arXiv Machine Learning

Hierarchical rank-evolving representation for physics-informed neural networks

arXiv:2608. 09483v1 Announce Type: new Abstract: Recently, tensor-based physics-informed neural networks (T-PINNs) have received increasing attention.

arXiv Machine Learning

Aug 3

Feature Interaction Modeling for Physics-Informed Neural Networks and Neural Operators

arXiv:2607. 28762v1 Announce Type: new Abstract: This work embeds feature interaction modules derived from factorization machines (FMs) into physics-informed neural networks (PINNs) and neural operator learning, to enhance model expressiveness for solution manifolds of parameterized partial differential equations (PDEs).

By Quan Gu, Hongxia Liu

benchmarks

arXiv Machine Learning

Jul 9

Tensor Train Diffusion: Leveraging Low-Rank Structures for High-Dimensional Score-Based Sampling

arXiv:2607. 06841v1 Announce Type: cross Abstract: Diffusion models offer a powerful framework for sampling from complex probability densities by learning to reverse a noising process.

By Robert Gruhlke, Julius Berner, David Sommer, Lorenz Richter

diffusion efficiency

arXiv Machine Learning

23h ago

Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements

arXiv:2509. 00203v3 Announce Type: replace Abstract: Parameterized partial differential equations (PDEs) underpin the mathematical modeling of complex systems in diverse domains, including engineering, healthcare, and physics.

By Xuyang Li, Mahdi Masmoudi, Rami Gharbi, Nizar Lajnef, Vishnu Naresh Boddeti

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 AI

Jul 15

Deep Learning-based Surrogate Modelling of the LOD Method for Multiscale Problems

arXiv:2607. 12570v1 Announce Type: cross Abstract: Multiscale problems are notoriously difficult to tackle using traditional numerical methods, as accurately resolving fine-scale features often requires prohibitively fine discretizations.

By Marc Haltmayer, Jaemin Seo, Yuseung Lee, Sungyeop Lee, Jaehoon Jeong, Jae Yong Lee

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

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 27

Latent PDE mapping for efficient physics-informed learning across geometries with limited data

arXiv:2607. 22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data.

By Ingvild Askim Adde, Mary M. Maleckar, Gabriel Balaban

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 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 AI

Jul 16

Spectral-Informed Neural Networks Outperform Spectral Methods in High-dimensional PDEs

arXiv:2607. 13566v1 Announce Type: cross Abstract: For low-dimensional problems ($d\leq3$), spectral methods can achieve exceptionally high accuracy.

By Tianchi Yu, Ivan Oseledets

rag

arXiv Machine Learning

Jul 20

A Physics-Informed Neural Network with a Modified Lorentzian Activation for Nonlocal Gradient-Flow Equations in Dynamic Density Functional Theory

arXiv:2607. 15291v1 Announce Type: cross Abstract: We develop a physics-informed neural network (PINN) framework for nonlocal partial differential equations arising in dynamic density functional theory (DDFT).

By Dimitrios Gourzoulidis, Soumaya Elkantassi, Serafim Kalliadasis

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