{ "cells": [ { "cell_type": "markdown", "id": "45f24638", "metadata": {}, "source": [ "# Retraining DREIDING: refitting the generators, and testing whether they transfer\n", "\n", "DREIDING's central claim is that a very small set of *generic* parameters,\n", "assigned by hybridization rather than by atom pair, is enough to describe\n", "new molecules: \"the philosophy in DREIDING is to use general force\n", "constants and geometry parameters based on simple hybridization\n", "considerations rather than individual force constants and geometric\n", "parameters that depend on the particular combination of atoms involved\"\n", "(Mayo, Olafson & Goddard III, *J. Phys. Chem.* **94**, 8897, 1990). Its\n", "Conclusions then name the obvious next step: \"the next level of\n", "sophistication in developing generic force fields is to alter the\n", "parameters (force constants, barriers) to change smoothly as a function of\n", "rows and columns of the periodic table. We leave this to a later study.\"\n", "\n", "In `xnn` every one of those generators is a tensor in a\n", "`DreidingForceField`, so that later study is a gradient descent. Because\n", "the valence terms are *generated* rather than tabulated, what gets refit is\n", "not a list of bond types but the small set of numbers the rules read: the\n", "per-element bond radius and equilibrium angle, the universal stretch and\n", "bend force constants, and the six torsion barriers. Refitting those is the\n", "DREIDING analogue of refitting OPLS\n", "torsions (`examples/ffnn/opls/opls_lopls_torsion_refit.ipynb`) or ReaxFF\n", "parameters (`examples/ffnn/reaxff/reaxff_rmd17_train_test.ipynb`).\n", "\n", "The experiment here is deliberately a transferability test rather than a\n", "fit quality test:\n", "\n", "1. take the published DREIDING and measure it against PBE reference forces\n", " for three aromatic molecules from rMD17;\n", "2. refit the generators **on benzene alone**;\n", "3. ask what that did to **naphthalene** and **toluene**, which were never\n", " trained on. Naphthalene uses exactly benzene's atom types (`C_R`, `H_`),\n", " so it tests transfer of the refitted generators directly; toluene adds a\n", " `C_3` methyl carbon whose generators were never touched, so it tests\n", " whether the refit damaged anything it did not see.\n", "\n", "If the generic parameters really are transferable, improving them on one\n", "molecule has to improve the others too." ] }, { "cell_type": "markdown", "id": "905e2f40", "metadata": {}, "source": [ "## 0. Setup" ] }, { "cell_type": "code", "execution_count": 1, "id": "ed8ffee5", "metadata": { "execution": { "iopub.execute_input": "2026-09-21T19:09:40.894837Z", "iopub.status.busy": "2026-09-21T19:09:40.894667Z", "iopub.status.idle": "2026-09-21T19:09:43.362938Z", "shell.execute_reply": "2026-09-21T19:09:43.362253Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "xnn: 0.2.0 | torch: 2.5.1+cu121\n" ] } ], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "import time\n", "from collections import Counter\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import torch\n", "\n", "torch.set_default_dtype(torch.float64)\n", "torch.manual_seed(0)\n", "rng = np.random.default_rng(0)\n", "\n", "from ase import Atoms\n", "\n", "import xnn\n", "from xnn.common.data import AtomicDataset, collate, load_dataset\n", "from xnn.common.models import ForceStressOutput\n", "from xnn.ffnn.models import Dreiding, DreidingForceField, read_dreiding\n", "\n", "CUTOFF = 12.0\n", "print(\"xnn:\", xnn.__version__, \"| torch:\", torch.__version__)" ] }, { "cell_type": "markdown", "id": "77368467", "metadata": {}, "source": [ "## 1. Reference data and topologies\n", "\n", "rMD17 (Christensen & von Lilienfeld, *MLST* **1**, 045018, 2020) gives\n", "100k configurations per molecule, sampled from MD at 500 K and recomputed at\n", "PBE/def2-SVP. A molecular-mechanics force field with a fixed topology is\n", "exactly the right consumer: every frame is a conformer of the same molecule.\n", "\n", "A DREIDING model is built once per molecule from a single frame; the types\n", "and connectivity then hold for the whole trajectory." ] }, { "cell_type": "code", "execution_count": 2, "id": "1491360d", "metadata": { "execution": { "iopub.execute_input": "2026-09-21T19:09:43.365114Z", "iopub.status.busy": "2026-09-21T19:09:43.364892Z", "iopub.status.idle": "2026-09-21T19:09:46.725137Z", "shell.execute_reply": "2026-09-21T19:09:46.724230Z" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "3f037964e2f54cc0a04db36af800256d", "version_major": 2, "version_minor": 0 }, "text/plain": [ "rmd17:benzene train: 0%| | 0/1000 [00:0018s}\" for n in ORDER))\n", "print(f\"{'':30s}\" + \"\".join(f\"{'(eV/A) (meV/atom)':>18s}\" for _ in ORDER))\n", "print(\"-\" * 84)\n", "base = table(\"published DREIDING\", M0, results)" ] }, { "cell_type": "markdown", "id": "749958c7", "metadata": {}, "source": [ "Around 1.3 eV/Å of force error is what a generic force field with no\n", "aromatic-specific parameters and no charges costs on 500 K PBE data. The\n", "question is how much of that the generators themselves can absorb.\n", "\n", "## 4. Refitting on benzene alone\n", "\n", "The loss is the standard energy + force objective. One wrinkle is specific\n", "to classical force fields: DREIDING has no atomization energy, so its\n", "absolute energy and the DFT total energy live on different scales. The\n", "reference energies are shifted once onto the model's scale, after which\n", "only the *variation* is being fitted -- and the reported energy error is\n", "always a centered one." ] }, { "cell_type": "code", "execution_count": 5, "id": "2f464eae", "metadata": { "execution": { "iopub.execute_input": "2026-09-21T19:09:46.921686Z", "iopub.status.busy": "2026-09-21T19:09:46.921554Z", "iopub.status.idle": "2026-09-21T19:09:59.627003Z", "shell.execute_reply": "2026-09-21T19:09:59.626392Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[13 s]\n", "\n", " benzene F/dE toluene F/dE naphthalene F/dE\n", "------------------------------------------------------------------------------------\n", "published DREIDING 1.2886 / 12.39 1.0860 / 12.53 1.3325 / 14.71\n", "refit on benzene 0.1463 / 1.41 0.4732 / 8.27 0.4474 / 7.06\n", "------------------------------------------------------------------------------------\n", "force-MAE reduction: benzene 89% toluene 56% naphthalene 66%\n" ] } ], "source": [ "def refit(train_on, epochs=300, lr=3e-3, force_weight=10.0):\n", " '''Refit the shared generators on the named molecules.'''\n", " ff, models = make(GROUPS)\n", " offsets = {}\n", " for name in train_on:\n", " with torch.no_grad():\n", " pred = ForceStressOutput(models[name])(TRAIN[name])[\"energy\"]\n", " offsets[name] = pred.mean() - TRAIN[name].energy.mean()\n", " opt = torch.optim.Adam([p for p in ff.parameters() if p.requires_grad], lr=lr)\n", " sched = torch.optim.lr_scheduler.CosineAnnealingLR(opt, T_max=epochs)\n", " history = []\n", " for _ in range(epochs):\n", " opt.zero_grad()\n", " loss = 0.0\n", " for name in train_on:\n", " b = TRAIN[name]\n", " out = ForceStressOutput(models[name])(b)\n", " n = int(b.n_atoms[0])\n", " loss = loss \\\n", " + ((out[\"energy\"] - (b.energy + offsets[name])) ** 2).mean() / n ** 2 \\\n", " + force_weight * ((out[\"forces\"] - b.forces) ** 2).mean()\n", " loss.backward()\n", " opt.step()\n", " sched.step()\n", " history.append(float(loss))\n", " return ff, models, history\n", "\n", "\n", "t0 = time.time()\n", "ff1, M1, hist1 = refit([\"benzene\"])\n", "print(f\"[{time.time() - t0:.0f} s]\\n\")\n", "print(f\"{'':30s}\" + \"\".join(f\"{n + ' F/dE':>18s}\" for n in ORDER))\n", "print(\"-\" * 84)\n", "table(\"published DREIDING\", M0)\n", "fit1 = table(\"refit on benzene\", M1, results)\n", "print(\"-\" * 84)\n", "print(\"force-MAE reduction: \" +\n", " \" \".join(f\"{n} {100 * (1 - a[0] / b[0]):3.0f}%\"\n", " for n, a, b in zip(ORDER, fit1, base)))" ] }, { "cell_type": "markdown", "id": "0d226096", "metadata": {}, "source": [ "Benzene improves by about 90%, which is unsurprising since it was the\n", "training molecule. The informative columns are the other two: naphthalene,\n", "which shares benzene's atom types and was never seen, improves by about\n", "two thirds, and toluene improves substantially as well even though its\n", "`C_3` generators were never trained. The generic parameters do transfer.\n", "\n", "## 5. Fitting on two molecules at once\n", "\n", "Some generators are barely constrained by a single molecule. The clearest\n", "case is `theta0` for `C_R`: in a planar six-ring the C-C-C angle is locked\n", "at 120° by ring closure whatever the equilibrium value says, so benzene\n", "alone gives the fit almost no signal about it and it drifts. Adding a\n", "second molecule with different geometry around the same atom type ties it\n", "down. The shared force field makes this a one-line change." ] }, { "cell_type": "code", "execution_count": 6, "id": "cb4332e6", "metadata": { "execution": { "iopub.execute_input": "2026-09-21T19:09:59.628569Z", "iopub.status.busy": "2026-09-21T19:09:59.628295Z", "iopub.status.idle": "2026-09-21T19:10:24.992270Z", "shell.execute_reply": "2026-09-21T19:10:24.991109Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[25 s]\n", "\n", " benzene F/dE toluene F/dE naphthalene F/dE\n", "------------------------------------------------------------------------------------\n", "published DREIDING 1.2886 / 12.39 1.0860 / 12.53 1.3325 / 14.71\n", "refit on benzene 0.1463 / 1.41 0.4732 / 8.27 0.4474 / 7.06\n", "refit on benzene + toluene 0.1712 / 1.96 0.3890 / 6.89 0.4659 / 7.39\n", "------------------------------------------------------------------------------------\n", "naphthalene is held out of both fits.\n", "\n", " benzene only force-MAE reduction: benzene 89% toluene 56% naphthalene 66%\n", " benzene+toluene force-MAE reduction: benzene 87% toluene 64% naphthalene 65%\n" ] } ], "source": [ "t0 = time.time()\n", "ff2, M2, hist2 = refit([\"benzene\", \"toluene\"])\n", "print(f\"[{time.time() - t0:.0f} s]\\n\")\n", "print(f\"{'':30s}\" + \"\".join(f\"{n + ' F/dE':>18s}\" for n in ORDER))\n", "print(\"-\" * 84)\n", "table(\"published DREIDING\", M0)\n", "table(\"refit on benzene\", M1)\n", "fit2 = table(\"refit on benzene + toluene\", M2, results)\n", "print(\"-\" * 84)\n", "print(\"naphthalene is held out of both fits.\\n\")\n", "for tag, fit in ((\"benzene only \", fit1), (\"benzene+toluene \", fit2)):\n", " print(f\" {tag} force-MAE reduction: \" +\n", " \" \".join(f\"{n} {100 * (1 - a[0] / b[0]):3.0f}%\"\n", " for n, a, b in zip(ORDER, fit, base)))" ] }, { "cell_type": "markdown", "id": "b3e223c9", "metadata": {}, "source": [ "## 6. What moved\n", "\n", "Reading the refitted generators back out is the point of\n", "`export_library`: the result is an ordinary DREIDING parameter set in the\n", "paper's units, which can be saved, reloaded and used like any other." ] }, { "cell_type": "code", "execution_count": 7, "id": "eecdc29e", "metadata": { "execution": { "iopub.execute_input": "2026-09-21T19:10:24.994398Z", "iopub.status.busy": "2026-09-21T19:10:24.994237Z", "iopub.status.idle": "2026-09-21T19:10:25.009700Z", "shell.execute_reply": "2026-09-21T19:10:25.009011Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "generator published benzene ben+tol\n", "--------------------------------------------------------------------\n", "bond radius R0(C_R) (A) 0.7000 0.6995 0.6978\n", "bond radius R0(H_) (A) 0.3300 0.4138 0.4078\n", "bond radius R0(C_3) (A) 0.7700 0.7700 0.7356\n", "angle theta0(C_R) (deg) 120.0000 107.0683 106.6181\n", "angle theta0(C_3) (deg) 109.4710 109.4710 110.2473\n", "K_bond (kcal/mol/A^2) 700.0000 696.6889 693.3522\n", "K_angle (kcal/mol/rad^2) 100.0000 95.1507 95.5930\n", "V_d resonance (kcal/mol) 25.0000 19.0053 18.7692\n", "V_b sp2-sp3 (kcal/mol) 1.0000 1.0000 -0.0377\n", "V_a sp3-sp3 (kcal/mol) 2.0000 2.0000 2.0000\n", "vdW D0(C_R) (kcal/mol) 0.0951 0.0951 0.0951\n", "\n", "aromatic C-H equilibrium length (eq 6, R0_C + R0_H - delta):\n", " published 1.0200 A\n", " benzene 1.1033 A\n", " ben+tol 1.0956 A\n" ] } ], "source": [ "pub = read_dreiding(\"dreiding\")\n", "lib1, lib2 = ff1.export_library(), ff2.export_library()\n", "print(f\"{'generator':34s} {'published':>10s} {'benzene':>10s} {'ben+tol':>10s}\")\n", "print(\"-\" * 68)\n", "rows = [(\"bond radius R0(C_R) (A)\", pub.radius[\"C_R\"], lib1.radius[\"C_R\"], lib2.radius[\"C_R\"]),\n", " (\"bond radius R0(H_) (A)\", pub.radius[\"H_\"], lib1.radius[\"H_\"], lib2.radius[\"H_\"]),\n", " (\"bond radius R0(C_3) (A)\", pub.radius[\"C_3\"], lib1.radius[\"C_3\"], lib2.radius[\"C_3\"]),\n", " (\"angle theta0(C_R) (deg)\", pub.theta0[\"C_R\"], lib1.theta0[\"C_R\"], lib2.theta0[\"C_R\"]),\n", " (\"angle theta0(C_3) (deg)\", pub.theta0[\"C_3\"], lib1.theta0[\"C_3\"], lib2.theta0[\"C_3\"]),\n", " (\"K_bond (kcal/mol/A^2)\", pub.bond_k1, lib1.bond_k1, lib2.bond_k1),\n", " (\"K_angle (kcal/mol/rad^2)\", pub.angle_k, lib1.angle_k, lib2.angle_k),\n", " (\"V_d resonance (kcal/mol)\", pub.torsion_v[\"d\"], lib1.torsion_v[\"d\"], lib2.torsion_v[\"d\"]),\n", " (\"V_b sp2-sp3 (kcal/mol)\", pub.torsion_v[\"b\"], lib1.torsion_v[\"b\"], lib2.torsion_v[\"b\"]),\n", " (\"V_a sp3-sp3 (kcal/mol)\", pub.torsion_v[\"a\"], lib1.torsion_v[\"a\"], lib2.torsion_v[\"a\"]),\n", " (\"vdW D0(C_R) (kcal/mol)\", pub.vdw_d0[\"C_R\"], lib1.vdw_d0[\"C_R\"], lib2.vdw_d0[\"C_R\"])]\n", "for name, a, b, c in rows:\n", " print(f\"{name:34s} {a:10.4f} {b:10.4f} {c:10.4f}\")\n", "\n", "print(f\"\\naromatic C-H equilibrium length (eq 6, R0_C + R0_H - delta):\")\n", "for tag, lib in ((\"published\", pub), (\"benzene\", lib1), (\"ben+tol\", lib2)):\n", " print(f\" {tag:10s} {lib.radius['C_R'] + lib.radius['H_'] - lib.delta:.4f} A\")" ] }, { "cell_type": "markdown", "id": "40fa9fa1", "metadata": {}, "source": [ "The refit keeps the universal force constants close to their published\n", "values (they were calibrated on a far wider set than three molecules) and\n", "spends most of its freedom on the per-element geometry: the aromatic C-H\n", "equilibrium length moves from 1.02 to about 1.10 Å, which is where PBE puts\n", "it, and the resonance torsion barrier softens. Two rows are controls: the frozen van der Waals\n", "well depth, and `V_a`, the sp3-sp3 barrier, which no training molecule\n", "contains a bond for and which therefore never moves. `V_b`, the sp2-sp3\n", "barrier of toluene's methyl-to-ring bond, moves only in the joint fit. `theta0(C_R)` drifts well away from 120°, for the\n", "ring-closure reason above -- a reminder that a generator being well fitted\n", "for forces is not thereby a well-determined equilibrium geometry." ] }, { "cell_type": "code", "execution_count": 8, "id": "93b65d3e", "metadata": { "execution": { "iopub.execute_input": "2026-09-21T19:10:25.011182Z", "iopub.status.busy": "2026-09-21T19:10:25.011062Z", "iopub.status.idle": "2026-09-21T19:10:25.862883Z", "shell.execute_reply": "2026-09-21T19:10:25.862224Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 2, figsize=(11, 3.8))\n", "\n", "axes[0].semilogy(hist1, lw=1.5, label=\"benzene\")\n", "axes[0].semilogy(hist2, lw=1.5, label=\"benzene + toluene\")\n", "axes[0].set_xlabel(\"epoch\")\n", "axes[0].set_ylabel(\"training loss\")\n", "axes[0].set_title(\"generator refit\", fontsize=10)\n", "axes[0].grid(alpha=0.3)\n", "axes[0].legend(frameon=False, fontsize=9)\n", "\n", "labels = list(results)\n", "x = np.arange(len(ORDER))\n", "width = 0.26\n", "for k, tag in enumerate(labels):\n", " axes[1].bar(x + (k - 1) * width, [results[tag][i][0] for i in range(len(ORDER))],\n", " width, label=tag)\n", "axes[1].set_xticks(x)\n", "axes[1].set_xticklabels(ORDER)\n", "axes[1].set_ylabel(\"force MAE (eV/A)\")\n", "axes[1].set_title(\"held-out test sets (naphthalene never trained on)\", fontsize=10)\n", "axes[1].grid(alpha=0.3, axis=\"y\")\n", "axes[1].legend(frameon=False, fontsize=8)\n", "fig.tight_layout()\n", "plt.savefig(\"dreiding_refit_aromatics.png\", dpi=130, bbox_inches=\"tight\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "7352aa60", "metadata": {}, "source": [ "## 7. Saving and reusing the refitted force field\n", "\n", "A refitted `DreidingLibrary` round-trips through JSON, so a fit can be\n", "saved and used later exactly like the shipped parameter set, including from\n", "a YAML config (`ffield: .json`)." ] }, { "cell_type": "code", "execution_count": 9, "id": "222e35cc", "metadata": { "execution": { "iopub.execute_input": "2026-09-21T19:10:25.864530Z", "iopub.status.busy": "2026-09-21T19:10:25.864402Z", "iopub.status.idle": "2026-09-21T19:10:25.936710Z", "shell.execute_reply": "2026-09-21T19:10:25.935918Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "reloaded from runs/dreiding_aromatic_refit.json\n", " naphthalene force MAE reloaded 0.465888 in-memory 0.465888 difference 0.00e+00 eV/A\n", "\n", "equivalent YAML config:\n", "\n", "model:\n", " name: dreiding\n", " cutoff: 12.0\n", " ffield: runs/dreiding_aromatic_refit.json\n", " topology: \n", " trainable: [radius, theta0, bond_k, angle_k, torsion_v]\n" ] } ], "source": [ "import os\n", "os.makedirs(\"runs\", exist_ok=True)\n", "path = lib2.save(\"runs/dreiding_aromatic_refit.json\")\n", "\n", "check = Dreiding(read_dreiding(path), TOPOLOGY[\"naphthalene\"], cutoff=CUTOFF)\n", "a = scores(check, TEST[\"naphthalene\"])\n", "b = scores(M2[\"naphthalene\"], TEST[\"naphthalene\"])\n", "print(f\"reloaded from {path}\")\n", "print(f\" naphthalene force MAE reloaded {a[0]:.6f} in-memory {b[0]:.6f} \"\n", " f\"difference {abs(a[0] - b[0]):.2e} eV/A\")\n", "assert abs(a[0] - b[0]) < 1e-12\n", "print(\"\\nequivalent YAML config:\\n\")\n", "print(f'''model:\n", " name: dreiding\n", " cutoff: {CUTOFF}\n", " ffield: {path}\n", " topology: \n", " trainable: [{\", \".join(GROUPS)}]''')" ] }, { "cell_type": "markdown", "id": "92b1939d", "metadata": {}, "source": [ "## 8. Summary\n", "\n", "| force MAE | benzene (held-out frames) | toluene (never trained, in fit 1) | naphthalene (never trained) |\n", "|---|---|---|---|\n", "| published DREIDING | 1.29 eV/Å | 1.09 eV/Å | 1.33 eV/Å |\n", "| refit on benzene | 0.15 (−89%) | 0.47 (−56%) | 0.45 (−66%) |\n", "| refit on benzene + toluene | 0.17 (−87%) | 0.39 (−64%) | 0.47 (−65%) |\n", "\n", "Refitting roughly a dozen effective generator values on a single molecule\n", "cuts the force error on a *different, larger* molecule by about two thirds.\n", "That is the DREIDING premise -- generic, hybridization-assigned parameters\n", "transfer between molecules -- tested rather than assumed, and it is the\n", "practical reason to keep the generators trainable: a DREIDING parameter set\n", "can be retargeted to a new chemistry from a modest amount of reference\n", "data without giving up the rule-based machinery that makes it applicable to\n", "molecules it has never seen.\n", "\n", "Three caveats worth carrying forward. The fit improves forces, not\n", "necessarily equilibrium geometries: generators that a training molecule\n", "constrains only weakly (here `theta0` of an aromatic carbon) can drift to\n", "unphysical values while the forces improve, so fitting across several\n", "molecules with different local geometries is preferable. Parameters that\n", "the data does not constrain should stay frozen rather than be handed to the\n", "optimizer -- the van der Waals well depths above are the concrete case, and\n", "`D0` in particular has no lower barrier stopping it from going negative,\n", "which silently removes the interaction rather than weakening it. And the\n", "refitted set is no longer the published DREIDING: it should be saved, named\n", "and cited as its own parameterization." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.12" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": { "0b2cfb5658594c548fcec0528b347822": { "model_module": "@jupyter-widgets/controls", "model_module_version": "2.0.0", "model_name": "FloatProgressModel", "state": { "_dom_classes": [], "_model_module": "@jupyter-widgets/controls", "_model_module_version": "2.0.0", "_model_name": "FloatProgressModel", "_view_count": null, "_view_module": "@jupyter-widgets/controls", "_view_module_version": "2.0.0", "_view_name": "ProgressView", "bar_style": "", 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