diff --git a/jitterbug/cli.py b/jitterbug/cli.py
index 9f0f271..c98bc8a 100644
--- a/jitterbug/cli.py
+++ b/jitterbug/cli.py
@@ -12,12 +12,17 @@
 from colmena.task_server import ParslTaskServer
 from parsl import Config, HighThroughputExecutor
 
+from jitterbug.model.dscribe import make_global_mbtr_model
 from jitterbug.parsl import get_energy, load_configuration
 from jitterbug.thinkers.exact import ExactHessianThinker
+from jitterbug.thinkers.static import ApproximateHessianThinker
 from jitterbug.utils import make_calculator
+from jitterbug.sampler import methods, UniformSampler
 
 logger = logging.getLogger(__name__)
 
+approx_methods = list(methods.keys())
+
 
 def main(args: Optional[list[str]] = None):
     """Run Jitterbug"""
@@ -28,7 +33,14 @@ def main(args: Optional[list[str]] = None):
                              'to store information about charged or radical molecules')
     parser.add_argument('--method', nargs=2, required=True,
                         help='Method to use to compute energies. Format: [method] [basis]. Example: B3LYP 6-31g*')
-    parser.add_argument('--exact', help='Compute Hessian using numerical derivatives', action='store_true')
+    parser.add_argument('--approach', default='exact',
+                        choices=['exact', 'static'],
+                        help='Method used to compute the Hessian. Either "exact", or'
+                             '"static" for a approximate method using a fixed set of structures.')
+    parser.add_argument('--amount-to-run', default=0.1, type=float,
+                        help='Amount of structures to run for approximate Hessian. '
+                             'Either number (if >1) or fraction of number required to compute exact Hessian,'
+                             '`6N + 2 * (3N) * (3N - 1) + 1`.')
     parser.add_argument('--parsl-config', help='Path to the Parsl configuration to use')
     args = parser.parse_args(args)
 
@@ -39,11 +51,7 @@ def main(args: Optional[list[str]] = None):
 
     # Make the run directory
     method, basis = (x.lower() for x in args.method)
-    if args.exact:
-        compute_name = 'exact'
-    else:
-        raise NotImplementedError()
-    run_dir = Path('run') / xyz_name / f'{method}_{basis}_{compute_name}'
+    run_dir = Path('run') / xyz_name / f'{method}_{basis}_{args.approach}'
     run_dir.mkdir(parents=True, exist_ok=True)
 
     # Start logging
@@ -92,14 +100,31 @@ def main(args: Optional[list[str]] = None):
 
     # Create a thinker
     queues = PipeQueues(topics=['simulation'])
-    if args.exact:
+    functions = []  # Additional functions needed by thinker
+    if args.approach == 'exact':
         thinker = ExactHessianThinker(
             queues=queues,
             atoms=atoms,
             run_dir=run_dir,
             num_workers=num_workers,
         )
-        functions = []  # No other functions to run
+    elif args.approach == 'static':
+        # Determine the number to run
+        exact_needs = len(atoms) * 3 * 2 + (len(atoms) * 3) * (len(atoms) * 3 - 1) * 2 + 1
+        if args.amount_to_run < 1:
+            num_to_run = int(args.amount_to_run * exact_needs)
+        else:
+            num_to_run = int(args.amount_to_run)
+        logger.info(f'Running {num_to_run} energies out of {exact_needs} required for exact Hessian')
+        thinker = ApproximateHessianThinker(
+            queues=queues,
+            atoms=atoms,
+            run_dir=run_dir,
+            num_workers=num_workers,
+            num_to_run=num_to_run,
+            sampler=UniformSampler(),  # TODO (wardlt): Make this configurable
+            model=make_global_mbtr_model(atoms)  # TODO (wardlt): Make this configurable
+        )
     else:
         raise NotImplementedError()
 
diff --git a/jitterbug/model/dscribe/__init__.py b/jitterbug/model/dscribe/__init__.py
index bfdf045..6d9ab56 100644
--- a/jitterbug/model/dscribe/__init__.py
+++ b/jitterbug/model/dscribe/__init__.py
@@ -1 +1,41 @@
 """Energy models using `DScribe <https://singroup.github.io/dscribe/latest/index.html>`_"""
+import ase
+from dscribe.descriptors.mbtr import MBTR
+from sklearn.pipeline import Pipeline
+from sklearn.preprocessing import StandardScaler
+from sklearn.model_selection import GridSearchCV
+from sklearn.kernel_ridge import KernelRidge
+import numpy as np
+
+from .globald import DScribeGlobalEnergyModel
+
+
+def make_global_mbtr_model(ref_atoms: ase.Atoms, n_points: int = 8, cutoff: float = 6.) -> DScribeGlobalEnergyModel:
+    """Make an MBTR model using scikit-learn
+
+    Args:
+        ref_atoms: Reference atoms to use for the model
+        n_points: Number of points to include in the MBTR grid
+        cutoff: Cutoff distance for the descriptors (units: Angstrom)
+    Returns:
+        Energy model, ready to be trained
+    """
+    species = list(set(ref_atoms.get_chemical_symbols()))
+    desc = MBTR(
+        species=species,
+        geometry={"function": "angle"},
+        grid={"min": 0., "max": 180, "n": n_points, "sigma": 180. / n_points / 2.},
+        weighting={"function": "smooth_cutoff", "r_cut": cutoff, "threshold": 1e-3},
+        periodic=False,
+    )
+    model = Pipeline(
+        [('scale', StandardScaler()),
+         ('krr', GridSearchCV(KernelRidge(kernel='rbf', alpha=1e-10),
+                              {'gamma': np.logspace(-5, 5, 32)}))]
+    )
+    return DScribeGlobalEnergyModel(
+        reference=ref_atoms,
+        model=model,
+        descriptors=desc,
+        num_calculators=2
+    )
diff --git a/jitterbug/sampler/__init__.py b/jitterbug/sampler/__init__.py
new file mode 100644
index 0000000..2bcf863
--- /dev/null
+++ b/jitterbug/sampler/__init__.py
@@ -0,0 +1,9 @@
+"""Functions to sample atomic configurations"""
+from typing import Type
+
+from .base import StructureSampler
+from .random import UniformSampler
+
+methods: dict[str, Type[StructureSampler]] = {
+    'uniform': UniformSampler
+}
diff --git a/jitterbug/sampler/base.py b/jitterbug/sampler/base.py
new file mode 100644
index 0000000..5a0a648
--- /dev/null
+++ b/jitterbug/sampler/base.py
@@ -0,0 +1,26 @@
+import ase
+
+
+class StructureSampler:
+    """Base class for generating structures used to train Hessian model
+
+    Options for the sampler should be defined in the initializer.
+    """
+
+    @property
+    def name(self) -> str:
+        """Name for the sampling strategy"""
+        raise NotImplementedError()
+
+    def produce_structures(self, atoms: ase.Atoms, count: int, seed: int = 1) -> list[ase.Atoms]:
+        """Generate a set of training structure
+
+        Args:
+            atoms: Unperturbed geometry
+            count: Number of structure to produce
+            seed: Random seed
+        Returns:
+            List of structures to be evaluated
+        """
+
+        raise NotImplementedError()
diff --git a/jitterbug/sampler/random.py b/jitterbug/sampler/random.py
new file mode 100644
index 0000000..5471544
--- /dev/null
+++ b/jitterbug/sampler/random.py
@@ -0,0 +1,38 @@
+"""Simple, friendly, random sampling"""
+from dataclasses import dataclass
+
+import numpy as np
+import ase
+
+from jitterbug.sampler.base import StructureSampler
+
+
+@dataclass
+class UniformSampler(StructureSampler):
+    """Sample randomly-chosen directions
+
+    Perturbs each atom in each direction a random amount between -:attr:`step_size` and :attr:`step_size`.
+    """
+
+    step_size: float = 0.005
+    """Amount to displace the atoms (units: Angstrom)"""
+
+    @property
+    def name(self) -> str:
+        return f'uniform_{self.step_size:.3e}'
+
+    def produce_structures(self, atoms: ase.Atoms, count: int, seed: int = 1) -> list[ase.Atoms]:
+        # Make the RNG
+        n_atoms = len(atoms)
+        rng = np.random.RandomState(seed + n_atoms)
+
+        output = []
+        for _ in range(count):
+            # Sample a perturbation
+            disp = rng.normal(-self.step_size, self.step_size, size=(n_atoms, 3))
+
+            # Make the new atoms
+            new_atoms = atoms.copy()
+            new_atoms.positions += disp
+            output.append(new_atoms)
+        return output
diff --git a/jitterbug/thinkers/base.py b/jitterbug/thinkers/base.py
new file mode 100644
index 0000000..62bff03
--- /dev/null
+++ b/jitterbug/thinkers/base.py
@@ -0,0 +1,39 @@
+from pathlib import Path
+
+import ase
+import numpy as np
+from colmena.queue import ColmenaQueues
+from colmena.thinker import BaseThinker, ResourceCounter
+
+
+class HessianThinker(BaseThinker):
+    """Base class for thinkers
+
+    Implementations must write their simulation data to the same spot"""
+
+    atoms: ase.Atoms
+    """Unperturbed atomic structure"""
+
+    run_dir: Path
+    """Path to the run directory"""
+    result_file: Path
+    """Path to file in which to store result records"""
+
+    def __init__(self, queues: ColmenaQueues, rec: ResourceCounter, run_dir: Path, atoms: ase.Atoms):
+        super().__init__(queues, rec)
+        self.atoms = atoms
+
+        # Prepare for outputs
+        self.run_dir = run_dir
+        self.run_dir.mkdir(exist_ok=True)
+        self.result_file = run_dir / 'simulation-results.json'
+
+    def compute_hessian(self) -> np.ndarray:
+        """Compute the Hessian using finite differences
+
+        Returns:
+            Hessian in the 2D form
+        Raises:
+            (ValueError) If there is missing data
+        """
+        raise NotImplementedError()
diff --git a/jitterbug/thinkers/exact.py b/jitterbug/thinkers/exact.py
index 5ab9a5b..aae908a 100644
--- a/jitterbug/thinkers/exact.py
+++ b/jitterbug/thinkers/exact.py
@@ -7,20 +7,19 @@
 import numpy as np
 from colmena.models import Result
 from colmena.queue import ColmenaQueues
-from colmena.thinker import BaseThinker, ResourceCounter, agent, result_processor
+from colmena.thinker import ResourceCounter, agent, result_processor
 
+from jitterbug.thinkers.base import HessianThinker
 from jitterbug.utils import read_from_string
 
 
-class ExactHessianThinker(BaseThinker):
+class ExactHessianThinker(HessianThinker):
     """Schedule the calculation of a complete set of numerical derivatives"""
 
     def __init__(self, queues: ColmenaQueues, num_workers: int, atoms: ase.Atoms, run_dir: Path, step_size: float = 0.005):
-        super().__init__(queues, ResourceCounter(num_workers))
-        self.atoms = atoms
+        super().__init__(queues, ResourceCounter(num_workers), run_dir, atoms)
 
         # Initialize storage for the energies
-        self.result_file = run_dir / 'simulation-results.json'
         self.step_size = step_size
         self.unperturbed_energy: Optional[float] = None
         self.single_perturb = np.zeros((len(atoms), 3, 2)) * np.nan  # Perturbation of a single direction. [atom_id, axis (xyz), dir_id (0 back, 1 forward)]
@@ -30,8 +29,6 @@ def __init__(self, queues: ColmenaQueues, num_workers: int, atoms: ase.Atoms, ru
 
         # Load what has been run already
         self.total_complete = 0
-        self.run_dir = run_dir
-        self.run_dir.mkdir(exist_ok=True)
         self.energy_path = self.run_dir / 'unperturbed.energy'
         self.single_path = self.run_dir / 'single_energies.csv'
         self.double_path = self.run_dir / 'double_energies.csv'
diff --git a/jitterbug/thinkers/static.py b/jitterbug/thinkers/static.py
new file mode 100644
index 0000000..744c29d
--- /dev/null
+++ b/jitterbug/thinkers/static.py
@@ -0,0 +1,108 @@
+"""Approach which uses a static set of structures to compute Hessian"""
+from pathlib import Path
+
+import ase
+import numpy as np
+from ase.db import connect
+from colmena.models import Result
+from colmena.queue import ColmenaQueues
+from colmena.thinker import ResourceCounter, agent, result_processor
+
+from .base import HessianThinker
+from jitterbug.sampler.base import StructureSampler
+from ..model.base import EnergyModel
+from ..utils import read_from_string
+
+
+class ApproximateHessianThinker(HessianThinker):
+    """Approach which approximates a Hessian by computing it from a forcefield fit to structures
+
+    Saves structures to an ASE db and labels them with the name of the sampler and the index
+    """
+
+    def __init__(self,
+                 queues: ColmenaQueues,
+                 num_workers: int,
+                 atoms: ase.Atoms,
+                 run_dir: Path,
+                 sampler: StructureSampler,
+                 num_to_run: int,
+                 model: EnergyModel,
+                 step_size: float = 0.005):
+        super().__init__(queues, ResourceCounter(num_workers), run_dir, atoms)
+        self.step_size = step_size
+        self.sampler = sampler
+        self.num_to_run = num_to_run
+        self.model = model
+
+        # Generate the structures to be sampled
+        self.to_sample = self.sampler.produce_structures(atoms, num_to_run)
+        sampler_name = self.sampler.name
+        self.logger.info(f'Generated {len(self.to_sample)} structures with strategy: {sampler_name}')
+
+        # Find how many we've done already
+        self.db_path = self.run_dir / 'atoms.db'
+        self.completed: set[int] = set()
+        with connect(self.db_path) as db:
+            for row in db.select(f'index<{self.num_to_run}', sampler=sampler_name):
+                atoms = row.toatoms(True)
+                ind = atoms.info['key_value_pairs']['index']
+                assert np.isclose(atoms.positions, self.to_sample[ind].positions).all(), f'Structure {ind} in the DB and generated structure are inconsistent'
+                self.completed.add(ind)
+        num_remaining = self.num_to_run - len(self.completed)
+        self.logger.info(f'Completed {len(self.completed)} structures already. Need to run {num_remaining} more')
+
+    @agent()
+    def submit_tasks(self):
+        """Submit all required tasks then start the shutdown process by exiting"""
+
+        for ind, atoms in enumerate(self.to_sample):
+            # Skip structures which we've done already
+            if ind in self.completed:
+                continue
+
+            # Submit it
+            self.rec.acquire(None, 1)
+            self.queues.send_inputs(
+                atoms,
+                method='get_energy',
+                task_info={'index': ind}
+            )
+
+    @result_processor
+    def store_energy(self, result: Result):
+        """Store the energy in the appropriate files"""
+        self.rec.release()
+
+        # Store the result object to disk
+        with self.result_file.open('a') as fp:
+            print(result.json(exclude={'inputs'}), file=fp)
+
+        if not result.success:
+            self.logger.warning(f'Calculation failed due to {result.failure_info.exception}')
+            return
+
+        # Store the result into the ASE database
+        sampler_name = self.sampler.name
+        index = result.task_info['index']
+        atoms = read_from_string(result.value, 'extxyz')
+        assert np.isclose(result.args[0].positions, atoms.positions).all()
+        self.completed.add(index)
+        with connect(self.db_path) as db:
+            db.write(atoms, sampler=sampler_name, index=index)
+        self.logger.info(f'Saved completed structure. Progress: {len(self.completed)}/{self.num_to_run}'
+                         f' ({len(self.completed) / self.num_to_run * 100:.2f}%)')
+
+    def compute_hessian(self) -> np.ndarray:
+        # Load the models
+        atoms = []
+        with connect(self.db_path) as db:
+            for row in db.select(f'index<{self.num_to_run}', sampler=self.sampler.name):
+                atoms.append(row.toatoms())
+        self.logger.info(f'Pulled {len(atoms)} atoms for a training set')
+
+        # Fit the model
+        model = self.model.train(atoms)
+        self.logger.info('Completed model fitting')
+
+        return self.model.mean_hessian(model)
diff --git a/tests/test_cli.py b/tests/test_cli.py
index 09f6ae7..b1dfafb 100644
--- a/tests/test_cli.py
+++ b/tests/test_cli.py
@@ -13,16 +13,26 @@ def test_exact_solver(file_dir, xyz):
     with open(devnull, 'w') as fo:
         with redirect_stdout(fo):
             main([
-                str(file_dir / xyz), '--exact', '--method', 'hf', 'sto-3g'
+                str(file_dir / xyz), '--approach', 'exact', '--method', 'hf', 'sto-3g'
             ])
     assert (Path('run') / xyz_name / 'hf_sto-3g_exact' / 'hessian.npy').exists()
 
 
+@mark.parametrize('amount', [32., 0.5])
+def test_approx_solver(amount, xyz_path):
+    with open(devnull, 'w') as fo:
+        with redirect_stdout(fo):
+            main([
+                str(xyz_path), '--approach', 'static', '--amount-to-run', str(amount), '--method', 'hf', 'sto-3g'
+            ])
+    assert (Path('run') / xyz_path.name[:-4] / 'hf_sto-3g_static' / 'hessian.npy').exists()
+
+
 def test_parsl_path(xyz_path, file_dir):
     with open(devnull, 'w') as fo:
         with redirect_stdout(fo):
             main([
-                str(xyz_path), '--exact', '--method', 'pm7', 'None',
+                str(xyz_path), '--approach', 'exact', '--method', 'pm7', 'None',
                 '--parsl-config', str(file_dir / 'example_config.py')
             ])
     assert (Path('run') / 'water' / 'pm7_none_exact' / 'hessian.npy').exists()
diff --git a/tests/test_samplers.py b/tests/test_samplers.py
new file mode 100644
index 0000000..82de96d
--- /dev/null
+++ b/tests/test_samplers.py
@@ -0,0 +1,21 @@
+from pytest import mark
+from ase.io import read
+import numpy as np
+
+from jitterbug.sampler import methods
+
+
+@mark.parametrize('method', ['uniform'])
+def test_random(method, xyz_path):
+    """Make sure we get the same structures each time"""
+
+    atoms = read(xyz_path)
+    sampler = methods[method]()
+    assert sampler.name.startswith(method)
+
+    # Generate two batches
+    samples_1 = sampler.produce_structures(atoms, 4)
+    samples_2 = sampler.produce_structures(atoms, 8)
+
+    for a1, a2 in zip(samples_1, samples_2):
+        assert np.isclose(a1.positions, a2.positions).all()
diff --git a/tests/test_thinkers.py b/tests/test_thinkers.py
index 10e097a..2957d90 100644
--- a/tests/test_thinkers.py
+++ b/tests/test_thinkers.py
@@ -10,8 +10,11 @@
 from pytest import fixture, mark
 
 from jitterbug.compare import compare_hessians
+from jitterbug.model.dscribe import make_global_mbtr_model
 from jitterbug.parsl import get_energy
+from jitterbug.sampler import UniformSampler
 from jitterbug.thinkers.exact import ExactHessianThinker
+from jitterbug.thinkers.static import ApproximateHessianThinker
 from jitterbug.utils import make_calculator
 
 
@@ -33,6 +36,11 @@ def ase_hessian(atoms, tmp_path) -> np.ndarray:
     return vib.get_vibrations().get_hessian_2d()
 
 
+@fixture()
+def mbtr(atoms):
+    return make_global_mbtr_model(atoms)
+
+
 @fixture(autouse=True)
 def task_server(queues):
     # Make the function
@@ -93,3 +101,47 @@ def test_exact(atoms, queues, tmpdir, ase_hessian):
     # Make sure it is close to ase's
     comparison = compare_hessians(atoms, hessian, ase_hessian)
     assert abs(comparison.zpe_error) < 0.2
+
+
+@mark.timeout(60)
+def test_approx(atoms, queues, tmpdir, ase_hessian, mbtr):
+    # Make the thinker
+    run_path = Path(tmpdir) / 'run'
+    thinker = ApproximateHessianThinker(
+        queues=queues,
+        num_workers=2,
+        atoms=atoms,
+        run_dir=run_path,
+        num_to_run=128,
+        model=mbtr,
+        sampler=UniformSampler()
+    )
+    assert run_path.exists()
+    assert thinker.completed == set()
+
+    # Run it
+    thinker.run()
+    assert len(thinker.completed) == 128
+
+    # Make sure it picks up from a previous run
+    thinker = ApproximateHessianThinker(
+        queues=queues,
+        num_workers=2,
+        atoms=atoms,
+        run_dir=run_path,
+        num_to_run=128,
+        model=mbtr,
+        sampler=UniformSampler()
+    )
+    assert len(thinker.completed) == 128
+
+    # Make sure it doesn't do any new calculations
+    start_size = (run_path / 'simulation-results.json').stat().st_size
+    thinker.run()
+    end_size = (run_path / 'simulation-results.json').stat().st_size
+    assert start_size == end_size
+
+    # Compute the Hessian
+    hessian = thinker.compute_hessian()
+    assert np.isfinite(hessian).all()
+    assert hessian.shape == (len(atoms) * 3, len(atoms) * 3)