arXiv:2607. 14563v1 Announce Type: new Abstract: Estimating spatially heterogeneous elastic properties from low-resolution displacement measurements is a severely ill-posed inverse elasticity problem because low resolution obscures spatial details needed to distinguish heterogeneous property variations, and small measurement perturbations or fitting errors are amplified through inverse estimation.
By Tatthapong Srikitrungruang, Jaesung Lee
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.
By Qian Hu, Bin Fan, Yao Xiao, Zhicheng Lin, Meixin Xiong
arXiv:2606. 11258v1 Announce Type: new Abstract: Gradient-based inversion of reaction-diffusion systems is typically approached via surrogate models or physics-informed neural networks (PINNs), while the most direct route, backpropagation through the PDE's structure itself, has largely been avoided.
By Yan Yang
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
arXiv:2606. 27354v1 Announce Type: cross Abstract: Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution.
By Haina Jiang, Liam Wang, Peng-Chen Chen, Min Seop Kwak, Seungryong Kim, Brian Bell, Jeong Joon Park
arXiv:2606. 25151v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) embed governing equations in their loss function, enabling mesh-free solutions to partial differential equations.
By David McShannon, Nicholas Dietrich
arXiv:2606. 02475v1 Announce Type: cross Abstract: Classical finite-difference solvers remain reliable tools for partial differential equations, but their efficiency depends on where mesh resolution is placed.
By Henry Kasumba, Ronald Katende
arXiv:2512. 08499v3 Announce Type: replace-cross Abstract: Development of reliable and physically interpretable probabilistic frameworks for industrial prognostics remain nascent, and existing literature is often insensitive as inputs move away from the training manifold.
By Waleed Razzaq, Yun-Bo Zhao
arXiv:2608. 15483v1 Announce Type: new Abstract: Modern deep networks are trained through long update trajectories, yet their temporal organization remains less systematically characterized than architectures, losses, or optimizers.
By Fanqi Wang, Weisheng Tang, Hairong Qi
arXiv:2606. 07153v1 Announce Type: cross Abstract: Physics-informed learning is increasingly used for partial differential equation (PDE)-governed inverse problems, but its reliability remains difficult to certify.
By Ronald Katende
arXiv:2606. 12050v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) combine machine learning with physical laws to solve differential equations.
By Ismail Huseynov, Arzu Ahmadova, Agamirza Bashirov
arXiv:2604. 01313v2 Announce Type: replace Abstract: High-fidelity simulations and complex inverse problems, such as detector modeling and unfolding, are computationally intensive bottlenecks across subatomic physics, yet essential for accurate physical interpretation.
By Zeyu Xia, Tyler Kim, Trevor Reed, Judy Fox, Geoffrey Fox, Adam Szczepaniak