enhance fsdp for 3rd devices

src/lightning/pytorch/trainer/connectors/accelerator_connector.py

@@ -463,11 +463,16 @@ def _check_strategy_and_fallback(self) -> None:
 
         if (
             strategy_flag in FSDPStrategy.get_registered_strategies() or type(self._strategy_flag) is FSDPStrategy
-        ) and self._accelerator_flag not in ("cuda", "gpu"):
+        ) and self._accelerator_flag not in ("cuda", "gpu") and isinstance(self._accelerator_flag, str):
             raise ValueError(
                 f"The strategy `{FSDPStrategy.strategy_name}` requires a GPU accelerator, but got:"
                 f" {self._accelerator_flag}"
             )
+        elif isinstance(self._accelerator_flag, Accelerator):
+            Warning(
+                f"Using a custom accelerator `{self._accelerator_flag.__class__.__name__}`."
+                f" Please ensure it is compatible with the selected strategy `{strategy_flag}`."
+            )
         if strategy_flag in _DDP_FORK_ALIASES and "fork" not in torch.multiprocessing.get_all_start_methods():
             raise ValueError(
                 f"You selected `Trainer(strategy='{strategy_flag}')` but process forking is not supported on this"
@@ -501,7 +506,7 @@ def _check_and_init_precision(self) -> Precision:
         if isinstance(self.strategy, DeepSpeedStrategy):
             return DeepSpeedPrecision(self._precision_flag)  # type: ignore[arg-type]
         if isinstance(self.strategy, FSDPStrategy):
-            return FSDPPrecision(precision=self._precision_input, device=self._accelerator_flag.get_device() if isinstance(self._accelerator_flag, Accelerator) else None)
+            return FSDPPrecision(precision=self._precision_flag, device=self._accelerator_flag.get_device() if isinstance(self._accelerator_flag, Accelerator) else None)
         if self._precision_flag in ("16-true", "bf16-true"):
             return HalfPrecision(self._precision_flag)  # type: ignore
         if self._precision_flag == "32-true":