diff --git a/envs/environment-cpu.yml b/envs/environment-cpu.yml
index f3719b2..7dc4eae 100644
--- a/envs/environment-cpu.yml
+++ b/envs/environment-cpu.yml
@@ -7,7 +7,7 @@ channels:
   - pytorch
   - conda-forge/label/libint_dev
 dependencies:
-  - python==3.10.*
+  - python==3.9.*
 
   # Standard data analysis tools
   - pandas==1.*
@@ -20,6 +20,9 @@ dependencies:
   # Quantum chemistry
   - psi4==1.8.*
 
+  # Interatomic forcefields
+  - dscribe==2.1.*
+
   # Use Conda PyTorch to avoid OpenMP disagreement with other libraries
   - pytorch==2.0.*
   - cpuonly
diff --git a/jitterbug/model/base.py b/jitterbug/model/base.py
index dc00870..48cd9b7 100644
--- a/jitterbug/model/base.py
+++ b/jitterbug/model/base.py
@@ -16,11 +16,13 @@ def train(self, data: list[Atoms]) -> object:
         """
         raise NotImplementedError()
 
-    def mean_hessian(self, model: object) -> list[np.ndarray]:
+    def mean_hessian(self, model: object) -> np.ndarray:
         """Produce the most-likely Hessian given the model
 
         Args:
-            model: Model trained by this
+            model: Model trained by this class
+        Returns:
+            The most-likely Hessian given the model
         """
 
     def sample_hessians(self, model: object, num_samples: int) -> list[np.ndarray]:
diff --git a/jitterbug/model/mbtr.py b/jitterbug/model/mbtr.py
new file mode 100644
index 0000000..f1e940c
--- /dev/null
+++ b/jitterbug/model/mbtr.py
@@ -0,0 +1,96 @@
+"""Learn a potential energy surface with the MBTR representation
+
+MBTR is an easy route for learning a forcefield because it represents
+a molecule as a single vector, which means we can case the learning
+problem as a simple "molecule->energy" learning problem. Other methods,
+such as SOAP, provided atomic-level features that must require an
+extra step "molecule->atoms->energy/atom->energy".
+"""
+from shutil import rmtree
+
+from ase.calculators.calculator import Calculator, all_changes
+from ase.vibrations import Vibrations
+from ase import Atoms
+from sklearn.linear_model import LinearRegression
+from dscribe.descriptors import MBTR
+import numpy as np
+
+from jitterbug.model.base import EnergyModel
+
+
+class MBTRCalculator(Calculator):
+    """A learnable forcefield based on GPR and fingerprints computed using DScribe"""
+
+    implemented_properties = ['energy', 'forces']
+    default_parameters = {
+        'descriptor': MBTR(
+            species=["H", "C", "N", "O"],
+            geometry={"function": "inverse_distance"},
+            grid={"min": 0, "max": 1, "n": 100, "sigma": 0.1},
+            weighting={"function": "exp", "scale": 0.5, "threshold": 1e-3},
+            periodic=False,
+            normalization="l2",
+        ),
+        'model': LinearRegression(),
+        'intercept': 0.,  # Normalizing parameters
+        'scale': 0.
+    }
+
+    def calculate(self, atoms=None, properties=('energy', 'forces'), system_changes=all_changes):
+        # Compute the energy using the learned model
+        desc = self.parameters['descriptor'].create_single(atoms)
+        energy_no_int = self.parameters['model'].predict(desc[None, :])
+        self.results['energy'] = energy_no_int[0] * self.parameters['scale'] + self.parameters['intercept']
+
+        # If desired, compute forces numerically
+        if 'forces' in properties:
+            # calculate_numerical_forces use that the calculation of the input atoms,
+            #  even though it is a method of a calculator and not of the input atoms :shrug:
+            temp_atoms: Atoms = atoms.copy()
+            temp_atoms.calc = self
+            self.results['forces'] = self.calculate_numerical_forces(temp_atoms)
+
+    def train(self, train_set: list[Atoms]):
+        """Train the embedded forcefield object
+
+        Args:
+            train_set: List of Atoms objects containing at least the energy
+        """
+
+        # Determine the mean energy and subtract it off
+        energies = np.array([atoms.get_potential_energy() for atoms in train_set])
+        self.parameters['intercept'] = energies.mean()
+        energies -= self.parameters['intercept']
+        self.parameters['scale'] = energies.std()
+        energies /= self.parameters['scale']
+
+        # Compute the descriptors and use them to fit the model
+        desc = self.parameters['descriptor'].create(train_set)
+        self.parameters['model'].fit(desc, energies)
+
+
+class MBTREnergyModel(EnergyModel):
+    """Use the MBTR representation to model the potential energy surface
+
+    Args:
+        calc: Calculator used to fit the potential energy surface
+        reference: Reference structure at which we compute the Hessian
+    """
+
+    def __init__(self, calc: MBTRCalculator, reference: Atoms):
+        super().__init__()
+        self.calc = calc
+        self.reference = reference
+
+    def train(self, data: list[Atoms]) -> MBTRCalculator:
+        self.calc.train(data)
+        return self.calc
+
+    def mean_hessian(self, model: MBTRCalculator) -> np.ndarray:
+        self.reference.calc = model
+        try:
+            vib = Vibrations(self.reference, name='mbtr-temp')
+            vib.run()
+            return vib.get_vibrations().get_hessian_2d()
+        finally:
+            rmtree('mbtr-temp', ignore_errors=True)
diff --git a/notebooks/proof-of-concept/1_compute-random-offsets.ipynb b/notebooks/proof-of-concept/1_compute-random-offsets.ipynb
index 8bde676..10ae373 100644
--- a/notebooks/proof-of-concept/1_compute-random-offsets.ipynb
+++ b/notebooks/proof-of-concept/1_compute-random-offsets.ipynb
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "id": "c6a28419-6831-4197-8973-00c5591e19cb",
    "metadata": {
     "tags": []
@@ -38,7 +38,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "id": "c6be56c5-a460-4acd-9b89-8c3d9c812f5f",
    "metadata": {
     "tags": [
@@ -51,7 +51,7 @@
     "method = 'hf'\n",
     "basis = 'def2-svpd'\n",
     "threads = min(os.cpu_count(), 12)\n",
-    "step_size: float = 0.005 # Perturbation amount, used as maximum L2 norm"
+    "step_size: float = 0.01 # Perturbation amount, used as maximum L2 norm"
    ]
   },
   {
@@ -64,7 +64,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "id": "0b6794cd-477f-45a1-b96f-2332804ddb20",
    "metadata": {},
    "outputs": [],
@@ -83,12 +83,23 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 4,
    "id": "ad9fd725-b1ba-4fec-ae41-959be0e540b3",
    "metadata": {
     "tags": []
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Atoms(symbols='O2N4C8H10', pbc=False, forces=..., calculator=SinglePointCalculator(...))"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "atoms = read(Path('data') / 'exact' / f'{run_name}.xyz')\n",
     "atoms"
@@ -113,7 +124,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 5,
    "id": "23502eea-0974-4248-8f19-e85447069c61",
    "metadata": {
     "tags": []
@@ -126,7 +137,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 6,
    "id": "bf1366fc-d9a7-4a98-b9c9-cb3a0209b406",
    "metadata": {
     "tags": []
@@ -146,7 +157,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 7,
    "id": "d4f21e81-5ec3-4877-a4d1-402077be2ee8",
    "metadata": {
     "tags": []
@@ -168,12 +179,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 8,
    "id": "0915595d-133a-43df-84fc-4ff6a3b538ea",
    "metadata": {
     "tags": []
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "  Memory set to   3.815 GiB by Python driver.\n",
+      "  Threads set to 12 by Python driver.\n"
+     ]
+    }
+   ],
    "source": [
     "calc = Psi4(method=method, basis=basis, num_threads=threads, memory='4096MB')"
    ]
@@ -188,12 +209,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 9,
    "id": "e2a28593-2634-4bb7-ae5b-8f557937bda1",
    "metadata": {
     "tags": []
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Need to run 2701 calculations for full accuracy.\n"
+     ]
+    }
+   ],
    "source": [
     "n_atoms = len(atoms)\n",
     "to_compute = 3 * n_atoms + 3 * n_atoms * (3 * n_atoms + 1) // 2 + 1\n",
@@ -202,12 +231,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 10,
    "id": "8bf40523-dcaa-4046-a9c6-74e35178e87f",
    "metadata": {
     "tags": []
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Already done 427. 2274 left to do.\n"
+     ]
+    }
+   ],
    "source": [
     "with connect(db_path) as db:\n",
     "    done = len(db)\n",
@@ -219,7 +256,31 @@
    "execution_count": null,
    "id": "a6fa1b33-defc-4b35-895d-052eb64453fb",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "  0%|                                                                                                                                                                                                                                                            | 0/2701 [00:00<?, ?it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "  Memory set to   3.815 GiB by Python driver.\n",
+      "  Threads set to 12 by Python driver.\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      " 59%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▍                                                                                                | 1600/2701 [2:06:01<2:33:24,  8.36s/it]"
+     ]
+    }
+   ],
    "source": [
     "pbar = tqdm(total=to_compute)\n",
     "pbar.update(done)\n",
@@ -271,7 +332,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.12"
+   "version": "3.9.17"
   }
  },
  "nbformat": 4,
diff --git a/notebooks/proof-of-concept/2_approximate-hessians.ipynb b/notebooks/proof-of-concept/2_approximate-hessians.ipynb
index 49d5823..505d56e 100644
--- a/notebooks/proof-of-concept/2_approximate-hessians.ipynb
+++ b/notebooks/proof-of-concept/2_approximate-hessians.ipynb
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 112,
+   "execution_count": 1,
    "id": "ebbbc7f5-3007-420f-861a-9f65f84436be",
    "metadata": {
     "tags": []
@@ -40,7 +40,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 113,
+   "execution_count": 2,
    "id": "99bd4c92-9a7b-4e88-ac45-dbf30fbfc9e0",
    "metadata": {
     "tags": [
@@ -66,7 +66,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 114,
+   "execution_count": 3,
    "id": "a8be3c37-bf1f-4ba4-ba8f-afff6d6bed7d",
    "metadata": {
     "tags": []
@@ -89,7 +89,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 115,
+   "execution_count": 4,
    "id": "797b96d8-050c-4bdf-9815-586cfb5bc311",
    "metadata": {
     "tags": []
@@ -119,7 +119,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 116,
+   "execution_count": 5,
    "id": "7389208d-9323-492c-8fc5-d05a372206c6",
    "metadata": {
     "tags": []
@@ -132,7 +132,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 117,
+   "execution_count": 6,
    "id": "a9965595-532c-4067-ba24-7620bd977007",
    "metadata": {
     "tags": []
@@ -154,7 +154,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 118,
+   "execution_count": 7,
    "id": "d6a7d756-37d3-44e0-b5e2-348d07c9d296",
    "metadata": {
     "tags": []
@@ -167,7 +167,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 119,
+   "execution_count": 8,
    "id": "35baa4a3-5e0e-4067-92ea-f29b3c080477",
    "metadata": {
     "tags": []
@@ -195,7 +195,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 120,
+   "execution_count": 9,
    "id": "70d80f87-9983-4bd5-a6ae-b9c966b0d838",
    "metadata": {
     "tags": []
@@ -207,7 +207,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 121,
+   "execution_count": 10,
    "id": "f548b145-0aa8-47f7-802b-6b7232a74bd3",
    "metadata": {
     "tags": []
@@ -219,7 +219,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 122,
+   "execution_count": 11,
    "id": "d7cd7762-6e12-4dcd-b564-67a33b18d9e0",
    "metadata": {
     "tags": []
@@ -239,7 +239,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 123,
+   "execution_count": 12,
    "id": "425b77a9-7fd7-40da-af6f-eaed197c9ab6",
    "metadata": {
     "tags": []
@@ -247,7 +247,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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",
+      "image/png": "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",
       "text/plain": [
        "<Figure size 400x200 with 2 Axes>"
       ]
@@ -280,7 +280,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 124,
+   "execution_count": 13,
    "id": "00a10907-667a-413c-851d-d47f0eff092b",
    "metadata": {},
    "outputs": [],
@@ -298,7 +298,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 125,
+   "execution_count": 14,
    "id": "d48893fd-df0d-4fa8-bfbe-0d04b71fbf1a",
    "metadata": {
     "tags": []
@@ -312,7 +312,7 @@
        "       [1.08009177e-03, 3.94902961e-03, 4.15881408e+00]])"
       ]
      },
-     "execution_count": 125,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -323,7 +323,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 126,
+   "execution_count": 15,
    "id": "9b311dea-5744-4211-81cb-40aa1183301e",
    "metadata": {
     "tags": []
@@ -337,7 +337,7 @@
        "       [8.59920621e-03, 6.10182117e-01, 2.73150623e+01]])"
       ]
      },
-     "execution_count": 126,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -348,7 +348,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 127,
+   "execution_count": 16,
    "id": "addd7bef-854a-4b9f-96e9-2aa01b652495",
    "metadata": {
     "tags": []
@@ -356,7 +356,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 400x200 with 2 Axes>"
       ]
@@ -389,7 +389,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 128,
+   "execution_count": 17,
    "id": "abbbbfd6-7d17-4b93-880a-3352903b56c4",
    "metadata": {
     "tags": []
@@ -401,7 +401,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 129,
+   "execution_count": 18,
    "id": "fdd80af3-8c18-40d8-b971-4a473bc91498",
    "metadata": {},
    "outputs": [
@@ -411,7 +411,7 @@
        "7.268532902551082"
       ]
      },
-     "execution_count": 129,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -422,7 +422,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 130,
+   "execution_count": 19,
    "id": "6b1af348-4bc9-4ced-9a12-44b3e49abe9c",
    "metadata": {
     "tags": []
@@ -434,7 +434,7 @@
        "5.5067174465850215"
       ]
      },
-     "execution_count": 130,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -462,7 +462,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 131,
+   "execution_count": 20,
    "id": "bce41a81-6c88-4b0c-9d8d-0891d1832fd6",
    "metadata": {
     "tags": []
@@ -483,7 +483,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 21,
    "id": "fe39ce86-1806-4367-8c86-e3ef58f81f84",
    "metadata": {
     "tags": []
@@ -493,7 +493,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      " 62%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▏                                                                                           | 10/16 [00:00<00:00, 16.03it/s]"
+      "100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 16/16 [00:04<00:00,  3.98it/s]\n"
      ]
     }
    ],
@@ -519,12 +519,23 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 22,
    "id": "1c6706a9-a27f-448f-81d4-957939bb2ca8",
    "metadata": {
     "tags": []
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 350x200 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "fig, ax = plt.subplots(figsize=(3.5, 2))\n",
     "\n",
@@ -572,7 +583,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.12"
+   "version": "3.9.17"
   }
  },
  "nbformat": 4,
diff --git a/notebooks/proof-of-concept/3_approximate-hessians-with-mbtr.ipynb b/notebooks/proof-of-concept/3_approximate-hessians-with-mbtr.ipynb
new file mode 100644
index 0000000..5fd8f8c
--- /dev/null
+++ b/notebooks/proof-of-concept/3_approximate-hessians-with-mbtr.ipynb
@@ -0,0 +1,745 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "201346ec-3f5a-4235-b8ef-4a0051373865",
+   "metadata": {},
+   "source": [
+    "# Generate Approximate Hessians\n",
+    "Like the previous notebook, fit an approximate model and use that to compute the Hessian. Instead of treating the Hessian parameters as separate, we try here to fit a forcefield using the data."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "ebbbc7f5-3007-420f-861a-9f65f84436be",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "%matplotlib inline\n",
+    "from matplotlib import pyplot as plt\n",
+    "from jitterbug.model.mbtr import MBTREnergyModel, MBTRCalculator\n",
+    "from sklearn.linear_model import LinearRegression, ElasticNetCV\n",
+    "from sklearn.model_selection import GridSearchCV\n",
+    "from sklearn.kernel_ridge import KernelRidge\n",
+    "from dscribe.descriptors import MBTR\n",
+    "from ase.vibrations import VibrationsData\n",
+    "from ase.db import connect\n",
+    "from pathlib import Path\n",
+    "from tqdm import tqdm\n",
+    "import numpy as np\n",
+    "import warnings"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "85a147c1-2758-465b-bc54-dc373d73a0f3",
+   "metadata": {},
+   "source": [
+    "Configuration"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "99bd4c92-9a7b-4e88-ac45-dbf30fbfc9e0",
+   "metadata": {
+    "tags": [
+     "parameters"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "molecule_name = 'caffeine'\n",
+    "method = 'hf'\n",
+    "basis = 'def2-svpd'\n",
+    "step_size: float = 0.01 # Perturbation amount, used as maximum L2 norm"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8505d400-8427-45b9-b626-3f9ca557d0c8",
+   "metadata": {},
+   "source": [
+    "Derived"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "a8be3c37-bf1f-4ba4-ba8f-afff6d6bed7d",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "run_name = f'{molecule_name}_{method}_{basis}'\n",
+    "out_dir = Path('data') / 'approx'\n",
+    "db_path = out_dir / f'{run_name}-random-d={step_size:.2e}.db'"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "de1f6aac-b93e-45a7-98e6-ffd5205916a6",
+   "metadata": {},
+   "source": [
+    "## Read in the Data\n",
+    "Get all computations for the desired calculation and the exact solution"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "797b96d8-050c-4bdf-9815-586cfb5bc311",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Loaded 1457 structures\n"
+     ]
+    }
+   ],
+   "source": [
+    "with connect(db_path) as db:\n",
+    "    data = [a.toatoms() for a in db.select('')]\n",
+    "print(f'Loaded {len(data)} structures')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cb1a8e03-b045-49a4-95fd-61636a48fbad",
+   "metadata": {},
+   "source": [
+    "Read in the exact Hessian"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "7389208d-9323-492c-8fc5-d05a372206c6",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "with open(f'data/exact/{run_name}-ase.json') as fp:\n",
+    "    exact_vibs = VibrationsData.read(fp)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "a9965595-532c-4067-ba24-7620bd977007",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "exact_hess = exact_vibs.get_hessian_2d()\n",
+    "exact_zpe = exact_vibs.get_zero_point_energy()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "04c60da8-4a1d-4ae3-b45d-b77e71fd598f",
+   "metadata": {},
+   "source": [
+    "## Fit a Hessian with All Data\n",
+    "Fit a model which explains the energy data by fitting a Hessian matrix using compressed sensing (i.e., Lasso)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fe72ad76-2772-4094-a9b7-065be9a356d4",
+   "metadata": {},
+   "source": [
+    "Make the MBTR calculator using half the available data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "5a5b4a37-bd58-4855-bc3e-85d4258a25c8",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 4min 28s, sys: 7.75 s, total: 4min 35s\n",
+      "Wall time: 23.4 s\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%time\n",
+    "mbtr = MBTRCalculator(\n",
+    "    model=GridSearchCV(\n",
+    "        KernelRidge(kernel='rbf', alpha=1e-6), {\n",
+    "            'alpha': np.logspace(-10, -7, 8),\n",
+    "            'gamma': np.logspace(-5, 5, 32)\n",
+    "    }),\n",
+    "    descriptor=MBTR(\n",
+    "        species=[\"H\", \"C\", \"N\", \"O\"],\n",
+    "        geometry={\"function\": \"distance\"},\n",
+    "        grid={\"min\": 0, \"max\": 6, \"n\": 64, \"sigma\": 0.05},\n",
+    "        weighting={\"function\": \"exp\", \"scale\": 0.1, \"threshold\": 1e-3},\n",
+    "        periodic=False,\n",
+    "    )\n",
+    ")\n",
+    "with warnings.catch_warnings():\n",
+    "    warnings.simplefilter('ignore')\n",
+    "    mbtr.train(data[:len(data) // 2])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "503240dd-b52c-4111-a024-ec44766940e5",
+   "metadata": {},
+   "source": [
+    "Plot the model performance"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "c0038a85-5a70-4a4e-b830-c3c54e5a8efc",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "pred_energy= [mbtr.get_potential_energy(x) * 1000 for x in data[len(data) // 2:]]\n",
+    "true_energy = [x.get_potential_energy() * 1000 for x in data[len(data) // 2:]]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "fba09717-7b2b-40a7-a6d3-543c40080d02",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(0, 0.5, '$E-E_0$, True (meV)')"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 350x350 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots(figsize=(3.5, 3.5))\n",
+    "\n",
+    "base_energy = data[0].get_potential_energy() * 1000  # in meV\n",
+    "ax.scatter(np.subtract(pred_energy, base_energy), np.subtract(true_energy, base_energy), s=2)\n",
+    "\n",
+    "ax.set_xlim(ax.get_ylim())\n",
+    "ax.set_ylim(ax.get_ylim())\n",
+    "ax.plot(ax.get_xlim(), ax.get_xlim(), 'k--')\n",
+    "\n",
+    "ax.set_xlabel('$E-E_0$, ML (meV)')\n",
+    "ax.set_ylabel('$E-E_0$, True (meV)')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "71e8e883-2c4b-4929-a000-297233dabe96",
+   "metadata": {},
+   "source": [
+    "Build the ASE-compatible calculator"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "d6a7d756-37d3-44e0-b5e2-348d07c9d296",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "model = MBTREnergyModel(reference=data[0], calc=mbtr)\n",
+    "with warnings.catch_warnings():\n",
+    "    warnings.simplefilter(\"ignore\")\n",
+    "    hess_model = model.train(data)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "372a4089-88cb-47ae-a917-190bc26287ff",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'alpha': 1e-10, 'gamma': 2.1017480113324872e-05}"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "hess_model.parameters['model'].best_params_"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "aa509659-701d-4001-8cc7-980c9d999976",
+   "metadata": {},
+   "source": [
+    "Compare the forces estimated at a zero displacement to the true value"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "70d80f87-9983-4bd5-a6ae-b9c966b0d838",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "actual_forces = data[0].get_forces()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "f548b145-0aa8-47f7-802b-6b7232a74bd3",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "pred_forces = hess_model.get_forces(data[0])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "d7cd7762-6e12-4dcd-b564-67a33b18d9e0",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Maximum force: 8.96e-03 eV/Angstrom\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(f'Maximum force: {np.abs(pred_forces).max():.2e} eV/Angstrom')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "425b77a9-7fd7-40da-af6f-eaed197c9ab6",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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",
+      "text/plain": [
+       "<Figure size 400x200 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, axs = plt.subplots(1, 2, figsize=(4, 2))\n",
+    "\n",
+    "for ax, l, h in zip(axs, ['Actual', 'Estimated'], [actual_forces, pred_forces]):\n",
+    "    ax.matshow(h, vmin=-0.05, vmax=0.05, aspect='auto', cmap='RdBu')\n",
+    "\n",
+    "    ax.set_xticklabels([])\n",
+    "    ax.set_yticklabels([])\n",
+    "    \n",
+    "    ax.set_title(l, fontsize=10)\n",
+    "\n",
+    "fig.tight_layout()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "46a0f2f8-f863-4de3-bd97-97ebd92676d4",
+   "metadata": {},
+   "source": [
+    "Get the mean Hessian"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "00a10907-667a-413c-851d-d47f0eff092b",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 47.7 s, sys: 33.7 ms, total: 47.7 s\n",
+      "Wall time: 47.7 s\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%time\n",
+    "approx_hessian = model.mean_hessian(hess_model)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f4de2e78-00c2-427f-b9bd-eb3ca881564b",
+   "metadata": {},
+   "source": [
+    "Compare to exact answer"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "d48893fd-df0d-4fa8-bfbe-0d04b71fbf1a",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[1.96495560e+01, 2.28518485e+01, 1.08009177e-03],\n",
+       "       [2.28518485e+01, 8.36964299e+01, 3.94902961e-03],\n",
+       "       [1.08009177e-03, 3.94902961e-03, 4.15881408e+00]])"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "exact_hess[:3, :3]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "9b311dea-5744-4211-81cb-40aa1183301e",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[1.90039475e+01, 2.26533979e+01, 2.14746706e-02],\n",
+       "       [2.26533979e+01, 8.32193023e+01, 1.32040896e-02],\n",
+       "       [2.14746706e-02, 1.32040896e-02, 3.78143259e+00]])"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "approx_hessian[:3, :3]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "addd7bef-854a-4b9f-96e9-2aa01b652495",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 400x200 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, axs = plt.subplots(1, 2, figsize=(4, 2))\n",
+    "\n",
+    "for ax, l, h in zip(axs, ['Exact', 'Approximate'], [exact_hess, approx_hessian]):\n",
+    "    ax.matshow(h, vmin=-100, vmax=100, cmap='RdBu')\n",
+    "\n",
+    "    ax.set_xticklabels([])\n",
+    "    ax.set_yticklabels([])\n",
+    "    \n",
+    "    ax.set_title(l, fontsize=10)\n",
+    "\n",
+    "fig.tight_layout()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b516bb4e-d27d-4ad6-ad4b-b873c81670ff",
+   "metadata": {},
+   "source": [
+    "Get the zero point energy"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "abbbbfd6-7d17-4b93-880a-3352903b56c4",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "approx_vibs = VibrationsData.from_2d(data[0], approx_hessian)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "fdd80af3-8c18-40d8-b971-4a473bc91498",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "5.132369908274389"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "approx_vibs.get_zero_point_energy()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "6b1af348-4bc9-4ced-9a12-44b3e49abe9c",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "5.5067174465850215"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "exact_zpe"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ab6a6645-bf0e-4ed7-874e-6a345063e0b5",
+   "metadata": {},
+   "source": [
+    "The two differ, but I'm not sure how important the difference is."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "29a44b3d-cd3e-44af-9bc2-3e0164b22a38",
+   "metadata": {},
+   "source": [
+    "Save it to disk"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "40fd3d44-df72-4b9d-b7b0-f09fabe74c0d",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "with open(f'data/approx/{run_name}_d={step_size:.2e}_mbtr.json', 'w') as fp:\n",
+    "    approx_vibs.write(fp)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6489882c-acaf-4a07-bbe9-d643f7c5c882",
+   "metadata": {},
+   "source": [
+    "## Plot as a Function of Data\n",
+    "See what happens as we add more data to the training"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "bce41a81-6c88-4b0c-9d8d-0891d1832fd6",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Plotting at 16 steps: 5, 101, 198, 295, 392, ...\n"
+     ]
+    }
+   ],
+   "source": [
+    "steps = np.linspace(5, len(data), 16, dtype=int)\n",
+    "print(f'Plotting at {len(steps)} steps: {\", \".join(map(str, steps[:5]))}, ...')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "id": "fe39ce86-1806-4367-8c86-e3ef58f81f84",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 16/16 [15:54<00:00, 59.66s/it]\n"
+     ]
+    }
+   ],
+   "source": [
+    "zpes = []\n",
+    "for count in tqdm(steps):\n",
+    "    with warnings.catch_warnings():\n",
+    "        warnings.simplefilter(\"ignore\")\n",
+    "        hess_model = model.train(data[:count])\n",
+    "    \n",
+    "    approx_hessian = model.mean_hessian(hess_model)\n",
+    "    approx_vibs = VibrationsData.from_2d(data[0], approx_hessian)\n",
+    "    zpes.append(approx_vibs.get_zero_point_energy())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c179c3ae-695f-44ad-b548-10002c4ff30b",
+   "metadata": {},
+   "source": [
+    "Plot it"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "1c6706a9-a27f-448f-81d4-957939bb2ca8",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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3OR2o//znP7nvzWYz9uzZg/Pnz2POnDlQKpUoKytDYGAgAgK6zmEvY4yXT0gRQnyDy2f5i4uLkZSUhJKSEhgMBkyYMAFKpRKvvvoqmpqa8N5773VGnR6ptLoRFfUGiIUCDKVpognp8lw+y5+Wlob4+HjU1NRALr82Ivm0adPw448/8lqcp7PvnQ7pqaLpLQghru+h7t+/HwcOHIBEInFYHhkZiUuXLvFWmDe4Nn8UHe4TQm5iD9VqtcJisbRafvHiRSiVSl6K8hZHi/gZEIUQ4htcDtQJEyY4jKgvEAig0+mQnp6O5ORkPmvzaLV6IwoqdAAoUAkhNi4f8r/55ptITEzEoEGD0NTUhDlz5qCgoABqtRqffPJJZ9TokeyXS/UPVbj0GXtCiO9yOVA1Gg1OnDiBrVu3Ijs7G1arFQsWLMDcuXMdTlL5uiP2Cfkiqf+UEGJzU4OjyOVyPPnkk3jyySf5rsdr2PtP+Rr/lBDi/ZzqQz106JDTL9jQ0OD0EH7eqslkwamLWgB0hp8Qco1TgTpv3jxMmDABn332GXQ6XZtt8vLy8OKLL2LAgAE4duwYr0V6mtxLWhgtVqgDpIgM8Xd3OYQQD+HUIX9eXh42btyIl156CXPnzkVUVBQ0Gg1kMhlqamqQn5+PhoYGTJ8+HZmZmV43nqmrrvWfBtPo9oQQjlOBKhaLkZqaitTUVBw7dgz79u1DUVERGhsbMWzYMPzpT39CYmIiunXrGoe/1H9KCGmLyyelYmNjERsb2xm1eAWrlSG7hD4hRQhprXMnevdB56/qUKs3QS4WYpDGfRMDEkI8DwWqi+z9p8MjgiAW0uYjhFxDieAi+4R8I6n/lBByHQpUFx1t3kONo/5TQsh1KFBdUFHXhJJqPfwEQGzvIHeXQwjxME4HanJyMrRaLXf/lVdeQW1tLXe/qqoKgwYN4rU4T2Mf/zQ6LBBKmdjN1RBCPI3Tgfr999/DYDBw99etW4fq6mruvtlsxpkzZ/itzsNcmz+K+k8JIa05HaiMsQ7vdwXUf0oI6Qj1oTqpwWBG3uU6ALSHSghpm9OBKhAIWn1uvSt9jv1EaS0sVoaeQXKEq7rOuK+EEOc5/dFTxhjmz58PqdQ2On1TUxOeeeYZKBQKAHDoX/VFR+jz+4SQG3A6UFNSUhzuP/74463azJs379Yr8lD2/tN46j8lhLTD6UDNyMjozDo8mtlixXFuQBTaQyWEtM2l0aaKi4vxww8/wGQyYfz48T5/3aldfnk9GowWKGUiRHXvWlNlE0Kc53Sg/vzzz0hOToZer7c9USTCli1bMHv27E4rzlPY+0/jIoPh59d1TsQRQlzj9Fn+lStXIjExERcvXkRVVRWeeuop/OUvf+nM2jyGvf+Uxj8lhHTE6UDNycnBmjVroNFoEBwcjDfeeANlZWWoqanpzPrcjjHGjTAVH0n9p4SQ9jkdqLW1tejevTt3X6FQwN/f3+Hz/L7oYk0jrtQZIBYKMCwiyN3lEEI8mEsnpfLy8lBeXs7dZ4zht99+Q319Pbds6NCh/FXnAez9pzE9VZCJhW6uhhDiyVwK1Pvvv7/VZ/gnT54MgUAAxhgEAgEsFguvBbqbfYQp6j8lhNyI04FaWFjI+5uvWbMG27ZtQ35+PuRyOcaOHYt169bhjjvu4P29btbRFmf4CSGkI04HamRkJO9vvnfvXixatAgjR46E2WzGihUrMHHiROTl5XEfaXWnWr0RZ6/oANAJKULIjTl9Uur+++/Htm3b2n28srIS/fr1c+nNd+3ahfnz52Pw4MEYNmwYMjIyUFJSguzsbJdep7Mca/50VL9QBUICpG6uhhDi6ZwO1KysLMycORPp6eltPm6xWFBcXHxLxdhnBOjWre3+SoPBgLq6OodbZ7LPcEp7p4QQZ7g0HuqGDRvwj3/8A9OmTYNOp+O1EMYYli5dinHjxiEmJqbNNmvWrIFKpeJuERERvNZwvaPcCFN0QooQcmMuBerDDz+MQ4cOIS8vD2PGjMGFCxd4KyQ1NRWnTp3CJ5980m6bF154AVqtlruVlpby9v7XM5gtOHnRtsdMZ/gJIc5wecT+O++8E4cPH0ZERARGjhyJ3bt333IRixcvxo4dO5CVlYVevXq1204qlSIwMNDh1llyL2lhNFuhDpCgT4h/p70PIcR33NQUKCqVCjt37sTChQuRnJyMN99886benDGG1NRUbNu2DT/99BP69u17U6/TGez9p3GRwV1qZgJCyM1z+rKptqY/Wbt2LUaMGIEFCxbgp59+cvnNFy1ahP/+97/46quvoFQquU9hqVQqyOXunWbkKDfDKR3uE0Kcc9OzntrNmjUL+/fvR05OjstvvmHDBmi1WowfPx7h4eHc7dNPP3X5tfhktTJkF9MI/YQQ1zi9h5qVldXu5UzDhw9HdnY2du7c6dKbe+pU1BcqdajRmyAT+2GwpvP6aQkhvsXpQE1ISOjw8ZCQEJ+ZU8refzo8IghiIc20TQhxDqVFG45Q/ykh5CZQoLbB3n9KA6IQQlxBgXqdiromFFfpIRAAsRSohBAXUKBexz7+aXRYIAJlYjdXQwjxJhSo17k2IR/tnRJCXEOBeh37hHzUf0oIcRUFagsNBjNOl9mGBKQz/IQQV1GgtnCytBYWK0PPIDk0Qe796CshxPtQoLbQckAUQghxFQVqC/b+UzohRQi5GRSozcwWK47RgCiEkFtAgdosu7gGDUYLlFIRonoo3V0OIcQLUaAC+Dz7Ip7cfAQAcPcANYR+NKA0IcR1To825Yt0BjNe2p6LbccvAQDG9AvB3x4Z7OaqCCHeqssGau4lLRZ/chyFlQ3wEwB/eiAKzyYOoL1TQshN63KByhjD5oNFWPNtPowWK8JVMvxz9gi6kJ8Qcsu6VKDWNBjx589PYvdvFQCACYN64LUZQxHkL3FzZYQQX9BlAvXXC1VI23oC5XVNkAj9sOKhOzFvTCTNaEoI4Y3PB6rFyvD2T+fwjx/PwsqAfmoF/m/OCAzWqNxdGiHEx/h0oJZrm5C29Th+LbR9Aup3sb3wt4cHQyH16dUmhLiJzybLT/lXsOx/p1DdYIS/RIjVj8Rgemwvd5dFCPFhPheoRrMVr+7Kx/v7CwEAgzWB+L/ZI9AvNMDNlRFCfJ1PBWpRZQMWf3IcOZe0AID5Y/vgheRoSEVCN1dGCOkKfCZQvzpxCSu+zIXOYEaQvxivzRiGCYN6uLssQkgX4hOBunJ7Dr7KqwUAjOrTDf+YPRzhKhogmhBye/lEoH55vAxCmT8W3zcQS+4bAJGQxnwhhNx+PhGo3ZUS/DNlNMb2V7u7FEJIF+YTgfr5M2PRR0NhSghxL584Nu4WIHV3CYQQ4huBSgghnoAClRBCeOLVfaiMMQBAXV2dmyshhPgqe77Y86YjXh2oVVVVAICIiAg3V0II8XX19fVQqToepc6rA7VbN9so+yUlJTdcUU9VV1eHiIgIlJaWIjAw0N3luIzqdz9vXwdPr58xhvr6emg0mhu29epA9fOzdQGrVCqP/EG4IjAw0KvXgep3P29fB0+u39kdNjopRQghPKFAJYQQnnh1oEqlUqSnp0Mq9d4L+719Hah+9/P2dfD2+lsSMGeuBSCEEHJDXr2HSgghnoQClRBCeEKBSgghPPHqQH333XfRt29fyGQyxMXFYd++fe4uCWvWrMHIkSOhVCrRvXt3PPLIIzhz5oxDm/nz50MgEDjc7rrrLoc2BoMBixcvhlqthkKhwNSpU3Hx4sXbsg4vv/xyq/rCwsK4xxljePnll6HRaCCXyzF+/HicPn3aY+rv06dPq/oFAgEWLVoEwPO2/88//4wpU6ZAo9FAIBBg+/btDo/ztb1ramrwxBNPQKVSQaVS4YknnkBtbW2nr4PJZMLy5csxZMgQKBQKaDQazJs3D2VlZQ6vMX78+FY/l8cee+y2rQMvmJfaunUrE4vFbNOmTSwvL4+lpaUxhULBiouL3VrXpEmTWEZGBsvNzWUnTpxgDz30EOvduzfT6XRcm5SUFJaUlMQuX77M3aqqqhxe55lnnmE9e/ZkmZmZ7NixYywxMZENGzaMmc3mTl+H9PR0NnjwYIf6KioquMfXrl3LlEol++KLL1hOTg6bNWsWCw8PZ3V1dR5Rf0VFhUPtmZmZDADLyspijHne9v/222/ZihUr2BdffMEAsC+//NLhcb62d1JSEouJiWEHDx5kBw8eZDExMWzy5Mmdvg61tbXsgQceYJ9++inLz89nhw4dYqNHj2ZxcXEOr5GQkMAWLlzo8HOpra11aNOZ68AHrw3UUaNGsWeeecZhWXR0NHv++efdVFHbKioqGAC2d+9ebllKSgp7+OGH231ObW0tE4vFbOvWrdyyS5cuMT8/P7Zr167OLJcxZgvUYcOGtfmY1WplYWFhbO3atdyypqYmplKp2HvvvccYc3/910tLS2P9+/dnVquVMebZ2//6MOJre+fl5TEA7JdffuHaHDp0iAFg+fn5nboObTl8+DAD4LADlJCQwNLS0tp9zu1ch5vllYf8RqMR2dnZmDhxosPyiRMn4uDBg26qqm1arW1Ka/u4A3Z79uxB9+7dERUVhYULF6KiooJ7LDs7GyaTyWH9NBoNYmJibtv6FRQUQKPRoG/fvnjsscdw4cIFAEBhYSHKy8sdapNKpUhISOBq84T67YxGI/7zn//gqaeegkAg4JZ7+va342t7Hzp0CCqVCqNHj+ba3HXXXVCpVG75m9FqtRAIBAgKCnJY/vHHH0OtVmPw4MFYtmwZ6uvrucc8bR3a4pWf5a+srITFYkGPHo7TRPfo0QPl5eVuqqo1xhiWLl2KcePGISYmhlv+4IMP4tFHH0VkZCQKCwuxcuVK3HfffcjOzoZUKkV5eTkkEgmCg4MdXu92rd/o0aPx73//G1FRUbhy5QpWr16NsWPH4vTp09z7t7Xti4uLAcDt9be0fft21NbWYv78+dwyT9/+LfG1vcvLy9G9e/dWr9+9e/fbvk5NTU14/vnnMWfOHIfP7s+dOxd9+/ZFWFgYcnNz8cILL+DkyZPIzMwE4Fnr0B6vDFS7lnscgC3Arl/mTqmpqTh16hT279/vsHzWrFnc9zExMYiPj0dkZCR27tyJ6dOnt/t6t2v9HnzwQe77IUOGYMyYMejfvz+2bNnCnby5mW3vjp/PBx98gAcffNBhpCBP3/5t4WN7t9X+dq+TyWTCY489BqvVinfffdfhsYULF3Lfx8TEYODAgYiPj8exY8cQGxsLwDPWoSNeecivVqshFApb/VeqqKho9Z/cXRYvXowdO3YgKysLvXr16rBteHg4IiMjUVBQAAAICwuD0WhETU2NQzt3rZ9CocCQIUNQUFDAne3vaNt7Sv3FxcXYvXs3fv/733fYzpO3P1/bOywsDFeuXGn1+levXr1t62QymTBz5kwUFhYiMzPzhiNLxcbGQiwWO/xc3L0ON+KVgSqRSBAXF8cdCthlZmZi7NixbqrKhjGG1NRUbNu2DT/99BP69u17w+dUVVWhtLQU4eHhAIC4uDiIxWKH9bt8+TJyc3Pdsn4GgwG//fYbwsPDuUOylrUZjUbs3buXq81T6s/IyED37t3x0EMPddjOk7c/X9t7zJgx0Gq1OHz4MNfm119/hVarvS3rZA/TgoIC7N69GyEhITd8zunTp2Eymbifi7vXwSluOhl2y+yXTX3wwQcsLy+P/fGPf2QKhYIVFRW5ta4//OEPTKVSsT179jhc/qHX6xljjNXX17PnnnuOHTx4kBUWFrKsrCw2ZswY1rNnz1aXwfTq1Yvt3r2bHTt2jN1333237bKj5557ju3Zs4dduHCB/fLLL2zy5MlMqVRy23bt2rVMpVKxbdu2sZycHDZ79uw2L+NxV/2MMWaxWFjv3r3Z8uXLHZZ74vavr69nx48fZ8ePH2cA2Pr169nx48e5M+B8be+kpCQ2dOhQdujQIXbo0CE2ZMgQ3i456mgdTCYTmzp1KuvVqxc7ceKEw9+FwWBgjDF27tw5tmrVKnbkyBFWWFjIdu7cyaKjo9mIESNu2zrwwWsDlTHG3nnnHRYZGckkEgmLjY11uDTJXQC0ecvIyGCMMabX69nEiRNZaGgoE4vFrHfv3iwlJYWVlJQ4vE5jYyNLTU1l3bp1Y3K5nE2ePLlVm85iv85RLBYzjUbDpk+fzk6fPs09brVaWXp6OgsLC2NSqZTde++9LCcnx2PqZ4yx77//ngFgZ86ccVjuids/Kyurzd+ZlJQUxhh/27uqqorNnTuXKZVKplQq2dy5c1lNTU2nr0NhYWG7fxf2a4NLSkrYvffey7p168YkEgnr378/W7JkSavrgztzHfhAo00RQghPvLIPlRBCPBEFKiGE8IQClRBCeEKBSgghPKFAJYQQnlCgEkIITyhQCSGEJxSohBDCEwpUQjqwefPmVmN2EtIeClTidm3N8SQQCJCUlOTu0jBr1iycPXvW3WUQL+HV46ES35GUlISMjAyHZVKptNPez2g0QiKR3LCdXC6HXC7vtDqIb6E9VOIRpFIpwsLCHG72EegFAgHef/99TJs2Df7+/hg4cCB27Njh8Py8vDwkJycjICAAPXr0wBNPPIHKykru8fHjxyM1NRVLly6FWq3GhAkTAAA7duzAwIEDIZfLkZiYiC1btkAgEHAzabZ1yP/1118jLi4OMpkM/fr1w6pVq2A2m7nHX375ZfTu3RtSqRQajQZLlizphC1GPBEFKvEKq1atwsyZM3Hq1CkkJydj7ty5qK6uBmAb+zMhIQHDhw/H0aNHsWvXLly5cgUzZ850eI0tW7ZAJBLhwIED2LhxI4qKijBjxgw88sgjOHHiBJ5++mmsWLGiwzq+//57PP7441iyZAny8vKwceNGbN68Ga+88goA4PPPP8ebb76JjRs3oqCgANu3b8eQIUM6Z6MQz+Pu4a4ISUlJYUKhkCkUCofb3/72N8aYbUjEv/71r1x7nU7HBAIB++677xhjjK1cuZJNnDjR4TVLS0sdhu9LSEhgw4cPd2izfPlyFhMT47BsxYoVDAA3JFxGRgZTqVTc4/fccw/7+9//7vCcjz76iIWHhzPGGHvjjTdYVFQUMxqNN7k1iDejPlTiERITE7FhwwaHZS1nih06dCj3vUKhgFKp5GYqzc7ORlZWFgICAlq97vnz5xEVFQUAiI+Pd3jszJkzGDlypMOyUaNGdVhndnY2jhw5wu2RAoDFYkFTUxP0ej0effRRvPXWW+jXrx+SkpKQnJyMKVOmQCSiP7WugH7KxCMoFAoMGDCg3cfFYrHDfYFAAKvVCgCwWq2YMmUK1q1b1+p59ukz7O/REmtjcjd2g+GBrVYrVq1a1eZkfjKZDBEREThz5gwyMzOxe/duPPvss3jttdewd+/eVutAfA8FKvF6sbGx+OKLL9CnTx+X9gSjo6Px7bffOiw7evToDd/rzJkzHYa/XC7H1KlTMXXqVCxatAjR0dHIycnhZu4kvosClXgEg8HQamZPkUgEtVp9w+cuWrQImzZtwuzZs/HnP/8ZarUa586dw9atW7Fp0yYIhcI2n/f0009j/fr1WL58ORYsWIATJ05g8+bNANqerhgAXnrpJUyePBkRERF49NFH4efnh1OnTiEnJwerV6/G5s2bYbFYMHr0aPj7++Ojjz6CXC5HZGSkaxuEeCU6y088wq5duxAeHu5wGzdunFPP1Wg0OHDgACwWCyZNmoSYmBikpaVBpVLBz6/9X/G+ffvi888/x7Zt2zB06FBs2LCBO8vf3jWwkyZNwjfffIPMzEyMHDkSd911F9avX88FZlBQEDZt2oS7774bQ4cOxY8//oivv/7aqVk+ifejOaUIaeGVV17Be++9h9LSUneXQrwQHfKTLu3dd9/FyJEjERISggMHDuC1115Damqqu8siXooClXRpBQUFWL16Naqrq9G7d28899xzeOGFF9xdFvFSdMhPCCE8oZNShBDCEwpUQgjhCQUqIYTwhAKVEEJ4QoFKCCE8oUAlhBCeUKASQghPKFAJIYQnFKiEEMKT/wc7mUGGCZVTNwAAAABJRU5ErkJggg==",
+      "text/plain": [
+       "<Figure size 350x200 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots(figsize=(3.5, 2))\n",
+    "\n",
+    "ax.plot(steps, zpes)\n",
+    "\n",
+    "ax.set_xlim([0, steps.max()])\n",
+    "ax.plot(ax.get_xlim(), [exact_zpe]*2, 'k--')\n",
+    "\n",
+    "ax.set_xlabel('Energies')\n",
+    "ax.set_ylabel('ZPE (eV)')\n",
+    "\n",
+    "fig.tight_layout()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e8788f74-c208-4939-aa9b-3bbdfd8310ee",
+   "metadata": {},
+   "source": [
+    "We consistently underestimate the ZPE. Is it because we have too few oscillators?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "384af4b3-5eb3-4eac-b176-160f19944853",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.9.17"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/pyproject.toml b/pyproject.toml
index 5189da8..03604e5 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -7,7 +7,7 @@ authors = [
 ]
 description = 'Faster Hessians through machine learning'
 readme = "README.md"
-requires-python = ">=3.10"
+requires-python = ">=3.9"
 license = { file = "LICENSE" }
 keywords = ["HPC", "AI", "Workflows", "Quantum Chemistry", "Chemical Engineering"]
 classifiers = [
diff --git a/tests/models/test_mbtr.py b/tests/models/test_mbtr.py
new file mode 100644
index 0000000..c500156
--- /dev/null
+++ b/tests/models/test_mbtr.py
@@ -0,0 +1,31 @@
+"""Test for a MBTR-based energy model"""
+import numpy as np
+
+from jitterbug.model.mbtr import MBTRCalculator, MBTREnergyModel
+
+
+def test_model(train_set):
+    # Create then fit the model
+    calc = MBTRCalculator()
+    calc.train(train_set)
+
+    # Predict the energy (we should be close!)
+    test_atoms = train_set[0].copy()
+    test_atoms.calc = calc
+    energy = test_atoms.get_potential_energy()
+    assert np.isclose(energy, train_set[0].get_potential_energy())
+
+    # See if force calculation works
+    forces = test_atoms.get_forces()
+    assert forces.shape == (3, 3)  # At least make sure we get the right shape, values are iffy
+
+
+def test_hessian(train_set):
+    """See if we can compute the Hessian"""
+    calc = MBTRCalculator()
+    model = MBTREnergyModel(calc, train_set[0])
+
+    # Run the fitting
+    hess_model = model.train(train_set)
+    hess = model.mean_hessian(hess_model)
+    assert hess.shape == (9, 9)