docs: document the floating-point precision of the model (#4240)

<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit

- **New Features**
- Added a new section on `precision` in the documentation, enhancing
navigation.
- Introduced detailed guidelines on floating-point precision settings
for the model.
- Included structured instructions for creating models with the PyTorch
backend.

- **Documentation**
- Expanded troubleshooting documentation related to model precision
issues, including data accuracy and training recommendations.
- Enhanced guidelines for integrating new components into user
configurations and ensuring model integrity across different backends.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

---------

Signed-off-by: Jinzhe Zeng <[email protected]>

doc/development/create-a-model-pt.md

@@ -137,6 +137,15 @@ class SomeAtomicModel(BaseAtomicModel, torch.nn.Module):
         pass
 ```
 
+### Floating-point precision
+
+When creating a new component, the floating-point precision should obey the [Floating-point precision of the model](../model/precision.md) section.
+In implementation, the component should
+
+- store parameters in the component precision, except those for output normalization;
+- store output normalization parameters in {py:data}`deepmd.pt.utils.env.GLOBAL_PT_FLOAT_PRECISION`;
+- before input normalization, cast the input tensor to the component precision; before output normalization, cast the output tensor to the {py:data}`deepmd.pt.utils.env.GLOBAL_PT_FLOAT_PRECISION`.
+
 ## Register new arguments
 
 To let someone uses your new component in their input file, you need to create a new method that returns some `Argument` of your new component, and then register new arguments. For example, the code below

doc/model/index.rst

@@ -24,3 +24,4 @@ Model
    linear
    pairtab
    change-bias
+   precision

doc/model/precision.md

@@ -0,0 +1,15 @@
+# Floating-point precision of the model
+
+The following options control the precision of the model:
+
+- The environment variable {envvar}`DP_INTERFACE_PREC` controls the interface precision of the model, the descriptor, and the fitting, the precision of the environmental matrix, and the precision of the normalized parameters for the environmental matrix and the fitting output.
+- The training parameters {ref}`precision <model[standard]/fitting_net[ener]/precision>` in the descriptor, the fitting, and the type embedding control the precision of neural networks in those components, and the subsequent operations after the output of neural networks.
+- The reduced output (e.g. total energy) is always `float64`.
+
+Usually, the following two combinations of options are recommended:
+
+- Setting {envvar}`DP_INTERFACE_PREC` to `high` (default) and all {ref}`precision <model[standard]/fitting_net[ener]/precision>` options to `float64` (default).
+- Setting {envvar}`DP_INTERFACE_PREC` to `high` (default) and all {ref}`precision <model[standard]/fitting_net[ener]/precision>` options to `float32`.
+
+The Python and C++ inference interfaces accept both `float64` and `float32` as the input and output arguments, whatever the floating-point precision of the model interface is.
+Usually, the MD programs (such as LAMMPS) only use `float64` in their interfaces.

doc/troubleshooting/precision.md

@@ -60,6 +60,7 @@ See [FAQ: How to tune Fitting/embedding-net size](./howtoset_netsize.md) for det
 
 In some cases, one may want to use the FP32 precision to make the model faster.
 For some applications, FP32 is enough and thus is recommended, but one should still be aware that the precision of FP32 is not as high as that of FP64.
+See [Floating-point precision of the model](../model/precision.md) section for how to set the precision.
 
 ## Training