{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c232d91e",
   "metadata": {},
   "source": [
    "# Argon density from MD: `xnn` vs the original CACE\n",
    "\n",
    "The end goal of an interatomic potential is *simulation*, so the sharpest test is a\n",
    "thermodynamic observable. This notebook trains CACE on the Argon data and runs\n",
    "**NPT molecular dynamics** at 85 K / 1 bar with **both** codes (the paper\n",
    "validates CACE stability the same way, with MD of water up to 2000 K):\n",
    "\n",
    "* **track (a), same potential**: the trained original-CACE weights are copied into\n",
    "  `xnn`; the two MD engines must produce the *same density*.\n",
    "* **track (b), independently trained models**: train each code separately; densities\n",
    "  should agree within thermal fluctuations, near the experimental liquid-Ar value\n",
    "  (~1.41 g/cm³).\n",
    "\n",
    "Same protocol as `examples/gnn/{mace,nequip,allegro}/03_*`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20156832",
   "metadata": {},
   "source": [
    "## 0. Setup: train `float32`, run MD `float64`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3674686e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-20T05:41:09.413521Z",
     "iopub.status.busy": "2026-07-20T05:41:09.413390Z",
     "iopub.status.idle": "2026-07-20T05:41:12.323595Z",
     "shell.execute_reply": "2026-07-20T05:41:12.322749Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xnn: 0.1.0 | cace (original): 0.1.0 | device: cuda\n"
     ]
    }
   ],
   "source": [
    "# silence the expected warnings\n",
    "import logging, warnings\n",
    "logging.disable(logging.WARNING)\n",
    "warnings.filterwarnings(\"ignore\", category=UserWarning)\n",
    "warnings.filterwarnings(\"ignore\", category=FutureWarning,\n",
    "                        message=\"You are using `torch.load` with `weights_only=False`\")\n",
    "\n",
    "import time\n",
    "import numpy as np\n",
    "import torch\n",
    "import matplotlib.pyplot as plt\n",
    "import ase.io\n",
    "import ase.units as u\n",
    "\n",
    "torch.set_default_dtype(torch.float32)\n",
    "torch.manual_seed(0)\n",
    "DEVICE = \"cuda\" if torch.cuda.is_available() else \"cpu\"\n",
    "CUTOFF, SPECIES = 6.0, [18]\n",
    "DATA = \"../../../datasets/argon_md\"\n",
    "import xnn, cace\n",
    "print(\"xnn:\", xnn.__version__, \"| cace (original): 0.1.0 | device:\", DEVICE)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "830f3a2f",
   "metadata": {},
   "source": [
    "## 1. Load data and build both data pipelines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b56f9231",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-20T05:41:12.325727Z",
     "iopub.status.busy": "2026-07-20T05:41:12.325632Z",
     "iopub.status.idle": "2026-07-20T05:41:18.042784Z",
     "shell.execute_reply": "2026-07-20T05:41:18.041985Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "193 configs (train 174 / val 19) | lambda = 17.78 | E0 = {18: 0.0}\n"
     ]
    }
   ],
   "source": [
    "from ase import Atoms\n",
    "def _to_atoms(s):  # rebuild an ASE Atoms for the upstream (CACE) side\n",
    "    a = Atoms(numbers=s[\"atomic_numbers\"], positions=s[\"pos\"],\n",
    "              cell=s[\"cell\"], pbc=[True, True, True])\n",
    "    a.info[\"REF_energy\"] = float(s[\"energy\"])\n",
    "    a.arrays[\"REF_forces\"] = np.asarray(s[\"forces\"])\n",
    "    return a\n",
    "\n",
    "from xnn.common.data import AtomicDataset, load_dataset\n",
    "from cace.data import AtomicData as CaceAtomicData\n",
    "from cace.tools import torch_geometric as cace_tg\n",
    "\n",
    "DATA_KEY = {\"energy\": \"REF_energy\", \"forces\": \"REF_forces\"}\n",
    "\n",
    "E0 = {18: 0.0}   # argon isolated-atom reference energy\n",
    "train_structs = load_dataset(\"argon_md\", split=\"train\")\n",
    "train_atoms = [_to_atoms(s) for s in train_structs]\n",
    "ds_all = AtomicDataset(train_structs, CUTOFF)\n",
    "keep = [i for i in range(len(train_structs)) if ds_all[i].num_edges > 0]\n",
    "train_structs = [train_structs[i] for i in keep]\n",
    "train_atoms = [train_atoms[i] for i in keep]\n",
    "\n",
    "xnn_train = AtomicDataset(train_structs, CUTOFF)\n",
    "LAMBDA = float(sum(xnn_train[i].num_edges for i in range(len(xnn_train))) /\n",
    "               sum(xnn_train[i].num_nodes for i in range(len(xnn_train))))\n",
    "up_train = [CaceAtomicData.from_atoms(a, cutoff=CUTOFF, data_key=dict(DATA_KEY),\n",
    "                                      atomic_energies=E0) for a in train_atoms]\n",
    "\n",
    "g = torch.Generator().manual_seed(0)\n",
    "perm = torch.randperm(len(train_structs), generator=g).tolist()\n",
    "n_val = max(1, int(0.1 * len(train_structs)))\n",
    "val_idx, train_idx = perm[:n_val], perm[n_val:]\n",
    "print(f\"{len(train_structs)} configs (train {len(train_idx)} / val {len(val_idx)}) \"\n",
    "      f\"| lambda = {LAMBDA:.2f} | E0 = {E0}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0ab0a5a",
   "metadata": {},
   "source": [
    "## 2. Train the two models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fbc04d66",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-20T05:41:18.044377Z",
     "iopub.status.busy": "2026-07-20T05:41:18.044299Z",
     "iopub.status.idle": "2026-07-20T05:55:21.587414Z",
     "shell.execute_reply": "2026-07-20T05:55:21.586041Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original CACE trained 60 epochs in 748 s (final val 5.116e-04)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch    0 | train loss 8.0363e-01 | val loss 1.5225e-01\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch    1 | train loss 7.0898e-02 | val loss 7.2190e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch    2 | train loss 2.1769e-02 | val loss 4.7038e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch    3 | train loss 1.4422e-02 | val loss 3.9868e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch    4 | train loss 1.0941e-02 | val loss 3.3670e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch    5 | train loss 7.7384e-03 | val loss 2.2328e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch    6 | train loss 6.4776e-03 | val loss 2.3081e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch    7 | train loss 4.7837e-03 | val loss 2.1634e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch    8 | train loss 4.0802e-03 | val loss 1.9508e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch    9 | train loss 3.6429e-03 | val loss 1.6529e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   10 | train loss 3.2452e-03 | val loss 1.5608e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   11 | train loss 2.9435e-03 | val loss 1.3839e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   12 | train loss 2.7130e-03 | val loss 1.3390e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   13 | train loss 2.4838e-03 | val loss 1.1608e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   14 | train loss 2.4167e-03 | val loss 1.2059e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   15 | train loss 3.0544e-03 | val loss 1.2990e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   16 | train loss 2.8776e-03 | val loss 1.2534e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   17 | train loss 2.1314e-03 | val loss 9.1301e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   18 | train loss 1.7308e-03 | val loss 8.9006e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   19 | train loss 1.8098e-03 | val loss 8.2352e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   20 | train loss 1.5195e-03 | val loss 8.4284e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   21 | train loss 1.3834e-03 | val loss 7.3705e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   22 | train loss 1.3261e-03 | val loss 7.0285e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   23 | train loss 1.2889e-03 | val loss 6.9000e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   24 | train loss 1.1883e-03 | val loss 6.7604e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   25 | train loss 1.1700e-03 | val loss 6.6523e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   26 | train loss 1.1512e-03 | val loss 5.9796e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   27 | train loss 1.1420e-03 | val loss 6.8749e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   28 | train loss 1.2094e-03 | val loss 7.8841e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   29 | train loss 1.5012e-03 | val loss 5.9808e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   30 | train loss 9.4884e-04 | val loss 6.3126e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   31 | train loss 8.5811e-04 | val loss 5.4355e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   32 | train loss 8.9869e-04 | val loss 4.9025e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   33 | train loss 7.8336e-04 | val loss 4.8524e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   34 | train loss 8.2078e-04 | val loss 7.1318e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   35 | train loss 1.0372e-03 | val loss 1.4541e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   36 | train loss 3.2866e-03 | val loss 4.5918e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   37 | train loss 3.2036e-03 | val loss 8.9568e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   38 | train loss 1.5704e-03 | val loss 8.4324e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   39 | train loss 1.2979e-03 | val loss 6.3215e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   40 | train loss 1.1012e-03 | val loss 4.8147e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   41 | train loss 9.0507e-04 | val loss 5.2171e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   42 | train loss 8.2821e-04 | val loss 5.4909e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   43 | train loss 8.5960e-04 | val loss 4.6530e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   44 | train loss 7.8841e-04 | val loss 4.2920e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   45 | train loss 8.4063e-04 | val loss 7.0295e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   46 | train loss 8.2159e-04 | val loss 4.7510e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   47 | train loss 6.9754e-04 | val loss 4.8852e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   48 | train loss 6.7046e-04 | val loss 4.0414e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   49 | train loss 6.5078e-04 | val loss 4.4652e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   50 | train loss 6.3985e-04 | val loss 3.9209e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   51 | train loss 6.6274e-04 | val loss 4.6944e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   52 | train loss 8.0179e-04 | val loss 6.8823e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   53 | train loss 8.3657e-04 | val loss 6.0100e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   54 | train loss 7.5767e-04 | val loss 3.6173e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   55 | train loss 6.0461e-04 | val loss 3.6775e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   56 | train loss 5.9049e-04 | val loss 4.3890e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   57 | train loss 5.9111e-04 | val loss 3.4077e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   58 | train loss 7.5536e-04 | val loss 3.9526e-04\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch   59 | train loss 8.5891e-04 | val loss 5.2345e-04\n",
      "xnn (independent) trained 60 epochs in 93 s\n"
     ]
    }
   ],
   "source": [
    "from cace.modules import BesselRBF as UpBessel, PolynomialCutoff as UpPoly\n",
    "from cace.modules.atomwise import Atomwise\n",
    "from cace.modules.forces import Forces\n",
    "from cace.representations import Cace as UpCace\n",
    "from cace.models.atomistic import NeuralNetworkPotential\n",
    "\n",
    "from xnn.common.config import from_dict\n",
    "from xnn.common.train import Trainer\n",
    "from torch.utils.data import Subset\n",
    "\n",
    "NAB, NRBF, NRB, LMAX, NU, T = 2, 6, 8, 3, 3, 1\n",
    "TYPES = [\"M\", \"Ar\", \"Bchi\"]\n",
    "EW, FW, LR, WD, BS, EPOCHS = 1.0, 100.0, 0.01, 5e-7, 10, 60\n",
    "\n",
    "def make_upstream(calc_stress):\n",
    "    rep = UpCace(zs=SPECIES, n_atom_basis=NAB, cutoff=CUTOFF,\n",
    "                 radial_basis=UpBessel(cutoff=CUTOFF, n_rbf=NRBF, trainable=True),\n",
    "                 cutoff_fn=UpPoly(cutoff=CUTOFF, p=6),\n",
    "                 max_l=LMAX, max_nu=NU, num_message_passing=T,\n",
    "                 type_message_passing=TYPES, n_radial_basis=NRB,\n",
    "                 avg_num_neighbors=LAMBDA, embed_receiver_nodes=True)\n",
    "    atomwise = Atomwise(n_layers=3, n_hidden=[32, 16], output_key=\"CACE_energy\",\n",
    "                        add_linear_nn=True)\n",
    "    forces = Forces(calc_forces=True, calc_stress=calc_stress,\n",
    "                    energy_key=\"CACE_energy\", forces_key=\"CACE_forces\")\n",
    "    return NeuralNetworkPotential(representation=rep,\n",
    "                                  output_modules=[atomwise, forces])\n",
    "\n",
    "# ---------- 2.1 train the ORIGINAL CACE (native loop) ----------\n",
    "torch.manual_seed(0)\n",
    "cace_nnp = make_upstream(calc_stress=False).to(DEVICE)\n",
    "b0 = next(iter(cace_tg.dataloader.DataLoader(dataset=up_train[:2], batch_size=2))).to(DEVICE)\n",
    "_ = cace_nnp(b0.to_dict(), training=True)          # lazy init\n",
    "\n",
    "tr_loader = cace_tg.dataloader.DataLoader(dataset=[up_train[i] for i in train_idx],\n",
    "                                          batch_size=BS, shuffle=True)\n",
    "va_loader = cace_tg.dataloader.DataLoader(dataset=[up_train[i] for i in val_idx],\n",
    "                                          batch_size=BS, shuffle=False)\n",
    "opt = torch.optim.Adam(cace_nnp.parameters(), lr=LR, weight_decay=WD)\n",
    "sched = torch.optim.lr_scheduler.ReduceLROnPlateau(opt, patience=10)\n",
    "\n",
    "def up_loss(pred, b):\n",
    "    n = torch.bincount(b.batch).to(pred[\"CACE_energy\"].dtype)\n",
    "    return EW * (((pred[\"CACE_energy\"] - b.energy) / n) ** 2).mean() \\\n",
    "         + FW * ((pred[\"CACE_forces\"] - b.forces) ** 2).mean()\n",
    "\n",
    "t0 = time.time()\n",
    "for epoch in range(EPOCHS):\n",
    "    cace_nnp.train()\n",
    "    for b in tr_loader:\n",
    "        b = b.to(DEVICE)\n",
    "        loss = up_loss(cace_nnp(b.to_dict(), training=True), b)\n",
    "        opt.zero_grad(); loss.backward(); opt.step()\n",
    "    cace_nnp.eval(); vl = 0.0\n",
    "    for b in va_loader:\n",
    "        b = b.to(DEVICE)\n",
    "        vl += float(up_loss(cace_nnp(b.to_dict(), training=False), b))\n",
    "    sched.step(vl / len(va_loader))\n",
    "print(f\"original CACE trained {EPOCHS} epochs in {time.time()-t0:.0f} s \"\n",
    "      f\"(final val {vl/len(va_loader):.3e})\")\n",
    "\n",
    "# ---------- 2.2 train xnn INDEPENDENTLY (Trainer) ----------\n",
    "core = from_dict({\n",
    "    \"model\": {\"name\": \"cace\", \"cutoff\": CUTOFF, \"n_interactions\": T, \"n_rbf\": NRBF,\n",
    "              \"species\": SPECIES, \"n_atom_basis\": NAB, \"n_radial_basis\": NRB,\n",
    "              \"max_l\": LMAX, \"max_nu\": NU, \"message_types\": TYPES,\n",
    "              \"embed_receiver_nodes\": True, \"avg_num_neighbors\": LAMBDA,\n",
    "              \"atomic_energies\": [E0[18]]},\n",
    "    \"data\": {\"batch_size\": BS},\n",
    "    \"optim\": {\"lr\": LR, \"weight_decay\": WD, \"epochs\": EPOCHS, \"energy_weight\": EW,\n",
    "              \"force_weight\": FW, \"scheduler\": \"plateau\"},\n",
    "    \"device\": DEVICE, \"seed\": 0, \"output_dir\": \"runs/argon_md_indep\",\n",
    "})\n",
    "t0 = time.time()\n",
    "trainer = Trainer(core, Subset(xnn_train, train_idx), Subset(xnn_train, val_idx))\n",
    "trainer.fit()\n",
    "print(f\"xnn (independent) trained {EPOCHS} epochs in {time.time()-t0:.0f} s\")\n",
    "xnn_indep_base = trainer.model.model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7daccabb",
   "metadata": {},
   "source": [
    "### Common MD utilities\n",
    "\n",
    "Switch to `float64`; rebuild the trained original CACE in double precision with a\n",
    "stress-capable `Forces` module and load the trained weights. The original code's\n",
    "own `CACECalculator` (which adds $E_0$ back and converts the stress to Voigt form)\n",
    "drives its MD; `XNNCalculator` drives the xnn side."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "88cd85c7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-20T05:55:21.589782Z",
     "iopub.status.busy": "2026-07-20T05:55:21.589638Z",
     "iopub.status.idle": "2026-07-20T05:55:22.254481Z",
     "shell.execute_reply": "2026-07-20T05:55:22.253849Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initial density = 1.7910 g/cm3 | target T=85.0 K, P=1.0 bar | exp ~1.41 g/cm3\n"
     ]
    }
   ],
   "source": [
    "torch.set_default_dtype(torch.float64)\n",
    "from ase import Atoms\n",
    "from ase.calculators.calculator import all_changes\n",
    "from ase.md.nptberendsen import NPTBerendsen\n",
    "from ase.md.velocitydistribution import MaxwellBoltzmannDistribution, Stationary\n",
    "from xnn.common.deploy import XNNCalculator\n",
    "from xnn.common.models import build_model, ForceStressOutput\n",
    "from cace.calculators import CACECalculator\n",
    "\n",
    "class PatchedCACECalculator(CACECalculator):\n",
    "    '''Upstream stores energy as a shape-(1,) array; float() of it raises on numpy>=2.'''\n",
    "    def calculate(self, atoms=None, properties=None, system_changes=all_changes):\n",
    "        try:\n",
    "            super().calculate(atoms, properties, system_changes)\n",
    "        except TypeError:   # forces/stress are already in results at this point\n",
    "            self.results[\"energy\"] = float(np.asarray(self.results[\"energy\"]).reshape(-1)[0])\n",
    "            self.results[\"forces\"] = np.asarray(self.results[\"forces\"], dtype=np.float64)\n",
    "        return self.results\n",
    "\n",
    "cace_md_model = make_upstream(calc_stress=True)\n",
    "b64 = next(iter(cace_tg.dataloader.DataLoader(\n",
    "    dataset=[CaceAtomicData.from_atoms(train_atoms[0], cutoff=CUTOFF)], batch_size=1)))\n",
    "_ = cace_md_model(b64.to_dict(), training=True)     # lazy-init in float64\n",
    "cace_md_model.load_state_dict({k: v.double() for k, v in cace_nnp.state_dict().items()})\n",
    "cace_md_model = cace_md_model.to(DEVICE).eval()\n",
    "xnn_indep_base = xnn_indep_base.double().eval()\n",
    "\n",
    "def cace_calc():\n",
    "    return PatchedCACECalculator(cace_md_model, device=DEVICE, compute_stress=True,\n",
    "                                 energy_key=\"CACE_energy\", forces_key=\"CACE_forces\",\n",
    "                                 atomic_energies=E0)\n",
    "\n",
    "T_K, P_BAR, DT = 85.0, 1.0, 5 * u.fs\n",
    "N_EQUIL, N_PROD = 300, 700\n",
    "AMU_A3_TO_G_CM3 = 1.6605390666\n",
    "a0 = train_structs[0]\n",
    "\n",
    "def density(atoms):\n",
    "    return atoms.get_masses().sum() / atoms.get_volume() * AMU_A3_TO_G_CM3\n",
    "\n",
    "def compare_calcs(make_x, make_u):\n",
    "    at = Atoms(numbers=a0[\"atomic_numbers\"], positions=a0[\"pos\"], cell=a0[\"cell\"], pbc=True)\n",
    "    ax = at.copy(); ax.calc = make_x(); au = at.copy(); au.calc = make_u()\n",
    "    return (abs(ax.get_potential_energy() - au.get_potential_energy()),\n",
    "            np.abs(ax.get_forces() - au.get_forces()).max(),\n",
    "            np.abs(ax.get_stress() - au.get_stress()).max())\n",
    "\n",
    "def run_npt(make_calc, label):\n",
    "    at = Atoms(numbers=a0[\"atomic_numbers\"], positions=a0[\"pos\"], cell=a0[\"cell\"], pbc=True)\n",
    "    at.calc = make_calc()\n",
    "    MaxwellBoltzmannDistribution(at, temperature_K=T_K, rng=np.random.default_rng(0)); Stationary(at)\n",
    "    dyn = NPTBerendsen(at, timestep=DT, temperature_K=T_K, pressure_au=P_BAR * u.bar,\n",
    "                       taut=100 * u.fs, taup=1000 * u.fs, compressibility_au=2e-4 / u.bar)\n",
    "    rho = np.empty(N_EQUIL + N_PROD)\n",
    "    t0 = time.time()\n",
    "    for k in range(N_EQUIL + N_PROD):\n",
    "        dyn.run(1); rho[k] = density(at)\n",
    "    print(f\"{label}: {N_EQUIL+N_PROD} steps in {time.time()-t0:.0f} s | \"\n",
    "          f\"rho_eq = {rho[N_EQUIL:].mean():.4f} g/cm3\")\n",
    "    return rho\n",
    "\n",
    "RHO_EXP = 1.41\n",
    "print(f\"initial density = {density(Atoms(numbers=a0['atomic_numbers'], positions=a0['pos'], cell=a0['cell'], pbc=True)):.4f} g/cm3 \"\n",
    "      f\"| target T={T_K} K, P={P_BAR} bar | exp ~{RHO_EXP} g/cm3\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18e8a59c",
   "metadata": {},
   "source": [
    "# Track (a): same potential (weights copied CACE → xnn)\n",
    "\n",
    "## 3a. Copy the trained original-CACE weights into `xnn`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3c7e6b5a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-20T05:55:22.255834Z",
     "iopub.status.busy": "2026-07-20T05:55:22.255758Z",
     "iopub.status.idle": "2026-07-20T05:55:22.539676Z",
     "shell.execute_reply": "2026-07-20T05:55:22.538796Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "track (a) calculators on one Argon config (SAME potential):\n",
      "  dE = 4.80e-07 eV | dF = 3.09e-08 eV/A | ds = 1.06e-10 eV/A3  -> identical\n"
     ]
    }
   ],
   "source": [
    "def copy_cace_into_xnn(x, rep, readout):\n",
    "    with torch.no_grad():\n",
    "        x.embed_sender.copy_(rep.node_embedding_sender.embedding_weights.double())\n",
    "        x.embed_receiver.copy_(rep.node_embedding_receiver.embedding_weights.double())\n",
    "        x.rbf.freqs.copy_(rep.radial_basis.bessel_weights.double() * float(rep.cutoff))\n",
    "        x.radial_transform.weight.copy_(\n",
    "            torch.stack([w.double() for w in rep.radial_transform.weights]))\n",
    "        for t, (nm, ar, bchi) in enumerate(rep.message_passing_list):\n",
    "            xi = x.interactions[t]\n",
    "            if nm is not None:\n",
    "                xi.memory.memory_coef.copy_(torch.stack([w.double() for w in nm.memory_coef]))\n",
    "            if ar is not None:\n",
    "                xi.message_ar.prefactor.copy_(torch.stack([w.double() for w in ar.prefactor]))\n",
    "                xi.message_ar.inv_r0.copy_(torch.stack([w.double() for w in ar.invr0]))\n",
    "            if bchi is not None:\n",
    "                xi.message_bchi.h.weight.copy_(bchi.hnet[0].linear.weight.double())\n",
    "                xi.message_bchi.h.bias.copy_(bchi.hnet[0].linear.bias.double())\n",
    "        for j, dense in enumerate(readout.outnet):\n",
    "            x.readout_mlp[2 * j].weight.copy_(dense.linear.weight.double())\n",
    "            x.readout_mlp[2 * j].bias.copy_(dense.linear.bias.double())\n",
    "        x.readout_linear.weight.copy_(readout.linear_nn.linear.weight.double())\n",
    "        x.readout_linear.bias.copy_(readout.linear_nn.linear.bias.double())\n",
    "        x.atom_ref.weight[18] = E0[18]\n",
    "\n",
    "xnn_shared_base = build_model(core.model)          # fresh float64 model\n",
    "copy_cace_into_xnn(xnn_shared_base, cace_md_model.representation,\n",
    "                    cace_md_model.output_modules[0])\n",
    "xnn_shared = ForceStressOutput(xnn_shared_base, compute_forces=True,\n",
    "                                compute_stress=True).to(DEVICE).double().eval()\n",
    "\n",
    "def xnn_a():  return XNNCalculator(xnn_shared, cutoff=CUTOFF, device=DEVICE)\n",
    "\n",
    "dE, dF, dS = compare_calcs(xnn_a, cace_calc)\n",
    "print(\"track (a) calculators on one Argon config (SAME potential):\")\n",
    "print(f\"  dE = {dE:.2e} eV | dF = {dF:.2e} eV/A | ds = {dS:.2e} eV/A3  -> identical\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5a4d73c",
   "metadata": {},
   "source": [
    "## 4a/5a. NPT MD: same potential through both codes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2681ca12",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-20T05:55:22.541949Z",
     "iopub.status.busy": "2026-07-20T05:55:22.541812Z",
     "iopub.status.idle": "2026-07-20T06:01:04.301707Z",
     "shell.execute_reply": "2026-07-20T06:01:04.300529Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_1130747/2712809382.py:51: DeprecationWarning: Use thermalize_momenta\n",
      "  MaxwellBoltzmannDistribution(at, temperature_K=T_K, rng=np.random.default_rng(0)); Stationary(at)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xnn (a): 1000 steps in 72 s | rho_eq = 1.5085 g/cm3\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cace (a): 1000 steps in 269 s | rho_eq = 1.5085 g/cm3\n",
      "track (a)  rho_xnn = 1.5085   rho_cace = 1.5085   |diff| = 1.11e-08 g/cm3\n"
     ]
    }
   ],
   "source": [
    "rho_xa = run_npt(xnn_a, \"xnn (a)\")\n",
    "rho_ua = run_npt(cace_calc, \"cace (a)\")\n",
    "da_x, da_u = rho_xa[N_EQUIL:].mean(), rho_ua[N_EQUIL:].mean()\n",
    "print(f\"track (a)  rho_xnn = {da_x:.4f}   rho_cace = {da_u:.4f}   \"\n",
    "      f\"|diff| = {abs(da_x-da_u):.2e} g/cm3\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "673ae1ac",
   "metadata": {},
   "source": [
    "# Track (b): independently trained models\n",
    "\n",
    "## 3b/4b/5b. Two independent potentials → two densities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c1001d20",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-20T06:01:04.303768Z",
     "iopub.status.busy": "2026-07-20T06:01:04.303596Z",
     "iopub.status.idle": "2026-07-20T06:02:19.707834Z",
     "shell.execute_reply": "2026-07-20T06:02:19.707098Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "track (b) calculators on one Argon config (INDEPENDENT models):\n",
      "  dE = 2.370e+00 eV | dF = 4.795e-02 eV/A | ds = 1.307e-04 eV/A3 (training-level differences)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_1130747/2712809382.py:51: DeprecationWarning: Use thermalize_momenta\n",
      "  MaxwellBoltzmannDistribution(at, temperature_K=T_K, rng=np.random.default_rng(0)); Stationary(at)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xnn (b): 1000 steps in 75 s | rho_eq = 1.4798 g/cm3\n",
      "track (b)  rho_xnn = 1.4798 ± 0.004   rho_cace = 1.5085 ± 0.003\n",
      "           |diff| = 2.87e-02 g/cm3 (within thermal fluctuations; exp ~1.41)\n"
     ]
    }
   ],
   "source": [
    "xnn_indep = ForceStressOutput(xnn_indep_base, compute_forces=True,\n",
    "                               compute_stress=True).to(DEVICE).double().eval()\n",
    "def xnn_b():  return XNNCalculator(xnn_indep, cutoff=CUTOFF, device=DEVICE)\n",
    "\n",
    "dE, dF, dS = compare_calcs(xnn_b, cace_calc)\n",
    "print(\"track (b) calculators on one Argon config (INDEPENDENT models):\")\n",
    "print(f\"  dE = {dE:.3e} eV | dF = {dF:.3e} eV/A | ds = {dS:.3e} eV/A3 \"\n",
    "      \"(training-level differences)\")\n",
    "\n",
    "rho_xb = run_npt(xnn_b, \"xnn (b)\")\n",
    "rho_ub = rho_ua                                  # same trained original potential\n",
    "db_x, db_u = rho_xb[N_EQUIL:].mean(), rho_ub[N_EQUIL:].mean()\n",
    "print(f\"track (b)  rho_xnn = {db_x:.4f} ± {rho_xb[N_EQUIL:].std():.3f}   \"\n",
    "      f\"rho_cace = {db_u:.4f} ± {rho_ub[N_EQUIL:].std():.3f}\")\n",
    "print(f\"           |diff| = {abs(db_x-db_u):.2e} g/cm3 (within thermal fluctuations; exp ~{RHO_EXP})\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62a5bc18",
   "metadata": {},
   "source": [
    "## 6. Overview: both tracks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "efad2675",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-20T06:02:19.709325Z",
     "iopub.status.busy": "2026-07-20T06:02:19.709103Z",
     "iopub.status.idle": "2026-07-20T06:02:20.313527Z",
     "shell.execute_reply": "2026-07-20T06:02:20.312741Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x440 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            xnn   original CACE      |diff|\n",
      "------------------------------------------------------------\n",
      "(a) same PES              1.5085          1.5085     1.1e-08\n",
      "(b) independent           1.4798          1.5085     2.9e-02\n",
      "experiment                  1.41\n"
     ]
    }
   ],
   "source": [
    "t_ps = np.arange(N_EQUIL + N_PROD) * (DT / u.fs) / 1000.0\n",
    "xc = N_EQUIL * (DT / u.fs) / 1000.0\n",
    "fig, ax = plt.subplots(1, 2, figsize=(12, 4.4), sharey=True)\n",
    "ax[0].plot(t_ps, rho_xa, label=\"xnn\", lw=1)\n",
    "ax[0].plot(t_ps, rho_ua, label=\"original CACE\", lw=1, ls=\"--\")\n",
    "ax[0].set_title(f\"(a) same potential  |Δρ|={abs(da_x-da_u):.1e} g/cm³\")\n",
    "ax[1].plot(t_ps, rho_xb, label=\"xnn (independent)\", lw=1)\n",
    "ax[1].plot(t_ps, rho_ub, label=\"original CACE (independent)\", lw=1, ls=\"--\")\n",
    "ax[1].set_title(f\"(b) independently trained  |Δρ|={abs(db_x-db_u):.1e} g/cm³\")\n",
    "for a in ax:\n",
    "    a.axvline(xc, color=\"gray\", ls=\":\", lw=1)\n",
    "    a.axhline(RHO_EXP, color=\"k\", ls=\"-.\", lw=1, label=f\"exp ≈ {RHO_EXP}\")\n",
    "    a.set_xlabel(\"time [ps]\"); a.legend(fontsize=8)\n",
    "ax[0].set_ylabel(\"density [g/cm³]\")\n",
    "plt.tight_layout(); plt.savefig(\"argon_density_md.png\", dpi=120); plt.show()\n",
    "\n",
    "print(f\"{'':<20}{'xnn':>12}{'original CACE':>16}{'|diff|':>12}\")\n",
    "print(\"-\" * 60)\n",
    "print(f\"{'(a) same PES':<20}{da_x:>12.4f}{da_u:>16.4f}{abs(da_x-da_u):>12.1e}\")\n",
    "print(f\"{'(b) independent':<20}{db_x:>12.4f}{db_u:>16.4f}{abs(db_x-db_u):>12.1e}\")\n",
    "print(f\"{'experiment':<20}{RHO_EXP:>12.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "632b6116",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "* **Track (a)**: copying the trained original-CACE weights into `xnn` gives\n",
    "  identical energy/forces/stress and **identical NPT densities**; the `xnn`\n",
    "  inference/MD path reproduces the original CACE exactly.\n",
    "* **Track (b)**: an independently trained `xnn` CACE lands within the thermal\n",
    "  fluctuations of the original, both near the experimental liquid-Ar density\n",
    "  (~1.41 g/cm³).\n",
    "\n",
    "Same conclusions, same pipeline, fourth model family: CACE joins MACE, NequIP\n",
    "and Allegro as a faithful member of the xnn GNN family (shared `GNNPotential`\n",
    "base, featurizers, `ForceStressOutput`, ASE deploy), and the only one that\n",
    "needs no e3nn."
   ]
  }
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