Equivariant Neural Eikonal Solvers for Scalable Travel-Time Prediction
A new framework called Equivariant Neural Eikonal Solvers has been developed by researchers, merging Equivariant Neural Fields (ENFs) with Neural Eikonal Solvers. This approach utilizes a singular neural field that relies on a common backbone, conditioned by signal-specific latent variables depicted as point clouds within a Lie group. The integration of ENFs guarantees an equivariant mapping from latent representations to the solution field, enhancing representation efficiency through weight-sharing, strong geometric grounding, and solution steerability. This steerability allows for transformations in the latent point cloud to create predictable and meaningful changes in the Eikonal solution. By combining these steerable representations with Physics-Informed Neural Networks (PINNs), the framework accurately models Eikonal travel-time solutions while maintaining generalization across homogeneous spaces. It is grid-free and scalable, overcoming the constraints of conventional grid-based techniques. The research is documented in a paper available on arXiv under identifier 2505.16035.
Key facts
- Framework integrates Equivariant Neural Fields with Neural Eikonal Solvers.
- Uses a single neural field with shared backbone conditioned on latent variables.
- Latent variables are represented as point clouds in a Lie group.
- Equivariant mapping ensures weight-sharing, geometric grounding, and steerability.
- Steerability enables predictable modifications to solutions via latent transformations.
- Coupled with Physics-Informed Neural Networks for accurate travel-time modeling.
- Grid-free and scalable approach for homogeneous spaces.
- Published on arXiv with ID 2505.16035.
Entities
Institutions
- arXiv