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
Jun 29

Mosaic: A Benchmark Suite for Differentiable Physics Solvers

arXiv:2606. 27895v1 Announce Type: cross Abstract: Differentiable partial differential equation (PDE) solvers underpin solver-in-the-loop ML training, gradient-based optimal control, and inverse problems, yet the practical cost of obtaining correct, usable gradients from a given solver on a given problem is largely undocumented.

By Andrin Rehmann, Heiko Zimmermann, Dion H\"afner
Hugging Face Trending Papers
Jul 8

Neural Operator-enabled Topology-informed Evolutionary Strategy for PDE-Constrained Optimization

The inverse design of physical systems governed by partial differential equations is computationally demanding due to the high dimensionality and non-convexity of design spaces. Generative models for inverse design often lack robustness and transferability, whereas evolutionary strategies are robust but struggle in high-dimensional spaces.