LaSIPDE: Latent-Space PDE Identification from High-Dimensional Observations

A 1.1 MB PDF authored by Imane Koulali and last updated on 2026-04-14. The work presents a framework for discovering governing partial differential equations from indirect, high-dimensional measurements, validated on Burgers and Korteweg–de Vries systems.

Use Cases

• Discovering governing PDEs from high-dimensional observations based on the described latent-space identification framework.
• Validating model reduction techniques that preserve spatial structure, as demonstrated on Burgers and KdV systems.
• Benchmarking methods for identifying dynamical operators like diffusion and nonlinear advection from indirect data.
• Studying the theoretical equivalence of discovered equations to ground-truth systems under affine transformations.

Strengths

• Validated on canonical dynamical systems (Burgers and Korteweg–de Vries).
• Framework enables simultaneous model reduction and PDE discovery.
• Released under a permissive CC-BY-4.0 license.

Limitations

• The dataset is a 1.1 MB PDF; the underlying numerical data is not directly accessible.
• Row count and column-level documentation are unknown.
• Description metadata is limited; actual data quality requires manual inspection after download.

Provenance

Source

figshare

Collection Method

Likely contains results from computational experiments for validating the proposed PDE discovery framework.

Freshness

Last updated 2026-04-14 04:14:22; freshness should be verified.