SPDE (spatial fields) — experimental

SFI extends stochastic force inference to spatial field data governed by stochastic partial differential equations (SPDEs). The SPDE toolbox provides composable finite-difference operators, grid-aware noise models, and integration with the standard SFI inference pipeline.

Experimental

The SPDE toolbox is functional but experimental in this release: its API may change, and only the linear estimators (infer_force_linear(), infer_diffusion_linear()) are validated on grid layouts.

• Spatial field inference (SPDE)
  • Conceptual picture
  • Composable operators
  • Noise models
  • Step-by-step example: 1D stochastic heat equation
  • Multi-field example: reaction-diffusion
  • Active nematic example
  • Extending the operator catalogue
• Structured fields: Layout, Sectors, and Embed
  • Why layouts?
  • The two-world architecture
  • Sectors
  • GridLayout: differential operators on regular grids
  • Example: Gray-Scott reaction-diffusion
  • Example: active nematic Q-tensor
  • Symmetry-based layouts beyond SPDEs
  • The stencil composition engine
  • Extras and grid setup