arXiv Machine Learning

Structure-Preserving Physics-Informed Neural Network for the Korteweg--de Vries (KdV) Equation

arXiv:2511. 00418v2 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) offer a flexible framework for solving nonlinear partial differential equations (PDEs), yet conventional implementations often fail to preserve key physical invariants during long-term integration.

arXiv AI

Jun 3

Oscillatory State-Space Models as Inductive Biases for Physics-Informed Neural PDE Solvers

arXiv:2606. 02623v1 Announce Type: cross Abstract: Solving time-dependent partial differential equations (PDEs) is an important problem in computational science and engineering.

By Abhishek Chandra, Taniya Kapoor

arXiv Machine Learning

Jun 16

Manifold-Orthogonal Dual-spectrum Extrapolation for Parameterized Physics-Informed Neural Networks

arXiv:2603. 13751v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) have achieved notable success in modeling dynamical systems governed by partial differential equations (PDEs).

By Zhangyong Liang, Huanhuan Gao

diffusion fine-tuning multimodal benchmarks

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

Aug 4

Adaptive Quantum Physics-Informed Neural Networks for Differential Equations with Applications to Fluid Dynamics

arXiv:2608. 00850v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have emerged as a versatile approach for solving nonlinear partial differential equations (PDEs), yet achieving high accuracy efficiently using these techniques remains challenging for high-dimensional or multiscale systems.

By Fabio Pereira dos Santos, Renato Portugal, J\'ulio de Castro Vargas Fernandes, Lucas Timotheo Sanches

diffusion benchmarks safety

arXiv AI

Jul 10

Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning

arXiv:2601. 00473v4 Announce Type: replace-cross Abstract: We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms.

By Abhisek Ganguly, Santosh Ansumali, Sauro Succi

safety

arXiv AI

Jun 16

PH-KAN: Port-Hamiltonian Kolmogorov-Arnold Network

arXiv:2606. 14708v1 Announce Type: cross Abstract: Data-driven machine learning approaches have become increasingly attractive for nonlinear system identification, but standard models often fail to preserve the underlying physical structure and remain difficult to interpret, especially when no analytical model is available.

By Achraf El Messaoudi (UMLP, ENSMM, FEMTO-ST), Karim Cherifi (UMLP, ENSMM, FEMTO-ST), Yann Le Gorrec (UMLP, ENSMM, FEMTO-ST), Yongxin Wu (UMLP, ENSMM, FEMTO-ST)

arXiv AI

Jun 29

LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries

arXiv:2510. 25731v2 Announce Type: replace-cross Abstract: Initial-boundary value problems (IBVPs) provide the essential framework for modelling a wide range of phenomena in physics and engineering.

By Ren\'e P. Klausen, Ivan Timofeev, Jonas Naujoks, Johannes Frank, Thomas Wiegand, Sebastian Lapuschkin, Wojciech Samek

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 Machine Learning

Jun 11

HAMNO: A Hierarchical Adaptive Multi-scale Neural Operator with Physics-Informed Learning for Dynamical Systems

arXiv:2606. 11963v1 Announce Type: new Abstract: Neural operators provide a powerful framework for learning solution mappings of partial differential equations directly in function space.

By Mostafa Bamdad, Mohammad Sadegh Eshaghi, Timon Rabczuk

arXiv Machine Learning

Jul 23

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs

arXiv:2607. 20378v1 Announce Type: new Abstract: Physics-informed learning of partial differential equations (PDEs) has been dominated by multilayer perceptrons (MLPs), whose spectral bias and dense parameterization limit both accuracy and interpretability.

By Amirhossein Sadr, Nima Soltani, Vahideh Moghtadaiee, Aida Pakniyat, Dara Rahmati, Saeid Gorgin

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