arXiv AI July 10, 2026 By Abhisek Ganguly, Santosh Ansumali, Sauro Succi

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.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv AI.

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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 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 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 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 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

Jun 11

Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems

arXiv:2606. 12337v1 Announce Type: cross Abstract: Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-informed neural networks (PINNs) have emerged as a flexible alternative.

By Zhen Zhang, Alessandro Alla, George Em Karniadakis

benchmarks

Related stories

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

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

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

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

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

Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems