This global collaboration between researchers from Tsinghua University, Bauhaus-Universität Weimar, Leibniz University Hannoverand Queensland University of Technology introduces AI4PDEs as a groundbreaking framework that bridges physics-based modeling with AI-driven methods. By consolidating state-of-the-art methodologies, the review explores diverse applications and outlines a roadmap for future research.
Core Methodologies:
- Physics-Informed Neural Networks (PINNs): Combining data and physical laws, PINNs solve forward and inverse problems, offering an efficient alternative to traditional methods.
- Operator Learning (OL): Techniques like Fourier Neural Operators (FNOs) model multiscale systems, reducing computational costs.
- Physics-Informed Neural Operators (PINO): Merging PINNs and OL, PINOs enhance predictions with greater accuracy and scalability.
Applications: AI4PDEs is transforming computational mechanics:
- Solid Mechanics
- Elasticity, elastoplasticity, hyperelasticity, fracture mechanics.
- Identification of material parameters, constitutive laws, topology optimization, and defect identification.
- Fluid Mechanics
- Hydrodynamics, aerodynamics, shock waves, multiphase flows, moving boundaries, and multiscale-multiphysics interactions.
- Field reconstruction and parameter estimation.
- Biomechanics
- Soft tissue deformation, blood flow, and morphogenesis.
- Modeling blood flow, material parameter identification in soft tissues, and protein structure prediction.
Challenges and Future Directions:
Despite its advancements, AI4PDEs faces challenges in handling sparse datasets, improving scalability, and integrating physical laws with AI models. The authors propose a collaborative approach, combining AI advancements with domain expertise to address these challenges.
This interdisciplinary work underscores the global significance of AI4PDEs and establishes it as a cornerstone for future computational mechanics research. To learn more, read the full review on arxiv.org/abs/2410.19843.
