Surrogate methods

PHYGRAV builds surrogates from high-fidelity tsunami and granular flow simulations using generalized Polynomial Chaos Expansions (gPCE) and sparse quadrature. This page summarizes the workflow and highlights model-specific notes.

gPCE Sparse grids Uncertainty quantification Validation

Surrogate pipeline

1) Inputs & sampling

Define stochastic inputs (e.g., slide volume, location) with independent priors. When data are sparse, uniform ranges follow the maximum-entropy principle.

nesting: Gauss–Patterson / delayed GP abscissas reused across orders

2) gPCE basis

Represent hazards ξ on Legendre polynomial bases for uniform priors: ξ̂(R)=Σ_{|α|≤p} ξα Ψα(R).

order p set for convergence Legendre ⇔ uniform priors

3) PSA fitting

Compute coefficients via pseudo-spectral approximation (Smolyak sparse grids), limiting the number of full simulations while retaining accuracy.

quadrature weights + nodes mitigates curse of dimensionality

4) Outputs & checks

Produce moments, sensitivities, and rapid scenario sweeps; validate against withheld simulations and publish standard outputs.

netCDF/maps targets ms-level evaluation

Models

Short summaries of the numerical cores used to generate training simulations.

Shaltop

Depth-averaged Savage–Hutter (Saint-Venant type) model for granular and fluid flows over complex topography, with multiple friction laws (Coulomb, Bingham, viscous).

equations: depth-averaged momentum + mass rheologies: Coulomb, μ(I), viscous

See Ressources/shaltop.tex for derivations, history, and validation cases.

LandslideTsurrogate

gPCE-based surrogate for landslide-generated tsunami hazards; calibrated on deterministic runs per zone with delayed Gauss–Patterson sampling.

quantity of interest: ξmax (elevation, speed, arrival) order p chosen to meet convergence targets

Source LaTeX: Ressources/tsurrogate.tex; includes sampling design and PSA details.

HySea (placeholder)

Numerical tsunami propagation and coastal impact solver; section to be expanded with equations and sampling once the draft is added.

status: to add equations/links bridge to surrogate training