PDEInvBench: A Comprehensive Dataset and Design Space Exploration of Neural Networks for PDE Inverse Problems
Researchers are exploring novel neural network architectures and training methodologies to enhance the solution of complex differential equations. Papers introduce reformulated neural operators that incorporate an auxiliary function dimension for improved embedding evolution, and branched neural rough differential equations that offer a unified framework for stochastic and manifold-valued dynamics. Other work focuses on physics-informed neural operators (PINOs), examining training pipelines for efficiency and robustness, and proposing curvature-aware dynamic precision approaches to balance computational cost and accuracy. AI
IMPACT Advances in neural operator and physics-informed network training offer more efficient and accurate solutions for complex scientific simulations.
- Neural Networks
- Physics-informed neural networks
- Fourier Neural Operator
- Holomorphic neural networks
- Denoising Diffusion Implicit Model
- MeanFlow-Enhanced Neural Operators
- Multi-Scale Separable Fourier Neural Networks
- Circuit-inspired High-Order Neural Networks
- Zhangyong Liang
- Nikolaus Vertovec
- DeepONet
- Neural Operators
- Physics-informed neural operators
- Continuous Vision Transformer
- Branched Neural Rough Differential Equations
- Haoze Song