docs: add mathematical formulas to atomic model classes

deepmd/dpmodel/atomic_model/dp_atomic_model.py

@@ -28,6 +28,18 @@
 class DPAtomicModel(BaseAtomicModel):
     """Model give atomic prediction of some physical property.
 
+    The atomic model computes atomic properties by first extracting a descriptor
+    from the atomic environment, then passing it through a fitting network:
+
+    .. math::
+        \mathcal{D}^i = \mathrm{Descriptor}(\mathbf{R}^i, \mathbf{R}_j, \mathrm{types}),
+
+    .. math::
+        \mathbf{y}^i = \mathrm{Fitting}(\mathcal{D}^i),
+
+    where :math:`\mathcal{D}^i` is the descriptor for atom :math:`i`, and
+    :math:`\mathbf{y}^i` is the predicted atomic property (energy, dipole, etc.).
+
     Parameters
     ----------
     descriptor

deepmd/dpmodel/atomic_model/linear_atomic_model.py

@@ -40,6 +40,18 @@
 class LinearEnergyAtomicModel(BaseAtomicModel):
     """Linear model make linear combinations of several existing models.
 
+    The linear model combines predictions from multiple atomic models:
+
+    .. math::
+        E^i = \sum_{k=1}^{K} w_k \cdot E_k^i,
+
+    where :math:`E_k^i` is the energy predicted by the :math:`k`-th sub-model
+    for atom :math:`i`, and :math:`w_k` is the corresponding weight. The weights
+    can be learned or manually specified.
+
+    This is useful for combining different interaction types, e.g., DP + ZBL
+    for short-range repulsion, or DP + D3 for dispersion corrections.
+
     Parameters
     ----------
     models : list[DPAtomicModel or PairTabAtomicModel]

deepmd/dpmodel/atomic_model/pairtab_atomic_model.py

@@ -45,6 +45,15 @@ class PairTabAtomicModel(BaseAtomicModel):
     At this moment, the model does not smooth the energy at the cutoff radius, so
     one needs to make sure the energy has been smoothed to zero.
 
+    The pairwise energy is computed by table lookup and interpolation:
+
+    .. math::
+        E^i = \sum_{j \in \mathcal{N}(i)} E_{t_i, t_j}(r_{ij}),
+
+    where :math:`E_{t_i, t_j}(r)` is the tabulated pairwise energy between atom types
+    :math:`t_i` and :math:`t_j` at distance :math:`r`, obtained via cubic spline
+    interpolation from the table data.
+
     Parameters
     ----------
     tab_file : str