arXiv AI June 3, 2026 By Aleksander Krasowski, Jonas R. Naujoks, Moritz Weckbecker, Galip \"U. Yolcu, Thomas Wiegand, Sebastian Lapuschkin, Wojciech Samek, Ren\'e P. Klausen

PINNfluence: Interpreting PINNs through Influence Functions

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arXiv:2409. 08958v3 Announce Type: replace-cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful deep learning approach for solving partial differential equations (PDEs) in the physical sciences, yet their behavior remains largely opaque and is typically understood through failure mode analyses rather than explicit interpretability.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

arXiv AI

Jul 17

LIGO-PINN: Learned Initialization via Gated Optimization to Alleviate Convergence Failures in Physics Informed Neural Networks

arXiv:2607. 14233v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have had a broad research impact in modeling domains governed by partial differential equations (PDE).

By Nilay Anurag, Shital Adhikari, Taniya Kapoor, Nikhil Muralidhar

benchmarks

arXiv AI

Sep 17

Enhancing Physics-Informed Neural Networks with Domain-aware Fourier Features: Towards Improved Performance and Interpretable Results

The paper proposes Domain-aware Fourier Features (DaFFs) for Physics-Informed Neural Networks (PINNs), embedding domain-specific geometry and boundary conditions into the positional encoding. DaFFs eliminate the need for explicit boundary loss terms, simplify optimization, and reduce training cost, leading to orders-of-magnitude lower errors and faster convergence compared to vanilla PINNs and RFF-based PINNs. An LRP-based explainability framework further shows that DaFFs produce more physically consistent relevance attributions, improving interpretability.

By Alberto Mi\~no Calero, Luis Salamanca, Konstantinos E. Tatsis

rag safety

arXiv Machine Learning

Sep 15

A derivative-fidelity failure mode in physics-informed neural networks: strengthened benchmark evidence from function-value training

arXiv:2609.13171v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) use automatic differentiation to impose differential-equation residuals, but good agreement in function values...

By Koji Koyamada

benchmarks

arXiv Machine Learning

4d ago

CI-PINN: Causal Integral Physics-Informed Neural Network for Solving Evolution Equations

arXiv:2609.36615v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) solve partial differential equations (PDEs) by incorporating governing physical laws into the training loss....

By Xiaodong Feng, Ziyu Sun, Tao Tang, Xiaoliang Wan, Tao Zhou

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

Aug 11

ProPINN: Demystifying Propagation Failures in Physics-Informed Neural Networks

arXiv:2502. 00803v3 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) have earned high expectations in solving partial differential equations (PDEs), but their optimization usually faces thorny challenges due to the unique derivative-dependent loss function.

By Yuezhou Ma, Haixu Wu, Hang Zhou, Huikun Weng, Jianmin Wang, Mingsheng Long

llms

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LIGO-PINN: Learned Initialization via Gated Optimization to Alleviate Convergence Failures in Physics Informed Neural Networks

Enhancing Physics-Informed Neural Networks with Domain-aware Fourier Features: Towards Improved Performance and Interpretable Results

A derivative-fidelity failure mode in physics-informed neural networks: strengthened benchmark evidence from function-value training

CI-PINN: Causal Integral Physics-Informed Neural Network for Solving Evolution Equations

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

ProPINN: Demystifying Propagation Failures in Physics-Informed Neural Networks