arXiv Machine Learning By Qian Hu, Bin Fan, Yao Xiao, Zhicheng Lin, Meixin Xiong

Target-Guided Selective Reweighting for Physics-Informed Neural Network Inverse Problems: A Transfer Learning Approach

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arXiv:2607. 05271v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) encounter ill-posed optimization, loss competition, and parameter compensation in partial differential equation (PDE) inverse problems.

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arXiv Machine Learning
Sep 18

Amortizing Physics-Informed Neural Solvers via Graph Hypernetworks

The paper introduces a method to amortize physics-informed neural networks (PINNs) across related partial differential equations (PDEs) by explicitly modeling equation relationships in an operator graph. Coefficient vectors encode numerical parameters, while the graph hypernetwork generates diagonal codes that initialize a meta‑trained factorized PINN for each target equation. Experiments on scalar convection‑diffusion‑reaction, two‑field Fisher‑KPP, and a capacitively coupled plasma model show that term‑based descriptors and graph conditioning improve solution accuracy compared to coefficient‑vector conditioning, especially for high‑reaction and coupled systems.

By Cheng Jing, Abhishek Verma, Kallol Bera, Yixuan He, Kookjin Lee
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
arXiv Machine Learning
Sep 15

Linearized PINN with pretrained nonlinear layers

The paper introduces a linearized Physics-Informed Neural Network (lPINN), a reduced‑order neural basis approach for solving forward and inverse differential equations. In an offline phase, lPINN learns continuous, differentiable neural basis functions from numerical solutions, which are then frozen for new problem instances; the online solution is obtained by minimizing the governing‑equation residual with additional constraints. Experiments on advection‑diffusion, Burgers', and nonlinear pendulum equations show that lPINN achieves lower solution and parameter errors than vanilla PINNs while reducing online inference times by up to three orders of magnitude, and its continuous representation generalizes to finer meshes without retraining.

By Wenhao Chen, Alexandre M. Tartakovsky