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diff --git a/_sources/examples_ml.rst b/_sources/examples_ml.rst
@@ -28,7 +28,6 @@ Machine Learning
 
   notebooks/ffnn
   notebooks/torch_and_heyoka
-  notebooks/NeuralHamiltonianODEs
   notebooks/NeuralODEs
+  notebooks/NeuralHamiltonianODEs
   notebooks/differentiable_atmosphere
-
diff --git a/_sources/notebooks/NeuralHamiltonianODEs.ipynb b/_sources/notebooks/NeuralHamiltonianODEs.ipynb
@@ -10,7 +10,7 @@
     "\n",
     "*Greydanus, S., Dzamba, M., & Yosinski, J.* (2019). Hamiltonian Neural Networks. Advances in neural information processing systems, 32.\n",
     "\n",
-    "in that only the perturbation of the Hamiltonian is parametrized by a network. Let us consider the same system as above, but this time using the Hamiltonian formalism. We will shortly summarize, in wht follows, the obvious as to show later how to obtain the same symbolically and using *heyoka*.\n",
+    "in that only the perturbation of the Hamiltonian is parametrized by a network. Let us consider the same system as [in the previous example](./NeuralODEs.ipynb), but this time using the Hamiltonian formalism. We will shortly summarize, in what follows, the obvious as to show later how to obtain the same symbolically and using *heyoka*.\n",
     "\n",
     "Let us first introduce our Lagrangian coordinates $\\mathbf q = [x, y]$ and their derivatives: $\\dot{\\mathbf q} = [v_x, v_y]$. Under this choice we may compute the kinetic energy of the system as:\n",
     "\n",
@@ -27,7 +27,7 @@
     "and thus its Lagrangian as:\n",
     "\n",
     "$$\n",
-    "\\mathcal (\\mathbf q, \\dot{\\mathbf q}) = T - U\n",
+    "\\left(\\mathbf q, \\dot{\\mathbf q}\\right) = T - U\n",
     "$$\n",
     "\n",
     "We can then compute the trivial *canonical momenta* $\\mathbf p=[p_x, p_y]$ as:\n",
@@ -257,7 +257,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.18"
+   "version": "3.10.6"
   }
  },
  "nbformat": 4,

diff --git a/_sources/notebooks/NeuralODEs.ipynb b/_sources/notebooks/NeuralODEs.ipynb
@@ -244,7 +244,7 @@
    "metadata": {},
    "source": [
     "## Performance test\n",
-    "Let us profile the speed of Taylor integration in the context of Neural ODE vs the `scipy.integrate` counterpart, used in most existsing tools that provide some easy access to some version of Neural ODEs.\n",
+    "Let us profile the speed of Taylor integration in the context of Neural ODE vs the {py:mod}`scipy.integrate` counterpart, used in most existsing tools that provide some easy access to some version of Neural ODEs.\n",
     "\n",
     "We start with setting up the Taylor Integration. We create random weights and biases for the `ffnn`. We also set a very high tolerance as to match what is commonly done in the context of ML work on Neural ODEs. (This test can be repeated at dfferent tolerances and will mostly allow for a similar conclusion).\n",
     "\n",
@@ -397,7 +397,7 @@
    "metadata": {},
    "source": [
     "### Scipy Counterpart\n",
-    "We assemble the rhs of our equations for use with the ``scipy.integrate`` suite. Note the simplicity of use of compiled functions for this task.\n",
+    "We assemble the rhs of our equations for use with the {py:mod}`scipy.integrate` suite. Note the simplicity of use of compiled functions for this task.\n",
     "This allows us to use identical jitted expressions also for the rhs of the case of the scipy calls. The comparison results are thus to be interpreted solely in the light of different numerical integration techniques.\n",
     "\n",
     "\n",

diff --git a/acknowledgement.html b/acknowledgement.html
@@ -211,8 +211,8 @@
 <li class="toctree-l1 has-children"><a class="reference internal" href="examples_ml.html">Machine Learning</a><input class="toctree-checkbox" id="toctree-checkbox-5" name="toctree-checkbox-5" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-5"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/ffnn.html">Feed-Forward Neural Networks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/torch_and_heyoka.html">Interfacing <em>torch</em> to <em>heyoka.py</em></a></li>
-<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralODEs.html">Neural ODEs</a></li>
+<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/differentiable_atmosphere.html">Differentiable Atmosphere</a></li>
 </ul>
 </li>

diff --git a/advanced_tutorials.html b/advanced_tutorials.html
@@ -211,8 +211,8 @@
 <li class="toctree-l1 has-children"><a class="reference internal" href="examples_ml.html">Machine Learning</a><input class="toctree-checkbox" id="toctree-checkbox-5" name="toctree-checkbox-5" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-5"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/ffnn.html">Feed-Forward Neural Networks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/torch_and_heyoka.html">Interfacing <em>torch</em> to <em>heyoka.py</em></a></li>
-<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralODEs.html">Neural ODEs</a></li>
+<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/differentiable_atmosphere.html">Differentiable Atmosphere</a></li>
 </ul>
 </li>

diff --git a/basic_tutorials.html b/basic_tutorials.html
@@ -211,8 +211,8 @@
 <li class="toctree-l1 has-children"><a class="reference internal" href="examples_ml.html">Machine Learning</a><input class="toctree-checkbox" id="toctree-checkbox-5" name="toctree-checkbox-5" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-5"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/ffnn.html">Feed-Forward Neural Networks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/torch_and_heyoka.html">Interfacing <em>torch</em> to <em>heyoka.py</em></a></li>
-<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralODEs.html">Neural ODEs</a></li>
+<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/differentiable_atmosphere.html">Differentiable Atmosphere</a></li>
 </ul>
 </li>

diff --git a/benchmarks.html b/benchmarks.html
@@ -211,8 +211,8 @@
 <li class="toctree-l1 has-children"><a class="reference internal" href="examples_ml.html">Machine Learning</a><input class="toctree-checkbox" id="toctree-checkbox-5" name="toctree-checkbox-5" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-5"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/ffnn.html">Feed-Forward Neural Networks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/torch_and_heyoka.html">Interfacing <em>torch</em> to <em>heyoka.py</em></a></li>
-<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralODEs.html">Neural ODEs</a></li>
+<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/differentiable_atmosphere.html">Differentiable Atmosphere</a></li>
 </ul>
 </li>

diff --git a/breaking_changes.html b/breaking_changes.html
@@ -211,8 +211,8 @@
 <li class="toctree-l1 has-children"><a class="reference internal" href="examples_ml.html">Machine Learning</a><input class="toctree-checkbox" id="toctree-checkbox-5" name="toctree-checkbox-5" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-5"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/ffnn.html">Feed-Forward Neural Networks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/torch_and_heyoka.html">Interfacing <em>torch</em> to <em>heyoka.py</em></a></li>
-<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralODEs.html">Neural ODEs</a></li>
+<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/differentiable_atmosphere.html">Differentiable Atmosphere</a></li>
 </ul>
 </li>

diff --git a/changelog.html b/changelog.html
@@ -213,8 +213,8 @@
 <li class="toctree-l1 has-children"><a class="reference internal" href="examples_ml.html">Machine Learning</a><input class="toctree-checkbox" id="toctree-checkbox-5" name="toctree-checkbox-5" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-5"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/ffnn.html">Feed-Forward Neural Networks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/torch_and_heyoka.html">Interfacing <em>torch</em> to <em>heyoka.py</em></a></li>
-<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralODEs.html">Neural ODEs</a></li>
+<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/differentiable_atmosphere.html">Differentiable Atmosphere</a></li>
 </ul>
 </li>

diff --git a/examples_astro.html b/examples_astro.html
@@ -211,8 +211,8 @@
 <li class="toctree-l1 has-children"><a class="reference internal" href="examples_ml.html">Machine Learning</a><input class="toctree-checkbox" id="toctree-checkbox-5" name="toctree-checkbox-5" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-5"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/ffnn.html">Feed-Forward Neural Networks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/torch_and_heyoka.html">Interfacing <em>torch</em> to <em>heyoka.py</em></a></li>
-<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralODEs.html">Neural ODEs</a></li>
+<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/differentiable_atmosphere.html">Differentiable Atmosphere</a></li>
 </ul>
 </li>

diff --git a/examples_event.html b/examples_event.html
@@ -211,8 +211,8 @@
 <li class="toctree-l1 has-children"><a class="reference internal" href="examples_ml.html">Machine Learning</a><input class="toctree-checkbox" id="toctree-checkbox-5" name="toctree-checkbox-5" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-5"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/ffnn.html">Feed-Forward Neural Networks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/torch_and_heyoka.html">Interfacing <em>torch</em> to <em>heyoka.py</em></a></li>
-<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralODEs.html">Neural ODEs</a></li>
+<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/differentiable_atmosphere.html">Differentiable Atmosphere</a></li>
 </ul>
 </li>

diff --git a/examples_ml.html b/examples_ml.html
@@ -211,8 +211,8 @@
 <li class="toctree-l1 current active has-children"><a class="current reference internal" href="#">Machine Learning</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-5" name="toctree-checkbox-5" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-5"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/ffnn.html">Feed-Forward Neural Networks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/torch_and_heyoka.html">Interfacing <em>torch</em> to <em>heyoka.py</em></a></li>
-<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralODEs.html">Neural ODEs</a></li>
+<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/differentiable_atmosphere.html">Differentiable Atmosphere</a></li>
 </ul>
 </li>
@@ -441,8 +441,8 @@ <h1>Machine Learning</h1>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="notebooks/ffnn.html">Feed-Forward Neural Networks</a></li>
 <li class="toctree-l1"><a class="reference internal" href="notebooks/torch_and_heyoka.html">Interfacing <em>torch</em> to <em>heyoka.py</em></a></li>
-<li class="toctree-l1"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="notebooks/NeuralODEs.html">Neural ODEs</a></li>
+<li class="toctree-l1"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l1"><a class="reference internal" href="notebooks/differentiable_atmosphere.html">Differentiable Atmosphere</a></li>
 </ul>
 </div>

diff --git a/examples_others.html b/examples_others.html
@@ -211,8 +211,8 @@
 <li class="toctree-l1 has-children"><a class="reference internal" href="examples_ml.html">Machine Learning</a><input class="toctree-checkbox" id="toctree-checkbox-5" name="toctree-checkbox-5" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-5"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/ffnn.html">Feed-Forward Neural Networks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/torch_and_heyoka.html">Interfacing <em>torch</em> to <em>heyoka.py</em></a></li>
-<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralODEs.html">Neural ODEs</a></li>
+<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/differentiable_atmosphere.html">Differentiable Atmosphere</a></li>
 </ul>
 </li>

diff --git a/genindex.html b/genindex.html
@@ -208,8 +208,8 @@
 <li class="toctree-l1 has-children"><a class="reference internal" href="examples_ml.html">Machine Learning</a><input class="toctree-checkbox" id="toctree-checkbox-5" name="toctree-checkbox-5" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-5"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/ffnn.html">Feed-Forward Neural Networks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/torch_and_heyoka.html">Interfacing <em>torch</em> to <em>heyoka.py</em></a></li>
-<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralODEs.html">Neural ODEs</a></li>
+<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/differentiable_atmosphere.html">Differentiable Atmosphere</a></li>
 </ul>
 </li>

diff --git a/index.html b/index.html
@@ -210,8 +210,8 @@
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 <li class="toctree-l2"><a class="reference internal" href="notebooks/ffnn.html">Feed-Forward Neural Networks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/torch_and_heyoka.html">Interfacing <em>torch</em> to <em>heyoka.py</em></a></li>
-<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralODEs.html">Neural ODEs</a></li>
+<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
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@@ -559,8 +559,8 @@ <h1>heyoka.py<a class="headerlink" href="#heyoka-py" title="Permalink to this he
 <li class="toctree-l1"><a class="reference internal" href="examples_ml.html">Machine Learning</a><ul>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/ffnn.html">Feed-Forward Neural Networks</a></li>
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 <li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralODEs.html">Neural ODEs</a></li>
+<li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralHamiltonianODEs.html">Neural Hamiltonian ODEs</a></li>
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diff --git a/install.html b/install.html
@@ -211,8 +211,8 @@
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 <li class="toctree-l2"><a class="reference internal" href="notebooks/NeuralODEs.html">Neural ODEs</a></li>
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 <li class="toctree-l2"><a class="reference internal" href="notebooks/differentiable_atmosphere.html">Differentiable Atmosphere</a></li>
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