.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/dynamics/06_fire_optimization.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_dynamics_06_fire_optimization.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_dynamics_06_fire_optimization.py:


FIRE Geometry Optimization (LJ Cluster)
======================================

This example demonstrates geometry optimization with the FIRE optimizer using:
- The **package LJ implementation** (neighbor-list accelerated)
- The **package FIRE kernels** (:mod:`nvalchemiops.dynamics.optimizers`)
- The shared example utilities in :mod:`examples.dynamics._dynamics_utils`

We optimize a small Lennard-Jones cluster (an isolated cluster inside a large box)
and plot convergence (energy and max force).

.. GENERATED FROM PYTHON SOURCE LINES 28-43

.. code-block:: Python


    from __future__ import annotations

    import matplotlib.pyplot as plt
    import numpy as np
    import warp as wp
    from _dynamics_utils import MDSystem, create_random_cluster

    from nvalchemiops.dynamics.optimizers import fire_step

    wp.init()

    device = "cuda:0" if wp.is_cuda_available() else "cpu"
    print(f"Using device: {device}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Using device: cuda:0




.. GENERATED FROM PYTHON SOURCE LINES 44-49

Create a Lennard-Jones Cluster
------------------------------

We use an "isolated cluster in a large box" approach (PBC far away),
which works well with the existing neighbor-list machinery.

.. GENERATED FROM PYTHON SOURCE LINES 49-79

.. code-block:: Python


    num_atoms = 32
    epsilon = 0.0104  # eV (argon-like)
    sigma = 3.40  # Å
    cutoff = 2.5 * sigma
    skin = 0.5
    box_L = 80.0  # Å (large to avoid self-interaction across PBC)

    cell = np.eye(3, dtype=np.float64) * box_L
    initial_positions = create_random_cluster(
        num_atoms=num_atoms,
        radius=12.0,
        min_dist=0.9 * sigma,
        center=np.array([0.5 * box_L, 0.5 * box_L, 0.5 * box_L]),
        seed=42,
    )

    system = MDSystem(
        positions=initial_positions,
        cell=cell,
        masses=np.full(num_atoms, 39.948, dtype=np.float64),  # amu (argon)
        epsilon=epsilon,
        sigma=sigma,
        cutoff=cutoff,
        skin=skin,
        switch_width=0.0,
        device=device,
        dtype=np.float64,
    )





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Initialized MD system with 32 atoms
      Cell: 80.00 x 80.00 x 80.00 Å
      Cutoff: 8.50 Å (+ 0.50 Å skin)
      LJ: ε = 0.0104 eV, σ = 3.40 Å
      Device: cuda:0, dtype: <class 'numpy.float64'>
      Units: x [Å], t [fs], E [eV], m [eV·fs²/Ų] (from amu), v [Å/fs]




.. GENERATED FROM PYTHON SOURCE LINES 80-88

FIRE Optimization Loop
----------------------

We use the unified ``fire_step`` API that handles:
- Velocity mixing (FIRE algorithm)
- Adaptive timestep (dt)
- Adaptive mixing parameter (alpha)
- MD-like position update with maxstep capping

.. GENERATED FROM PYTHON SOURCE LINES 88-194

.. code-block:: Python


    max_steps = 3000
    force_tolerance = 1e-3  # eV/Å (max force)

    # FIRE parameters
    dt0 = 1.0
    dt_max = 10.0
    dt_min = 1e-3
    alpha0 = 0.1
    f_inc = 1.1
    f_dec = 0.5
    f_alpha = 0.99
    n_min = 5
    maxstep = 0.2 * sigma  # Å (max displacement per iteration)

    # Device-side FIRE state arrays (shape = (1,) for single system)
    wp_dtype = system.wp_dtype
    dt_wp = wp.array([dt0], dtype=wp_dtype, device=device)
    alpha_wp = wp.array([alpha0], dtype=wp_dtype, device=device)
    alpha_start_wp = wp.array([alpha0], dtype=wp_dtype, device=device)
    f_alpha_wp = wp.array([f_alpha], dtype=wp_dtype, device=device)
    dt_min_wp = wp.array([dt_min], dtype=wp_dtype, device=device)
    dt_max_wp = wp.array([dt_max], dtype=wp_dtype, device=device)
    maxstep_wp = wp.array([maxstep], dtype=wp_dtype, device=device)
    n_steps_positive_wp = wp.zeros(1, dtype=wp.int32, device=device)
    n_min_wp = wp.array([n_min], dtype=wp.int32, device=device)
    f_dec_wp = wp.array([f_dec], dtype=wp_dtype, device=device)
    f_inc_wp = wp.array([f_inc], dtype=wp_dtype, device=device)
    uphill_flag_wp = wp.zeros(1, dtype=wp.int32, device=device)

    # Accumulators for diagnostic scalars (vf, vv, ff) - must be zeroed before each step
    vf_wp = wp.zeros(1, dtype=wp_dtype, device=device)
    vv_wp = wp.zeros(1, dtype=wp_dtype, device=device)
    ff_wp = wp.zeros(1, dtype=wp_dtype, device=device)

    # History for plotting
    energy_hist: list[float] = []
    maxf_hist: list[float] = []
    dt_hist: list[float] = []
    alpha_hist: list[float] = []

    print("\n" + "=" * 95)
    print("FIRE GEOMETRY OPTIMIZATION (LJ cluster)")
    print("=" * 95)
    print(f"  atoms: {num_atoms}, cutoff={cutoff:.2f} Å, box={box_L:.1f} Å")
    print(f"  max_steps={max_steps}, force_tol={force_tolerance:.2e} eV/Å")
    print(f"  dt0={dt0}, dt_max={dt_max}, alpha0={alpha0}, n_min={n_min}")
    print(f"  dt_min={dt_min}, maxstep={maxstep:.3f} Å")

    log_interval = 100
    check_interval = 50

    for step in range(max_steps):
        # Compute forces at current positions
        energies = system.compute_forces()

        # Zero the accumulators before each FIRE step
        vf_wp.zero_()
        vv_wp.zero_()
        ff_wp.zero_()

        # Single FIRE step using the unified API
        # This performs: diagnostic computation, velocity mixing, parameter update, MD step
        fire_step(
            positions=system.wp_positions,
            velocities=system.wp_velocities,
            forces=system.wp_forces,
            masses=system.wp_masses,
            alpha=alpha_wp,
            dt=dt_wp,
            alpha_start=alpha_start_wp,
            f_alpha=f_alpha_wp,
            dt_min=dt_min_wp,
            dt_max=dt_max_wp,
            maxstep=maxstep_wp,
            n_steps_positive=n_steps_positive_wp,
            n_min=n_min_wp,
            f_dec=f_dec_wp,
            f_inc=f_inc_wp,
            uphill_flag=uphill_flag_wp,
            vf=vf_wp,
            vv=vv_wp,
            ff=ff_wp,
        )

        # Logging / stopping criteria (host read only at intervals)
        if step % check_interval == 0 or step == max_steps - 1:
            pe = float(energies.numpy().sum())
            fmax = float(np.linalg.norm(system.wp_forces.numpy(), axis=1).max())

            energy_hist.append(pe)
            maxf_hist.append(fmax)
            dt_hist.append(float(dt_wp.numpy()[0]))
            alpha_hist.append(float(alpha_wp.numpy()[0]))

            if step % log_interval == 0 or step == max_steps - 1:
                print(
                    f"step={step:5d}  PE={pe:12.6f} eV  max|F|={fmax:10.3e} eV/Å  "
                    f"dt={dt_hist[-1]:6.3f}  alpha={alpha_hist[-1]:7.4f}  "
                    f"n+={int(n_steps_positive_wp.numpy()[0]):3d}"
                )

            if fmax < force_tolerance:
                print(f"\nConverged at step {step} (max|F|={fmax:.3e} eV/Å).")
                break





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    ===============================================================================================
    FIRE GEOMETRY OPTIMIZATION (LJ cluster)
    ===============================================================================================
      atoms: 32, cutoff=8.50 Å, box=80.0 Å
      max_steps=3000, force_tol=1.00e-03 eV/Å
      dt0=1.0, dt_max=10.0, alpha0=0.1, n_min=5
      dt_min=0.001, maxstep=0.680 Å
    step=    0  PE=   -0.022508 eV  max|F|= 3.541e-01 eV/Å  dt= 0.500  alpha= 0.1000  n+=  0
    step=  100  PE=   -0.321531 eV  max|F|= 1.081e-02 eV/Å  dt=10.000  alpha= 0.0381  n+=100
    step=  200  PE=   -0.394863 eV  max|F|= 2.618e-02 eV/Å  dt=10.000  alpha= 0.0139  n+=200
    step=  300  PE=   -0.457969 eV  max|F|= 2.563e-02 eV/Å  dt=10.000  alpha= 0.0051  n+=300
    step=  400  PE=   -0.511123 eV  max|F|= 1.267e-02 eV/Å  dt=10.000  alpha= 0.0430  n+= 88
    step=  500  PE=   -0.567782 eV  max|F|= 1.829e-02 eV/Å  dt=10.000  alpha= 0.0157  n+=188
    step=  600  PE=   -0.621281 eV  max|F|= 3.008e-02 eV/Å  dt=10.000  alpha= 0.0058  n+=288
    step=  700  PE=   -0.668527 eV  max|F|= 6.530e-03 eV/Å  dt=10.000  alpha= 0.0662  n+= 45
    step=  800  PE=   -0.744103 eV  max|F|= 1.079e-02 eV/Å  dt=10.000  alpha= 0.0242  n+=145
    step=  900  PE=   -0.810186 eV  max|F|= 1.669e-02 eV/Å  dt=10.000  alpha= 0.0089  n+=245
    step= 1000  PE=   -0.872658 eV  max|F|= 1.165e-02 eV/Å  dt=10.000  alpha= 0.0611  n+= 53
    step= 1100  PE=   -0.934003 eV  max|F|= 1.227e-02 eV/Å  dt=10.000  alpha= 0.0224  n+=153
    step= 1200  PE=   -0.954023 eV  max|F|= 3.749e-03 eV/Å  dt=10.000  alpha= 0.0457  n+= 82
    step= 1300  PE=   -0.996963 eV  max|F|= 8.952e-03 eV/Å  dt=10.000  alpha= 0.0167  n+=182
    step= 1400  PE=   -1.016477 eV  max|F|= 6.099e-03 eV/Å  dt=10.000  alpha= 0.0747  n+= 33
    step= 1500  PE=   -1.034997 eV  max|F|= 4.540e-03 eV/Å  dt=10.000  alpha= 0.0273  n+=133
    step= 1600  PE=   -1.078106 eV  max|F|= 1.045e-02 eV/Å  dt=10.000  alpha= 0.0100  n+=233
    step= 1700  PE=   -1.097269 eV  max|F|= 1.413e-02 eV/Å  dt= 8.858  alpha= 0.0941  n+= 10
    step= 1800  PE=   -1.109143 eV  max|F|= 2.956e-03 eV/Å  dt=10.000  alpha= 0.0345  n+=110
    step= 1900  PE=   -1.117740 eV  max|F|= 1.849e-03 eV/Å  dt=10.000  alpha= 0.0778  n+= 29
    step= 2000  PE=   -1.119411 eV  max|F|= 2.907e-03 eV/Å  dt=10.000  alpha= 0.0285  n+=129
    step= 2100  PE=   -1.127265 eV  max|F|= 1.813e-03 eV/Å  dt=10.000  alpha= 0.0818  n+= 24

    Converged at step 2150 (max|F|=5.054e-04 eV/Å).




.. GENERATED FROM PYTHON SOURCE LINES 195-196

Plot convergence

.. GENERATED FROM PYTHON SOURCE LINES 196-210

.. code-block:: Python


    steps = np.arange(len(energy_hist))

    fig, ax = plt.subplots(2, 1, figsize=(7.0, 5.5), sharex=True, constrained_layout=True)
    ax[0].plot(steps, energy_hist, lw=1.5)
    ax[0].set_ylabel("Potential Energy (eV)")
    ax[0].set_title("FIRE Optimization Convergence")

    ax[1].semilogy(steps, maxf_hist, lw=1.5)
    ax[1].axhline(force_tolerance, color="k", ls="--", lw=1.0, label="tolerance")
    ax[1].set_xlabel("Log point index")
    ax[1].set_ylabel(r"max$|F|$ (eV/$\AA$)")
    ax[1].legend(frameon=False, loc="best")




.. image-sg:: /examples/dynamics/images/sphx_glr_06_fire_optimization_001.png
   :alt: FIRE Optimization Convergence
   :srcset: /examples/dynamics/images/sphx_glr_06_fire_optimization_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x76780a650cd0>



.. GENERATED FROM PYTHON SOURCE LINES 211-212

Visualize initial vs final geometry (XY projection)

.. GENERATED FROM PYTHON SOURCE LINES 212-228

.. code-block:: Python


    pos0 = initial_positions
    pos1 = system.wp_positions.numpy()

    fig2, ax2 = plt.subplots(
        1, 2, figsize=(8.0, 3.5), sharex=True, sharey=True, constrained_layout=True
    )
    ax2[0].scatter(pos0[:, 0], pos0[:, 1], s=20)
    ax2[0].set_title("Initial (XY)")
    ax2[0].set_xlabel("x (Å)")
    ax2[0].set_ylabel("y (Å)")
    ax2[1].scatter(pos1[:, 0], pos1[:, 1], s=20)
    ax2[1].set_title("Optimized (XY)")
    ax2[1].set_xlabel("x (Å)")

    plt.show()



.. image-sg:: /examples/dynamics/images/sphx_glr_06_fire_optimization_002.png
   :alt: Initial (XY), Optimized (XY)
   :srcset: /examples/dynamics/images/sphx_glr_06_fire_optimization_002.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 1.607 seconds)


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