partial differential equations
Partial differential equations (PDEs) are equations that involve the rates of change of a quantity with respect to multiple variables. In AI, PDEs can be used to model various phenomena in physics and engineering, allowing researchers to incorporate physical laws into machine learning models, particularly in physics-informed neural networks.
- A Plug-and-Play Query Synthesis Active Learning Framework for Neural PDE Solvers
- AneuG-Flow: A Large-Scale Synthetic Dataset of Diverse Intracranial Aneurysm Geometries and Hemodynamics
- Axial Neural Networks for Dimension-Free Foundation Models
- Boundary-Value PDEs Meet Higher-Order Differential Topology-aware GNNs
- CALM-PDE: Continuous and Adaptive Convolutions for Latent Space Modeling of Time-dependent PDEs
- Collapsing Taylor Mode Automatic Differentiation
- Continuous Simplicial Neural Networks
- Hybrid Boundary Physics-Informed Neural Networks for Solving Navier-Stokes Equations with Complex Boundary
- Light-Weight Diffusion Multiplier and Uncertainty Quantification for Fourier Neural Operators
- Mitigating Instability in High Residual Adaptive Sampling for PINNs via Langevin Dynamics
- Neuro-Spectral Architectures for Causal Physics-Informed Networks
- PINN Balls: Scaling Second-Order Methods for PINNs with Domain Decomposition and Adaptive Sampling
- PINNs with Learnable Quadrature
- Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints
- Revisiting Orbital Minimization Method for Neural Operator Decomposition
- Solving Partial Differential Equations via Radon Neural Operator
- Solving and Learning Partial Differential Equations with Variational Q-Exponential Processes
- SpiderSolver: A Geometry-Aware Transformer for Solving PDEs on Complex Geometries
- Thompson Sampling in Function Spaces via Neural Operators
- UGM2N: An Unsupervised and Generalizable Mesh Movement Network via M-Uniform Loss