fluid_stats.py

#!/usr/bin/env python3
"""
Compute energy spectra from vorticity field data.

This script loads vorticity trajectory data from a .npy file and computes
the azimuthally averaged energy spectrum E(k). It outputs both the spectrum
data as a .npz file and a visualization plot as a .png file.

To run direct numerical simulations and get fluid fields, please use Jax-CFD: https://github.com/google/jax-cfd
Commit hash we used: 0c17e3855702f884265b97bd6ff0793c34f3155e

Usage:
    uv run python fluid_stats.py path/to/vorticity.npy --out_dir results/
"""

import argparse
import logging
import os
from functools import partial

import jax
import jax.numpy as jnp
import matplotlib.pyplot as plt
import numpy as np
from jax import jit, vmap
from tqdm import tqdm

# Configure logging
logging.basicConfig(
    level=logging.INFO,
    format="%(asctime)s - %(levelname)s - %(message)s",
    datefmt="%Y-%m-%d %H:%M:%S",
)
logger = logging.getLogger(__name__)


# =============================================================================
# Core computation functions
# =============================================================================


@jit
def vorticity_to_velocity(vorticity):
    """
    Convert vorticity to velocity components using the streamfunction.

    Solves the Poisson equation in Fourier space: psi_hat = -vorticity_hat / k^2
    Then computes velocity from streamfunction: u_x = -d(psi)/dy, u_y = d(psi)/dx

    Parameters
    ----------
    vorticity : jnp.ndarray, shape (X, Y)
        2D vorticity field on a square grid.

    Returns
    -------
    u_x : jnp.ndarray, shape (X, Y)
        x-component of velocity.
    u_y : jnp.ndarray, shape (X, Y)
        y-component of velocity.
    """
    N = vorticity.shape[0]

    # Compute streamfunction from vorticity using Poisson equation
    # In Fourier space: psi_hat = -vorticity_hat / k^2
    vort_hat = jnp.fft.fft2(vorticity)

    # Create wavenumber arrays
    kx = jnp.fft.fftfreq(N, d=1.0) * 2 * jnp.pi
    ky = jnp.fft.fftfreq(N, d=1.0) * 2 * jnp.pi
    KX, KY = jnp.meshgrid(kx, ky, indexing="ij")
    K2 = KX**2 + KY**2

    # Avoid division by zero at k=0
    K2 = K2.at[0, 0].set(1.0)
    psi_hat = -vort_hat / K2
    psi_hat = psi_hat.at[0, 0].set(0.0)  # Set mean streamfunction to zero

    # Compute velocity components from streamfunction
    # u_x = -d(psi)/dy, u_y = d(psi)/dx
    u_x_hat = -1j * KY * psi_hat
    u_y_hat = 1j * KX * psi_hat

    u_x = jnp.real(jnp.fft.ifft2(u_x_hat))
    u_y = jnp.real(jnp.fft.ifft2(u_y_hat))

    return u_x, u_y


@partial(jit, static_argnames=["k_max"])
def energy_spectrum_single(u_x, u_y, k_max=None):
    """
    Compute azimuthally averaged energy spectrum E(k) for a single velocity field.

    The energy spectrum is computed by binning the 2D Fourier-transformed
    velocity field by wavenumber magnitude |k|.

    Parameters
    ----------
    u_x : jnp.ndarray, shape (X, Y)
        x-component of velocity.
    u_y : jnp.ndarray, shape (X, Y)
        y-component of velocity.
    k_max : int, optional
        Maximum wavenumber to compute. If None, uses N//3 (2/3 dealiasing rule).

    Returns
    -------
    E : jnp.ndarray, shape (k_max+1,)
        Energy spectrum E(k) for k = 0, 1, ..., k_max.
    """
    N = u_x.shape[0]

    # FFT, shifted so k=0 is at centre
    Ux = jnp.fft.fftshift(jnp.fft.fft2(u_x))
    Ux = Ux / (N**2)
    Uy = jnp.fft.fftshift(jnp.fft.fft2(u_y))
    Uy = Uy / (N**2)

    # Integer wave numbers
    kx = jnp.fft.fftshift(jnp.fft.fftfreq(N)) * N
    ky = kx
    KX, KY = jnp.meshgrid(kx, ky)
    K = jnp.hypot(KX, KY).astype(jnp.int32)

    if k_max is None:  # Nyquist under 2/3 de-alias
        k_max = N // 3

    # Vectorized computation of energy spectrum
    def compute_E_k(k):
        mask = K == k
        return 0.5 * jnp.sum(jnp.abs(Ux) ** 2 * mask + jnp.abs(Uy) ** 2 * mask)

    k_vals = jnp.arange(k_max + 1)
    E = vmap(compute_E_k)(k_vals)

    return E


@partial(jit, static_argnames=["k_max"])
def energy_spectrum_from_vorticity(vorticity, k_max=None):
    """
    Compute energy spectrum from vorticity field using vmap.

    Suitable for moderate resolution fields (up to ~1024x1024).
    For larger resolutions, use energy_spectrum_from_vorticity_lax_map.

    Parameters
    ----------
    vorticity : jnp.ndarray, shape (T, X, Y)
        Vorticity field over T time steps on an X x Y grid.
    k_max : int, optional
        Maximum wavenumber. If None, uses N//3 (2/3 dealiasing rule).

    Returns
    -------
    E : jnp.ndarray, shape (T, k_max+1)
        Energy spectrum for each time step.
    """
    N = vorticity.shape[1]

    if k_max is None:
        k_max = N // 3

    def process_timestep(vort_t):
        u_x, u_y = vorticity_to_velocity(vort_t)
        return energy_spectrum_single(u_x, u_y, k_max)

    # Vectorize over time dimension
    E = vmap(process_timestep)(vorticity)

    return E


@partial(jit, static_argnames=["k_max", "batch_size"])
def energy_spectrum_from_vorticity_lax_map(vorticity, k_max=None, batch_size=16):
    """
    Compute energy spectrum from vorticity field using jax.lax.map.

    Memory-efficient version suitable for high resolution fields (>1024x1024).
    Processes timesteps sequentially to reduce memory footprint.

    Parameters
    ----------
    vorticity : jnp.ndarray, shape (T, X, Y)
        Vorticity field over T time steps on an X x Y grid.
    k_max : int, optional
        Maximum wavenumber. If None, uses N//3 (2/3 dealiasing rule).
    batch_size : int, optional
        Batch size for lax.map processing. Default is 16.

    Returns
    -------
    E : jnp.ndarray, shape (T, k_max+1)
        Energy spectrum for each time step.
    """
    N = vorticity.shape[1]

    if k_max is None:
        k_max = N // 3

    def process_timestep(vort_t):
        u_x, u_y = vorticity_to_velocity(vort_t)
        return energy_spectrum_single(u_x, u_y, k_max)

    # Use lax.map instead of vmap for memory efficiency
    E = jax.lax.map(process_timestep, vorticity, batch_size=batch_size)

    return E


# =============================================================================
# Main script
# =============================================================================


def parse_args():
    """Parse command line arguments."""
    parser = argparse.ArgumentParser(
        description=(
            "Compute energy spectra from 2D vorticity trajectory data. "
            "Loads vorticity fields from a .npy file, computes the azimuthally "
            "averaged energy spectrum E(k), and saves both the spectrum data "
            "and a visualization plot."
        ),
        formatter_class=argparse.RawDescriptionHelpFormatter,
        epilog="""
Examples:
    uv run python fluid_stats.py simulation.npy
    uv run python fluid_stats.py data/vorticity.npy --out_dir results/

Input format:
    The input .npy file should contain a 4D array with shape (batch, time, X, Y)
    where batch is the number of independent trajectories, time is the number
    of snapshots, and X, Y are the spatial grid dimensions.
        """,
    )

    parser.add_argument(
        "input_file",
        type=str,
        help=(
            "Path to the input .npy file containing vorticity data. "
            "Expected shape: (batch, time, X, Y) where X and Y are the "
            "spatial grid dimensions (must be square, i.e., X == Y)."
        ),
    )

    parser.add_argument(
        "--out_dir",
        type=str,
        default=".",
        help=(
            "Directory to save output files. Will be created if it does not "
            "exist. Output files are named based on the input filename. "
            "Default: current directory."
        ),
    )

    return parser.parse_args()


def main():
    """Main entry point for energy spectrum computation."""
    args = parse_args()

    # Setup
    logger.info("JAX devices: %s", jax.devices())

    # Validate input file
    if not os.path.exists(args.input_file):
        logger.error("Input file not found: %s", args.input_file)
        raise FileNotFoundError(f"Input file not found: {args.input_file}")

    if not args.input_file.endswith(".npy"):
        logger.warning(
            "Input file does not have .npy extension: %s", args.input_file
        )

    # Create output directory
    os.makedirs(args.out_dir, exist_ok=True)

    # Generate output filenames from input filename
    input_basename = os.path.splitext(os.path.basename(args.input_file))[0]
    data_filename = f"{input_basename}_spectrum_data.npz"
    plot_filename = f"{input_basename}_spectrum.png"
    data_path = os.path.join(args.out_dir, data_filename)
    plot_path = os.path.join(args.out_dir, plot_filename)

    # Load data
    logger.info("Loading data from: %s", args.input_file)
    field = np.load(args.input_file)
    logger.info("Loaded field with shape: %s", field.shape)

    # Validate shape
    if field.ndim != 4:
        logger.error(
            "Expected 4D array (batch, time, X, Y), got %dD array", field.ndim
        )
        raise ValueError(
            f"Expected 4D array (batch, time, X, Y), got {field.ndim}D array"
        )

    batch_size, time_steps, height, width = field.shape
    if height != width:
        logger.error(
            "Expected square spatial grid (X == Y), got %d x %d", height, width
        )
        raise ValueError(
            f"Expected square spatial grid (X == Y), got {height} x {width}"
        )

    resolution = height
    k_max = resolution // 3
    logger.info(
        "Processing %d trajectories with %d timesteps at %dx%d resolution",
        batch_size,
        time_steps,
        resolution,
        resolution,
    )
    logger.info("Maximum wavenumber (k_max): %d", k_max)

    # Compute energy spectrum
    logger.info("Computing energy spectra...")
    spectra_list = []

    for i in tqdm(range(batch_size), desc="Computing spectra"):
        if resolution > 1024:
            # Use memory-efficient lax.map for large resolutions
            single_spectrum = energy_spectrum_from_vorticity_lax_map(
                field[i], k_max
            )
        else:
            # Use vmap for moderate resolutions
            single_spectrum = energy_spectrum_from_vorticity(field[i], k_max)
        spectra_list.append(single_spectrum)

    # Stack all spectra
    all_spectra = jnp.stack(spectra_list)
    logger.info("All spectra shape: %s", all_spectra.shape)

    # Compute mean spectrum (over batch and time)
    mean_spectrum = all_spectra.reshape(-1, all_spectra.shape[-1]).mean(axis=0)
    logger.info("Mean spectrum shape: %s", mean_spectrum.shape)

    # Save spectrum data
    logger.info("Saving spectrum data to: %s", data_path)
    np.savez_compressed(
        data_path,
        mean_spectrum=np.array(mean_spectrum),
        all_spectra=np.array(all_spectra),
        k_values=np.arange(len(mean_spectrum)),
        resolution=resolution,
        batch_size=batch_size,
        time_steps=time_steps,
    )

    # Generate plot
    logger.info("Generating energy spectrum plot...")
    plt.figure(figsize=(10, 6))

    # Plot mean spectrum (skip k=0)
    offset = 1
    spectrum = mean_spectrum[offset:]
    k_values = np.arange(offset, len(mean_spectrum))
    plt.loglog(k_values, spectrum, "b-", linewidth=2, label="Mean spectrum")

    # Add k^{-5/3} reference line (Kolmogorov scaling for 3D turbulence)
    # and k^{-3} reference line (enstrophy cascade in 2D turbulence)
    k_match = min(10, len(spectrum) // 3)
    if k_match > 0:
        ref_value = float(spectrum[k_match - 1])

        # k^{-3} line (2D enstrophy cascade)
        scaling_k3 = ref_value * (k_match**3)
        k_theory = np.logspace(0, np.log10(len(mean_spectrum)), 100)
        power_law_k3 = scaling_k3 * k_theory ** (-3)
        plt.loglog(
            k_theory,
            power_law_k3,
            "k--",
            alpha=0.7,
            linewidth=1.5,
            label=r"$k^{-3}$ (enstrophy cascade)",
        )

        # k^{-5/3} line (inverse energy cascade)
        scaling_k53 = ref_value * (k_match ** (5 / 3))
        power_law_k53 = scaling_k53 * k_theory ** (-5 / 3)
        plt.loglog(
            k_theory,
            power_law_k53,
            "r--",
            alpha=0.7,
            linewidth=1.5,
            label=r"$k^{-5/3}$ (energy cascade)",
        )

    plt.xlabel("Wavenumber k", fontsize=12)
    plt.ylabel("Energy Spectrum E(k)", fontsize=12)
    plt.title(f"Energy Spectrum ({resolution}x{resolution} resolution)", fontsize=14)
    plt.legend()
    plt.grid(True, alpha=0.3)
    xlim = plt.xlim()
    plt.xlim(1, xlim[1])
    plt.tight_layout()

    # Save plot
    plt.savefig(plot_path, dpi=300, bbox_inches="tight")
    plt.close()
    logger.info("Plot saved to: %s", plot_path)

    logger.info("Done!")


if __name__ == "__main__":
    main()