Add dataset augmentation and reduction utilities for SINDY workflow

[ChrisRackauckas-Claude]

Summary

This PR implements the feature requested in #332, adding dataset augmentation and reduction utilities to automate the SINDY workflow:

New Functions

1. delay_embedding(X, num_delays; τ=1) - Create time-delay coordinates from data

   • Supports both vector and matrix inputs
   • Configurable delay interval τ
   • Useful for Takens' embedding theorem and HAVOK analysis

2. hankel_matrix(x, num_rows) - Build Hankel matrices from 1D time series

   • Enables Hankel DMD and related methods
   • Standard format for time-delay analysis

3. truncated_svd(X, rank) - Compute truncated singular value decomposition

   • Returns named tuple with U, S, V truncated to specified rank
   • Building block for dimension reduction

4. reduce_dimension(X, rank) - Project data onto top singular vectors

   • Manual rank specification
   • reduce_dimension(X) - Automatic rank selection using optimal threshold

Use Case: HAVOK Analysis

These utilities enable HAVOK-style workflows:

using DataDrivenDiffEq

# Embed scalar time series using delay coordinates
x = lorenz_solution[1, :]  # Scalar measurement
H = hankel_matrix(x, 100)  # Build Hankel matrix

# Reduce dimension via SVD
X_reduced = reduce_dimension(H, 15)  # Keep top 15 modes

# Create problem with embedded coordinates
prob = DiscreteDataDrivenProblem(X_reduced)

# Discover dynamics with SINDY
# ... (use DataDrivenSparse)

References

• Brunton et al. (2017) "Chaos as an intermittently forced linear system" https://doi.org/10.1038/s41467-017-00030-8
• Arbabi & Mezic (2017) "Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the Koopman operator"

Testing

All existing tests pass plus new tests for:

• Hankel matrix construction and structure
• Delay embedding dimensions and correctness
• Truncated SVD accuracy
• Dimension reduction behavior

Fixes #332

cc @ChrisRackauckas

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