diff --git a/CHANGELOG.md b/CHANGELOG.md
index f940e63a8..c477799b2 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -15,6 +15,7 @@
 
 ## Bug fixes
 
+-   Fixed `Interpolant` ids to allow processing ([#962](https://github.com/pybamm-team/PyBaMM/pull/962)
 -   Changed simulation attributes to assign copies rather than the objects themselves ([#952](https://github.com/pybamm-team/PyBaMM/pull/952)
 -   Added default values to base model so that it works with the `Simulation` class ([#952](https://github.com/pybamm-team/PyBaMM/pull/952)
 -   Fixed solver to recompute initial conditions when inputs are changed ([#951](https://github.com/pybamm-team/PyBaMM/pull/951)
diff --git a/pybamm/expression_tree/interpolant.py b/pybamm/expression_tree/interpolant.py
index 19a6e5448..de49da96f 100644
--- a/pybamm/expression_tree/interpolant.py
+++ b/pybamm/expression_tree/interpolant.py
@@ -31,7 +31,13 @@ class Interpolant(pybamm.Function):
     """
 
     def __init__(
-        self, data, child, name=None, interpolator="cubic spline", extrapolate=True
+        self,
+        data,
+        child,
+        name=None,
+        interpolator="cubic spline",
+        extrapolate=True,
+        entries_string=None,
     ):
         if data.ndim != 2 or data.shape[1] != 2:
             raise ValueError(
@@ -56,16 +62,38 @@ class Interpolant(pybamm.Function):
             name = "interpolating function ({})".format(name)
         else:
             name = "interpolating function"
+        self.data = data
+        self.entries_string = entries_string
         super().__init__(
             interpolating_function, child, name=name, derivative="derivative"
         )
         # Store information as attributes
-        self.data = data
         self.x = data[:, 0]
         self.y = data[:, 1]
         self.interpolator = interpolator
         self.extrapolate = extrapolate
 
+    @property
+    def entries_string(self):
+        return self._entries_string
+
+    @entries_string.setter
+    def entries_string(self, value):
+        # We must include the entries in the hash, since different arrays can be
+        # indistinguishable by class, name and domain alone
+        # Slightly different syntax for sparse and non-sparse matrices
+        if value is not None:
+            self._entries_string = value
+        else:
+            entries = self.data
+            self._entries_string = entries.tostring()
+
+    def set_id(self):
+        """ See :meth:`pybamm.Symbol.set_id()`. """
+        self._id = hash(
+            (self.__class__, self.name, self.entries_string) + tuple(self.domain)
+        )
+
     def _function_new_copy(self, children):
         """ See :meth:`Function._function_new_copy()` """
         return pybamm.Interpolant(
@@ -73,5 +101,6 @@ class Interpolant(pybamm.Function):
             *children,
             name=self.name,
             interpolator=self.interpolator,
-            extrapolate=self.extrapolate
+            extrapolate=self.extrapolate,
+            entries_string=self.entries_string
         )

Processing Interpolants bug
When there are multiple interpolants in the model, they all have the same id so they get processed to the same object
diff --git a/tests/unit/test_parameters/test_parameter_values.py b/tests/unit/test_parameters/test_parameter_values.py
index 39156f62a..351f7b23e 100644
--- a/tests/unit/test_parameters/test_parameter_values.py
+++ b/tests/unit/test_parameters/test_parameter_values.py
@@ -331,11 +331,11 @@ class TestParameterValues(unittest.TestCase):
         x = np.linspace(0, 10)[:, np.newaxis]
         data = np.hstack([x, 2 * x])
         parameter_values = pybamm.ParameterValues(
-            {"a": 3.01, "Diffusivity": ("times two", data)}
+            {"a": 3.01, "Times two": ("times two", data)}
         )
 
         a = pybamm.Parameter("a")
-        func = pybamm.FunctionParameter("Diffusivity", {"a": a})
+        func = pybamm.FunctionParameter("Times two", {"a": a})
 
         processed_func = parameter_values.process_symbol(func)
         self.assertIsInstance(processed_func, pybamm.Interpolant)
@@ -346,6 +346,16 @@ class TestParameterValues(unittest.TestCase):
         processed_diff_func = parameter_values.process_symbol(diff_func)
         self.assertEqual(processed_diff_func.evaluate(), 2)
 
+        # interpolant defined up front
+        interp2 = pybamm.Interpolant(data, a)
+        processed_interp2 = parameter_values.process_symbol(interp2)
+        self.assertEqual(processed_interp2.evaluate(), 6.02)
+
+        data3 = np.hstack([x, 3 * x])
+        interp3 = pybamm.Interpolant(data3, a)
+        processed_interp3 = parameter_values.process_symbol(interp3)
+        self.assertEqual(processed_interp3.evaluate(), 9.03)
+
     def test_interpolant_against_function(self):
         parameter_values = pybamm.ParameterValues({})
         parameter_values.update(

pip install -e .[dev,docs]
parse_log_pytest
pytest
pytest
apt-get update apt-get install -y gcc gfortran libopenblas-dev liblapack-dev
3.7
pytest --no-header -rA --tb=line --color=no -p no:cacheprovider -W ignore::DeprecationWarning
alabaster==0.7.13
anyio==3.7.1
anytree==2.12.1
argon2-cffi==23.1.0
argon2-cffi-bindings==21.2.0
attrs @ file:///croot/attrs_1668696182826/work
autograd==1.6.2
Babel==2.14.0
backcall==0.2.0
beautifulsoup4==4.13.3
black==23.3.0
bleach==6.0.0
casadi==3.7.0
certifi @ file:///croot/certifi_1671487769961/work/certifi
cffi==1.15.1
charset-normalizer==3.4.1
click==8.1.8
comm==0.1.4
cycler==0.11.0
debugpy==1.7.0
decorator==5.1.1
defusedxml==0.7.1
docutils==0.17.1
entrypoints==0.4
exceptiongroup==1.2.2
fastjsonschema==2.21.1
flake8==5.0.4
flit_core @ file:///opt/conda/conda-bld/flit-core_1644941570762/work/source/flit_core
fonttools==4.38.0
future==1.0.0
guzzle-sphinx-theme==0.7.11
idna==3.10
imagesize==1.4.1
importlib-metadata==4.2.0
importlib-resources==5.12.0
iniconfig @ file:///home/linux1/recipes/ci/iniconfig_1610983019677/work
ipykernel==6.16.2
ipython==7.34.0
ipython-genutils==0.2.0
ipywidgets==8.1.5
jedi==0.19.2
Jinja2==3.1.6
json5==0.9.16
jsonschema==4.17.3
jupyter==1.1.1
jupyter-console==6.6.3
jupyter-server==1.24.0
jupyter_client==7.4.9
jupyter_core==4.12.0
jupyterlab==3.5.3
jupyterlab-pygments==0.2.2
jupyterlab_server==2.15.2
jupyterlab_widgets==3.0.13
kiwisolver==1.4.5
MarkupSafe==2.1.5
matplotlib==3.5.3
matplotlib-inline==0.1.6
mccabe==0.7.0
mistune==3.0.2
mypy-extensions==1.0.0
nbclassic==1.2.0
nbclient==0.7.4
nbconvert==7.6.0
nbformat==5.8.0
nest-asyncio==1.6.0
notebook==6.5.7
notebook_shim==0.2.4
numpy==1.21.6
packaging @ file:///croot/packaging_1671697413597/work
pandas==1.3.5
pandocfilters==1.5.1
parso==0.8.4
pathspec==0.11.2
pexpect==4.9.0
pickleshare==0.7.5
Pillow==9.5.0
pkgutil_resolve_name==1.3.10
platformdirs==4.0.0
pluggy @ file:///tmp/build/80754af9/pluggy_1648042572264/work
prometheus-client==0.17.1
prompt_toolkit==3.0.48
psutil==7.0.0
ptyprocess==0.7.0
py @ file:///opt/conda/conda-bld/py_1644396412707/work
-e git+https://github.com/pybamm-team/PyBaMM.git@9b72b1eca260de254f045e3c884fffe6cc7a1a4c#egg=pybamm
pycodestyle==2.9.1
pycparser==2.21
pyflakes==2.5.0
Pygments==2.17.2
pyparsing==3.1.4
pyrsistent==0.19.3
pytest==7.1.2
python-dateutil==2.9.0.post0
pytz==2025.2
pyzmq==26.2.1
requests==2.31.0
scikit-fem==8.1.0
scipy==1.7.3
Send2Trash==1.8.3
six==1.17.0
sniffio==1.3.1
snowballstemmer==2.2.0
soupsieve==2.4.1
Sphinx==4.3.2
sphinxcontrib-applehelp==1.0.2
sphinxcontrib-devhelp==1.0.2
sphinxcontrib-htmlhelp==2.0.0
sphinxcontrib-jsmath==1.0.1
sphinxcontrib-qthelp==1.0.3
sphinxcontrib-serializinghtml==1.1.5
terminado==0.17.1
tinycss2==1.2.1
tomli @ file:///opt/conda/conda-bld/tomli_1657175507142/work
tornado==6.2
traitlets==5.9.0
typed-ast==1.5.5
typing_extensions==4.7.1
urllib3==2.0.7
wcwidth==0.2.13
webencodings==0.5.1
websocket-client==1.6.1
widgetsnbextension==4.0.13
zipp @ file:///croot/zipp_1672387121353/work

name: PyBaMM
channels:
  - defaults
  - https://repo.anaconda.com/pkgs/main
  - https://repo.anaconda.com/pkgs/r
  - conda-forge
dependencies:
  - _libgcc_mutex=0.1=main
  - _openmp_mutex=5.1=1_gnu
  - attrs=22.1.0=py37h06a4308_0
  - ca-certificates=2025.2.25=h06a4308_0
  - certifi=2022.12.7=py37h06a4308_0
  - flit-core=3.6.0=pyhd3eb1b0_0
  - importlib_metadata=4.11.3=hd3eb1b0_0
  - iniconfig=1.1.1=pyhd3eb1b0_0
  - ld_impl_linux-64=2.40=h12ee557_0
  - libffi=3.4.4=h6a678d5_1
  - libgcc-ng=11.2.0=h1234567_1
  - libgomp=11.2.0=h1234567_1
  - libstdcxx-ng=11.2.0=h1234567_1
  - ncurses=6.4=h6a678d5_0
  - openssl=1.1.1w=h7f8727e_0
  - packaging=22.0=py37h06a4308_0
  - pip=22.3.1=py37h06a4308_0
  - pluggy=1.0.0=py37h06a4308_1
  - py=1.11.0=pyhd3eb1b0_0
  - pytest=7.1.2=py37h06a4308_0
  - python=3.7.16=h7a1cb2a_0
  - readline=8.2=h5eee18b_0
  - setuptools=65.6.3=py37h06a4308_0
  - sqlite=3.45.3=h5eee18b_0
  - tk=8.6.14=h39e8969_0
  - tomli=2.0.1=py37h06a4308_0
  - wheel=0.38.4=py37h06a4308_0
  - xz=5.6.4=h5eee18b_1
  - zipp=3.11.0=py37h06a4308_0
  - zlib=1.2.13=h5eee18b_1
  - pip:
      - alabaster==0.7.13
      - anyio==3.7.1
      - anytree==2.12.1
      - argon2-cffi==23.1.0
      - argon2-cffi-bindings==21.2.0
      - autograd==1.6.2
      - babel==2.14.0
      - backcall==0.2.0
      - beautifulsoup4==4.13.3
      - black==23.3.0
      - bleach==6.0.0
      - casadi==3.7.0
      - cffi==1.15.1
      - charset-normalizer==3.4.1
      - click==8.1.8
      - comm==0.1.4
      - cycler==0.11.0
      - debugpy==1.7.0
      - decorator==5.1.1
      - defusedxml==0.7.1
      - docutils==0.17.1
      - entrypoints==0.4
      - exceptiongroup==1.2.2
      - fastjsonschema==2.21.1
      - flake8==5.0.4
      - fonttools==4.38.0
      - future==1.0.0
      - guzzle-sphinx-theme==0.7.11
      - idna==3.10
      - imagesize==1.4.1
      - importlib-metadata==4.2.0
      - importlib-resources==5.12.0
      - ipykernel==6.16.2
      - ipython==7.34.0
      - ipython-genutils==0.2.0
      - ipywidgets==8.1.5
      - jedi==0.19.2
      - jinja2==3.1.6
      - json5==0.9.16
      - jsonschema==4.17.3
      - jupyter==1.1.1
      - jupyter-client==7.4.9
      - jupyter-console==6.6.3
      - jupyter-core==4.12.0
      - jupyter-server==1.24.0
      - jupyterlab==3.5.3
      - jupyterlab-pygments==0.2.2
      - jupyterlab-server==2.15.2
      - jupyterlab-widgets==3.0.13
      - kiwisolver==1.4.5
      - markupsafe==2.1.5
      - matplotlib==3.5.3
      - matplotlib-inline==0.1.6
      - mccabe==0.7.0
      - mistune==3.0.2
      - mypy-extensions==1.0.0
      - nbclassic==1.2.0
      - nbclient==0.7.4
      - nbconvert==7.6.0
      - nbformat==5.8.0
      - nest-asyncio==1.6.0
      - notebook==6.5.7
      - notebook-shim==0.2.4
      - numpy==1.21.6
      - pandas==1.3.5
      - pandocfilters==1.5.1
      - parso==0.8.4
      - pathspec==0.11.2
      - pexpect==4.9.0
      - pickleshare==0.7.5
      - pillow==9.5.0
      - pkgutil-resolve-name==1.3.10
      - platformdirs==4.0.0
      - prometheus-client==0.17.1
      - prompt-toolkit==3.0.48
      - psutil==7.0.0
      - ptyprocess==0.7.0
      - pycodestyle==2.9.1
      - pycparser==2.21
      - pyflakes==2.5.0
      - pygments==2.17.2
      - pyparsing==3.1.4
      - pyrsistent==0.19.3
      - python-dateutil==2.9.0.post0
      - pytz==2025.2
      - pyzmq==26.2.1
      - requests==2.31.0
      - scikit-fem==8.1.0
      - scipy==1.7.3
      - send2trash==1.8.3
      - six==1.17.0
      - sniffio==1.3.1
      - snowballstemmer==2.2.0
      - soupsieve==2.4.1
      - sphinx==4.3.2
      - sphinxcontrib-applehelp==1.0.2
      - sphinxcontrib-devhelp==1.0.2
      - sphinxcontrib-htmlhelp==2.0.0
      - sphinxcontrib-jsmath==1.0.1
      - sphinxcontrib-qthelp==1.0.3
      - sphinxcontrib-serializinghtml==1.1.5
      - terminado==0.17.1
      - tinycss2==1.2.1
      - tornado==6.2
      - traitlets==5.9.0
      - typed-ast==1.5.5
      - typing-extensions==4.7.1
      - urllib3==2.0.7
      - wcwidth==0.2.13
      - webencodings==0.5.1
      - websocket-client==1.6.1
      - widgetsnbextension==4.0.13
prefix: /opt/conda/envs/PyBaMM

tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_process_interpolant
tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_check_parameter_values tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_evaluate tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_init tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_inplace tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_interpolant_against_function tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_multi_var_function_parameter tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_multi_var_function_with_parameters tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_process_complex_expression tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_process_empty_model tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_process_function_parameter tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_process_inline_function_parameters tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_process_input_parameter tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_process_model tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_process_symbol tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_read_parameters_csv tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_update tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_update_from_chemistry tests/unit/test_parameters/test_parameter_values.py::TestParameterValues::test_update_model
pybamm/expression_tree/interpolant.py CHANGELOG.md
pybamm/expression_tree/interpolant.py CHANGELOG.md