Loss Landscape Geometry of Partial Differential Equation Emulators: Or, Symmetry Learning via Gradient Alignment
cs.LG, physics.comp-ph
Submitted: 2026-01-28
Updated: 2026-08-25
Code: https://github.com/aai-institute/pyDVL
Terminology
Sources
- A Closer Look at Memorization in Deep Networks
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- Lie Point Symmetry and Physics Informed Networks
- Steerable CNNs
- Don't Unroll Adjoint: Differentiating SSA-Form Programs
- Neural Tangent Kernel: Convergence and Generalization in Neural Networks
- Residual Pathway Priors for Soft Equivariance Constraints
- Emergent properties of the local geometry of neural loss landscapes
- Understanding Black-box Predictions via Influence Functions
- Stiffness: A New Perspective on Generalization in Neural Networks
- PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers
- Equivariant geometric convolutions for emulation of dynamical systems
- The Lie Derivative for Measuring Learned Equivariance
- Towards Multi-spatiotemporal-scale Generalized PDE Modeling
- Optimizing Neural Networks with Kronecker-factored Approximate Curvature
- ClimaX: A foundation model for weather and climate
- The Local Elasticity of Neural Networks
- Poseidon: Efficient Foundation Models for PDEs
- Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
- Approximately Equivariant Networks for Imperfectly Symmetric Dynamics
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