

By Yingjie Shao, Ioannis N. Athanasiadis, George van Voorn, Taniya Kapoor

rag benchmarks

arXiv Machine Learning

Jun 5

On the training of physics-informed neural operators for solving parametric partial differential equations

arXiv:2606. 06164v1 Announce Type: new Abstract: Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data.

By Nanxi Chen, Chuanjie Cui, Airong Chen, Sifan Wang, Rujin Ma

llms computer-vision benchmarks

arXiv Machine Learning

1d ago

PIKFNO: An Interpretable Neural Operator Based on Physics Informed Kernel Function

arXiv:2608. 14619v1 Announce Type: new Abstract: This work proposes a new interpretable neural operator framework, termed the Physics Informed Kernel Function Neural Operator (PIKFNO), which explicitly incorporates physics informed kernel functions derived from governing equations into the neural operator architecture.

By Yuan Guo, Hanshu Chen, Zhuojia Fu

safety

arXiv Machine Learning

Jul 3

An Optimisation Framework for the Well-Conditioned Training of Physics-Informed Neural Networks

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 Machine Learning

Aug 6

Continual-Learning Physics-Informed Neural Networks for Parameterized Partial Differential Equations

arXiv:2608. 04778v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) incorporate governing equations into neural-network training and can approximate PDE solutions without requiring large observational datasets.

By Xujia Chen, Xinyue Hu, Letian Chen, Yi Liu, Wenhui Fan

benchmarks

arXiv Machine Learning

Jul 28

Variational Boosting for Physics-Informed Neural Networks

arXiv:2607. 23940v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve differential equations by minimizing the residual of a nonlinear operator over a neural parameterization of the solution.

By Pavlos Protopapas, Kaylee Vo

safety

arXiv Machine Learning

Jun 16

Petrov-Galerkin Variational Physics-Informed Neural Network Framework for Two-Dimensional Singularly Perturbed Problems

arXiv:2606. 16510v1 Announce Type: cross Abstract: This study proposes a Petrov-Galerkin based Variational Physics-Informed Neural Network (VPINN) for efficiently solving two-dimensional singularly perturbed problems (SPPs) with one and two small perturbation parameters.

By Vijay Kumar, Gautam Singh

arXiv Machine Learning

Jun 18

TINNs: Time-Induced Neural Networks for Solving Time-Dependent PDEs

arXiv:2601. 20361v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time.

By Chen-Yang Dai, Che-Chia Chang, Te-Sheng Lin, Ming-Chih Lai, Chieh-Hsin Lai

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