Repository: WenjieDu/PyPOTS (language: python)

Issue:
Add FITS
### 1. Model description


FITS should be included in PyPOTS, and could start from the imputation task.

```bibtex
@inproceedings{xu2024fits,
title={{FITS}: Modeling Time Series with \$10k\$ Parameters},
author={Zhijian Xu and Ailing Zeng and Qiang Xu},
booktitle={The Twelfth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=bWcnvZ3qMb}
}

```


### 2. Check open-source status

- [X] The model implementation is publicly available

### 3. Provide useful information for the implementation

https://github.com/VEWOXIC/FITS
Add FITS
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<!-- Remove if not applicable -->

1. fixing #519;

## Before submitting

<!-- You can remove checks that are not relevant to this PR. -->

- [x] This PR is made to fix a typo or improve the docs (you can dismiss the other checks if this is the case).
- [x] Was this discussed/approved via a GitHub issue? Please add a link to it if that's the case.
- [x] I have commented my code, particularly in hard-to-understand areas.
- [x] I have written necessary tests and already run them locally.



Discussion / hints:

Fix patch:
diff --git a/README.md b/README.md
index 0556fb10..47ee47fa 100644
--- a/README.md
+++ b/README.md
@@ -121,6 +121,7 @@ The paper references and links are all listed at the bottom of this file.
 |:--------------|:---------------------------------------------------------------------------------------------------------------------------------|:--------:|:--------:|:--------:|:--------:|:--------:|:-------------------|
 | LLM           | <a href="https://time-series.ai"><img src="https://time-series.ai/static/figs/robot.svg" width="26px"> Time-Series.AI</a>  [^36] |    ✅     |    ✅     |    ✅     |    ✅     |    ✅     | `Later in 2024`    |
 | Neural Net    | TEFN🧑‍🔧[^39]                                                                                                                   |    ✅     |          |          |          |          | `2024 - arXiv`     |
+| Neural Net    | FITS🧑‍🔧[^41]                                                                                                                   |    ✅     |          |          |          |          | `2024 - ICLR`      |
 | Neural Net    | TimeMixer[^37]                                                                                                                   |    ✅     |          |          |          |          | `2024 - ICLR`      |
 | Neural Net    | iTransformer🧑‍🔧[^24]                                                                                                           |    ✅     |          |          |          |          | `2024 - ICLR`      |
 | Neural Net    | ModernTCN[^38]                                                                                                                   |    ✅     |          |          |          |          | `2024 - ICLR`      |
@@ -501,7 +502,10 @@ Time-Series.AI</a>
 [^38]: Luo, D., & Wang X. (2024).
 [ModernTCN: A Modern Pure Convolution Structure for General Time Series Analysis](https://openreview.net/forum?id=vpJMJerXHU).
 *ICLR 2024*.
-[^39]: Zhan, T., He, Y., Li, Z., & Deng, Y. (2024).
+[^39]: Zhan, T., He, Y., Deng, Y., Li, Z., Du, W., & Wen, Q. (2024).
 [Time Evidence Fusion Network: Multi-source View in Long-Term Time Series Forecasting](https://arxiv.org/abs/2405.06419).
 *arXiv 2024*.
-[^40]: [Wikipedia: Linear interpolation](https://en.wikipedia.org/wiki/Linear_interpolation)
\ No newline at end of file
+[^40]: [Wikipedia: Linear interpolation](https://en.wikipedia.org/wiki/Linear_interpolation)
+[^41]: Xu, Z., Zeng, A., & Xu, Q. (2024).
+[FITS: Modeling Time Series with 10k parameters](https://openreview.net/forum?id=bWcnvZ3qMb).
+*ICLR 2024*.
diff --git a/README_zh.md b/README_zh.md
index ef47a408..55978e01 100644
--- a/README_zh.md
+++ b/README_zh.md
@@ -106,6 +106,7 @@ PyPOTS当前支持多变量POTS数据的插补, 预测, 分类, 聚类以及异
 |:--------------|:---------------------------------------------------------------------------------------------------------------------------------|:------:|:------:|:------:|:------:|:--------:|:-------------------|
 | LLM           | <a href="https://time-series.ai"><img src="https://time-series.ai/static/figs/robot.svg" width="26px"> Time-Series.AI</a>  [^36] |   ✅    |   ✅    |   ✅    |   ✅    |    ✅     | `Later in 2024`    |
 | Neural Net    | TEFN🧑‍🔧[^39]                                                                                                                   |   ✅    |        |        |        |          | `2024 - arXiv`     |
+| Neural Net    | FITS🧑‍🔧[^41]                                                                                                                   |   ✅    |        |        |        |          | `2024 - ICLR`      |
 | Neural Net    | TimeMixer[^37]                                                                                                                   |   ✅    |        |        |        |          | `2024 - ICLR`      |
 | Neural Net    | iTransformer🧑‍🔧[^24]                                                                                                           |   ✅    |        |        |        |          | `2024 - ICLR`      |
 | Neural Net    | ModernTCN[^38]                                                                                                                   |   ✅    |        |        |        |          | `2024 - ICLR`      |
@@ -474,7 +475,10 @@ Time-Series.AI</a>
 [^38]: Luo, D., & Wang X. (2024).
 [ModernTCN: A Modern Pure Convolution Structure for General Time Series Analysis](https://openreview.net/forum?id=vpJMJerXHU).
 *ICLR 2024*.
-[^39]: Zhan, T., He, Y., Li, Z., & Deng, Y. (2024).
+[^39]: Zhan, T., He, Y., Deng, Y., Li, Z., Du, W., & Wen, Q. (2024).
 [Time Evidence Fusion Network: Multi-source View in Long-Term Time Series Forecasting](https://arxiv.org/abs/2405.06419).
 *arXiv 2024*.
-[^40]: [Wikipedia: Linear interpolation](https://en.wikipedia.org/wiki/Linear_interpolation)
\ No newline at end of file
+[^40]: [Wikipedia: Linear interpolation](https://en.wikipedia.org/wiki/Linear_interpolation)
+[^41]: Xu, Z., Zeng, A., & Xu, Q. (2024).
+[FITS: Modeling Time Series with 10k parameters](https://openreview.net/forum?id=bWcnvZ3qMb).
+*ICLR 2024*.
diff --git a/docs/conf.py b/docs/conf.py
index 5b8e3822..f21afad7 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -62,7 +62,7 @@
 intersphinx_mapping = {
     "python": ("https://docs.python.org/3", None),
     "sphinx": ("https://www.sphinx-doc.org/en/master", None),
-    "torch": ("https://pytorch.org/docs/master/", None),
+    "torch": ("https://pytorch.org/docs/main/", None),
     "numpy": ("https://numpy.org/doc/stable/", None),
     "pandas": ("https://pandas.pydata.org/docs/", None),
 }
diff --git a/docs/index.rst b/docs/index.rst
index 1d1fe36f..4aaeb762 100644
--- a/docs/index.rst
+++ b/docs/index.rst
@@ -135,6 +135,8 @@ The paper references are all listed at the bottom of this readme file.
 +================+===========================================================+======+======+======+======+======+=======================+
 | Neural Net     | TEFN🧑‍🔧           :cite:`zhan2024tefn`                  |  ✅  |      |      |      |      | ``2024 - arXiv``      |
 +----------------+-----------------------------------------------------------+------+------+------+------+------+-----------------------+
+| Neural Net     | FITS🧑‍🔧           :cite:`xu2024fits`                    |  ✅  |      |      |      |      | ``2024 - ICLR``       |
++----------------+-----------------------------------------------------------+------+------+------+------+------+-----------------------+
 | Neural Net     | TimeMixer      :cite:`wang2024timemixer`                  |  ✅  |      |      |      |      | ``2024 - ICLR``       |
 +----------------+-----------------------------------------------------------+------+------+------+------+------+-----------------------+
 | Neural Net     | iTransformer🧑‍🔧 :cite:`liu2024itransformer`             |  ✅  |      |      |      |      | ``2024 - ICLR``       |
diff --git a/docs/pypots.imputation.rst b/docs/pypots.imputation.rst
index b7a94b03..a7b47b07 100644
--- a/docs/pypots.imputation.rst
+++ b/docs/pypots.imputation.rst
@@ -19,6 +19,24 @@ pypots.imputation.transformer
    :show-inheritance:
    :inherited-members:
 
+pypots.imputation.tefn
+------------------------------------
+
+.. automodule:: pypots.imputation.tefn
+   :members:
+   :undoc-members:
+   :show-inheritance:
+   :inherited-members:
+
+pypots.imputation.fits
+------------------------------------
+
+.. automodule:: pypots.imputation.fits
+   :members:
+   :undoc-members:
+   :show-inheritance:
+   :inherited-members:
+
 pypots.imputation.timemixer
 ------------------------------------
 
diff --git a/docs/references.bib b/docs/references.bib
index 171d63c5..ce0014ea 100644
--- a/docs/references.bib
+++ b/docs/references.bib
@@ -766,7 +766,7 @@ @article{bai2018tcn
 
 @article{zhan2024tefn,
 title={Time Evidence Fusion Network: Multi-source View in Long-Term Time Series Forecasting},
-author={Zhan, Tianxiang and He, Yuanpeng and Li, Zhen and Deng, Yong},
+author={Zhan, Tianxiang and He, Yuanpeng and Deng, Yong and Li, Zhen and Du, Wenjie and Wen, Qingsong},
 journal={arXiv preprint arXiv:2405.06419},
 year={2024}
 }
diff --git a/pypots/imputation/fits/__init__.py b/pypots/imputation/fits/__init__.py
new file mode 100644
index 00000000..23cbae58
--- /dev/null
+++ b/pypots/imputation/fits/__init__.py
@@ -0,0 +1,24 @@
+"""
+The package including the modules of FITS.
+
+Refer to the paper
+`Zhijian Xu, Ailing Zeng, and Qiang Xu.
+FITS: Modeling Time Series with 10k parameters.
+In The Twelfth International Conference on Learning Representations, 2024.
+<https://openreview.net/pdf?id=bWcnvZ3qMb>`_
+
+Notes
+-----
+This implementation is inspired by the official one https://github.com/VEWOXIC/FITS
+
+"""
+
+# Created by Wenjie Du <wenjay.du@gmail.com>
+# License: BSD-3-Clause
+
+
+from .model import FITS
+
+__all__ = [
+    "FITS",
+]
diff --git a/pypots/imputation/fits/core.py b/pypots/imputation/fits/core.py
new file mode 100644
index 00000000..701ec4ca
--- /dev/null
+++ b/pypots/imputation/fits/core.py
@@ -0,0 +1,86 @@
+"""
+The core wrapper assembles the submodules of FITS imputation model
+and takes over the forward progress of the algorithm.
+"""
+
+# Created by Wenjie Du <wenjay.du@gmail.com>
+# License: BSD-3-Clause
+
+import torch.nn as nn
+
+from ...nn.functional import nonstationary_norm, nonstationary_denorm
+from ...nn.modules.fits import BackboneFITS
+from ...nn.modules.saits import SaitsLoss, SaitsEmbedding
+
+
+class _FITS(nn.Module):
+    def __init__(
+        self,
+        n_steps: int,
+        n_features: int,
+        cut_freq: int,
+        individual: bool,
+        ORT_weight: float = 1,
+        MIT_weight: float = 1,
+        apply_nonstationary_norm: bool = False,
+    ):
+        super().__init__()
+
+        self.n_steps = n_steps
+        self.apply_nonstationary_norm = apply_nonstationary_norm
+
+        self.saits_embedding = SaitsEmbedding(
+            n_features * 2,
+            n_features,
+            with_pos=False,
+        )
+        self.backbone = BackboneFITS(
+            n_steps,
+            n_features,
+            0,  # n_pred_steps is not used in the imputation task
+            cut_freq,
+            individual,
+        )
+
+        # for the imputation task, the output dim is the same as input dim
+        self.output_projection = nn.Linear(n_features, n_features)
+        self.saits_loss_func = SaitsLoss(ORT_weight, MIT_weight)
+
+    def forward(self, inputs: dict, training: bool = True) -> dict:
+        X, missing_mask = inputs["X"], inputs["missing_mask"]
+
+        if self.apply_nonstationary_norm:
+            # Normalization from Non-stationary Transformer
+            X, means, stdev = nonstationary_norm(X, missing_mask)
+
+        # WDU: the original FITS paper isn't proposed for imputation task. Hence the model doesn't take
+        # the missing mask into account, which means, in the process, the model doesn't know which part of
+        # the input data is missing, and this may hurt the model's imputation performance. Therefore, I apply the
+        # SAITS embedding method to project the concatenation of features and masks into a hidden space, as well as
+        # the output layers to project back from the hidden space to the original space.
+        enc_out = self.saits_embedding(X, missing_mask)
+
+        # FITS encoder processing
+        enc_out = self.backbone(enc_out)
+        if self.apply_nonstationary_norm:
+            # De-Normalization from Non-stationary Transformer
+            enc_out = nonstationary_denorm(enc_out, means, stdev)
+
+        # project back the original data space
+        reconstruction = self.output_projection(enc_out)
+
+        imputed_data = missing_mask * X + (1 - missing_mask) * reconstruction
+        results = {
+            "imputed_data": imputed_data,
+        }
+
+        # if in training mode, return results with losses
+        if training:
+            X_ori, indicating_mask = inputs["X_ori"], inputs["indicating_mask"]
+            loss, ORT_loss, MIT_loss = self.saits_loss_func(reconstruction, X_ori, missing_mask, indicating_mask)
+            results["ORT_loss"] = ORT_loss
+            results["MIT_loss"] = MIT_loss
+            # `loss` is always the item for backward propagating to update the model
+            results["loss"] = loss
+
+        return results
diff --git a/pypots/imputation/fits/data.py b/pypots/imputation/fits/data.py
new file mode 100644
index 00000000..4f7b0b62
--- /dev/null
+++ b/pypots/imputation/fits/data.py
@@ -0,0 +1,24 @@
+"""
+Dataset class for FITS.
+"""
+
+# Created by Wenjie Du <wenjay.du@gmail.com>
+# License: BSD-3-Clause
+
+from typing import Union
+
+from ..saits.data import DatasetForSAITS
+
+
+class DatasetForFITS(DatasetForSAITS):
+    """Actually FITS uses the same data strategy as SAITS, needs MIT for training."""
+
+    def __init__(
+        self,
+        data: Union[dict, str],
+        return_X_ori: bool,
+        return_y: bool,
+        file_type: str = "hdf5",
+        rate: float = 0.2,
+    ):
+        super().__init__(data, return_X_ori, return_y, file_type, rate)
diff --git a/pypots/imputation/fits/model.py b/pypots/imputation/fits/model.py
new file mode 100644
index 00000000..2664da26
--- /dev/null
+++ b/pypots/imputation/fits/model.py
@@ -0,0 +1,308 @@
+"""
+The implementation of FITS for the partially-observed time-series imputation task.
+
+"""
+
+# Created by Wenjie Du <wenjay.du@gmail.com>
+# License: BSD-3-Clause
+
+from typing import Union, Optional
+
+import numpy as np
+import torch
+from torch.utils.data import DataLoader
+
+from .core import _FITS
+from .data import DatasetForFITS
+from ..base import BaseNNImputer
+from ...data.checking import key_in_data_set
+from ...data.dataset import BaseDataset
+from ...optim.adam import Adam
+from ...optim.base import Optimizer
+
+
+class FITS(BaseNNImputer):
+    """The PyTorch implementation of the FITS model.
+    FITS is originally proposed by Xu et al. in :cite:`xu2024fits`.
+
+    Parameters
+    ----------
+    n_steps :
+        The number of time steps in the time-series data sample.
+
+    n_features :
+        The number of features in the time-series data sample.
+
+    n_layers :
+        The number of layers in the FITS model.
+
+    d_model :
+        The dimension of the model.
+
+    n_heads :
+        The number of heads in each layer of FITS.
+
+    d_ffn :
+        The dimension of the feed-forward network.
+
+    factor :
+        The factor of the auto correlation mechanism for the FITS model.
+
+    moving_avg_window_size :
+        The window size of moving average.
+
+    dropout :
+        The dropout rate for the model.
+
+    ORT_weight :
+        The weight for the ORT loss, the same as SAITS.
+
+    MIT_weight :
+        The weight for the MIT loss, the same as SAITS.
+
+    batch_size :
+        The batch size for training and evaluating the model.
+
+    epochs :
+        The number of epochs for training the model.
+
+    patience :
+        The patience for the early-stopping mechanism. Given a positive integer, the training process will be
+        stopped when the model does not perform better after that number of epochs.
+        Leaving it default as None will disable the early-stopping.
+
+    optimizer :
+        The optimizer for model training.
+        If not given, will use a default Adam optimizer.
+
+    num_workers :
+        The number of subprocesses to use for data loading.
+        `0` means data loading will be in the main process, i.e. there won't be subprocesses.
+
+    device :
+        The device for the model to run on. It can be a string, a :class:`torch.device` object, or a list of them.
+        If not given, will try to use CUDA devices first (will use the default CUDA device if there are multiple),
+        then CPUs, considering CUDA and CPU are so far the main devices for people to train ML models.
+        If given a list of devices, e.g. ['cuda:0', 'cuda:1'], or [torch.device('cuda:0'), torch.device('cuda:1')] , the
+        model will be parallely trained on the multiple devices (so far only support parallel training on CUDA devices).
+        Other devices like Google TPU and Apple Silicon accelerator MPS may be added in the future.
+
+    saving_path :
+        The path for automatically saving model checkpoints and tensorboard files (i.e. loss values recorded during
+        training into a tensorboard file). Will not save if not given.
+
+    model_saving_strategy :
+        The strategy to save model checkpoints. It has to be one of [None, "best", "better", "all"].
+        No model will be saved when it is set as None.
+        The "best" strategy will only automatically save the best model after the training finished.
+        The "better" strategy will automatically save the model during training whenever the model performs
+        better than in previous epochs.
+        The "all" strategy will save every model after each epoch training.
+
+    verbose :
+        Whether to print out the training logs during the training process.
+    """
+
+    def __init__(
+        self,
+        n_steps: int,
+        n_features: int,
+        cut_freq: int,
+        individual: bool = False,
+        ORT_weight: float = 1,
+        MIT_weight: float = 1,
+        apply_nonstationary_norm: bool = False,
+        batch_size: int = 32,
+        epochs: int = 100,
+        patience: int = None,
+        optimizer: Optional[Optimizer] = Adam(),
+        num_workers: int = 0,
+        device: Optional[Union[str, torch.device, list]] = None,
+        saving_path: str = None,
+        model_saving_strategy: Optional[str] = "best",
+        verbose: bool = True,
+    ):
+        super().__init__(
+            batch_size,
+            epochs,
+            patience,
+            num_workers,
+            device,
+            saving_path,
+            model_saving_strategy,
+            verbose,
+        )
+
+        self.n_steps = n_steps
+        self.n_features = n_features
+        # model hype-parameters
+        self.individual = individual
+        self.cut_freq = cut_freq
+        self.ORT_weight = ORT_weight
+        self.MIT_weight = MIT_weight
+        self.apply_nonstationary_norm = apply_nonstationary_norm
+
+        # set up the model
+        self.model = _FITS(
+            self.n_steps,
+            self.n_features,
+            self.cut_freq,
+            self.individual,
+            self.ORT_weight,
+            self.MIT_weight,
+            self.apply_nonstationary_norm,
+        )
+        self._send_model_to_given_device()
+        self._print_model_size()
+
+        # set up the optimizer
+        self.optimizer = optimizer
+        self.optimizer.init_optimizer(self.model.parameters())
+
+    def _assemble_input_for_training(self, data: list) -> dict:
+        (
+            indices,
+            X,
+            missing_mask,
+            X_ori,
+            indicating_mask,
+        ) = self._send_data_to_given_device(data)
+
+        inputs = {
+            "X": X,
+            "missing_mask": missing_mask,
+            "X_ori": X_ori,
+            "indicating_mask": indicating_mask,
+        }
+
+        return inputs
+
+    def _assemble_input_for_validating(self, data: list) -> dict:
+        return self._assemble_input_for_training(data)
+
+    def _assemble_input_for_testing(self, data: list) -> dict:
+        indices, X, missing_mask = self._send_data_to_given_device(data)
+
+        inputs = {
+            "X": X,
+            "missing_mask": missing_mask,
+        }
+
+        return inputs
+
+    def fit(
+        self,
+        train_set: Union[dict, str],
+        val_set: Optional[Union[dict, str]] = None,
+        file_type: str = "hdf5",
+    ) -> None:
+        # Step 1: wrap the input data with classes Dataset and DataLoader
+        training_set = DatasetForFITS(train_set, return_X_ori=False, return_y=False, file_type=file_type)
+        training_loader = DataLoader(
+            training_set,
+            batch_size=self.batch_size,
+            shuffle=True,
+            num_workers=self.num_workers,
+        )
+        val_loader = None
+        if val_set is not None:
+            if not key_in_data_set("X_ori", val_set):
+                raise ValueError("val_set must contain 'X_ori' for model validation.")
+            val_set = DatasetForFITS(val_set, return_X_ori=True, return_y=False, file_type=file_type)
+            val_loader = DataLoader(
+                val_set,
+                batch_size=self.batch_size,
+                shuffle=False,
+                num_workers=self.num_workers,
+            )
+
+        # Step 2: train the model and freeze it
+        self._train_model(training_loader, val_loader)
+        self.model.load_state_dict(self.best_model_dict)
+        self.model.eval()  # set the model as eval status to freeze it.
+
+        # Step 3: save the model if necessary
+        self._auto_save_model_if_necessary(confirm_saving=True)
+
+    def predict(
+        self,
+        test_set: Union[dict, str],
+        file_type: str = "hdf5",
+    ) -> dict:
+        """Make predictions for the input data with the trained model.
+
+        Parameters
+        ----------
+        test_set : dict or str
+            The dataset for model validating, should be a dictionary including keys as 'X',
+            or a path string locating a data file supported by PyPOTS (e.g. h5 file).
+            If it is a dict, X should be array-like of shape [n_samples, sequence length (n_steps), n_features],
+            which is time-series data for validating, can contain missing values, and y should be array-like of shape
+            [n_samples], which is classification labels of X.
+            If it is a path string, the path should point to a data file, e.g. a h5 file, which contains
+            key-value pairs like a dict, and it has to include keys as 'X' and 'y'.
+
+        file_type :
+            The type of the given file if test_set is a path string.
+
+        Returns
+        -------
+        file_type :
+            The dictionary containing the clustering results and latent variables if necessary.
+
+        """
+        # Step 1: wrap the input data with classes Dataset and DataLoader
+        self.model.eval()  # set the model as eval status to freeze it.
+        test_set = BaseDataset(
+            test_set,
+            return_X_ori=False,
+            return_X_pred=False,
+            return_y=False,
+            file_type=file_type,
+        )
+        test_loader = DataLoader(
+            test_set,
+            batch_size=self.batch_size,
+            shuffle=False,
+            num_workers=self.num_workers,
+        )
+        imputation_collector = []
+
+        # Step 2: process the data with the model
+        with torch.no_grad():
+            for idx, data in enumerate(test_loader):
+                inputs = self._assemble_input_for_testing(data)
+                results = self.model.forward(inputs, training=False)
+                imputation_collector.append(results["imputed_data"])
+
+        # Step 3: output collection and return
+        imputation = torch.cat(imputation_collector).cpu().detach().numpy()
+        result_dict = {
+            "imputation": imputation,
+        }
+        return result_dict
+
+    def impute(
+        self,
+        test_set: Union[dict, str],
+        file_type: str = "hdf5",
+    ) -> np.ndarray:
+        """Impute missing values in the given data with the trained model.
+
+        Parameters
+        ----------
+        test_set :
+            The data samples for testing, should be array-like of shape [n_samples, sequence length (n_steps),
+            n_features], or a path string locating a data file, e.g. h5 file.
+
+        file_type :
+            The type of the given file if X is a path string.
+
+        Returns
+        -------
+        array-like, shape [n_samples, sequence length (n_steps), n_features],
+            Imputed data.
+        """
+
+        result_dict = self.predict(test_set, file_type=file_type)
+        return result_dict["imputation"]
diff --git a/pypots/nn/modules/fits/__init__.py b/pypots/nn/modules/fits/__init__.py
new file mode 100644
index 00000000..38733b7d
--- /dev/null
+++ b/pypots/nn/modules/fits/__init__.py
@@ -0,0 +1,24 @@
+"""
+The package including the modules of FITS.
+
+Refer to the paper
+`Zhijian Xu, Ailing Zeng, and Qiang Xu.
+FITS: Modeling Time Series with 10k parameters.
+In The Twelfth International Conference on Learning Representations, 2024.
+<https://openreview.net/pdf?id=bWcnvZ3qMb>`_
+
+Notes
+-----
+This implementation is inspired by the official one https://github.com/VEWOXIC/FITS
+
+"""
+
+# Created by Wenjie Du <wenjay.du@gmail.com>
+# License: BSD-3-Clause
+
+from .backbone import BackboneFITS
+
+
+__all__ = [
+    "BackboneFITS",
+]
diff --git a/pypots/nn/modules/fits/backbone.py b/pypots/nn/modules/fits/backbone.py
new file mode 100644
index 00000000..272cc800
--- /dev/null
+++ b/pypots/nn/modules/fits/backbone.py
@@ -0,0 +1,69 @@
+"""
+
+"""
+
+# Created by Wenjie Du <wdu@time-series.ai>
+# License: BSD-3-Clause
+
+import torch
+import torch.nn as nn
+
+
+class BackboneFITS(nn.Module):
+    def __init__(
+        self,
+        n_steps: int,
+        n_features: int,
+        n_pred_steps: int,
+        cut_freq: int,
+        individual: bool,
+    ):
+        super().__init__()
+        self.n_steps = n_steps
+        self.n_features = n_features
+        self.n_pred_steps = n_pred_steps
+        self.individual = individual
+
+        self.dominance_freq = cut_freq
+        self.length_ratio = (n_steps + n_pred_steps) / n_steps
+
+        if self.individual:
+            self.freq_upsampler = nn.ModuleList()
+            for i in range(self.n_features):
+                self.freq_upsampler.append(
+                    nn.Linear(self.dominance_freq, int(self.dominance_freq * self.length_ratio)).to(torch.cfloat)
+                )
+        else:
+            # complex layer for frequency upsampling
+            self.freq_upsampler = nn.Linear(self.dominance_freq, int(self.dominance_freq * self.length_ratio)).to(
+                torch.cfloat
+            )
+
+    def forward(self, x):
+        low_specx = torch.fft.rfft(x, dim=1)
+        assert low_specx.size(1) >= self.dominance_freq, (
+            f"The sequence length after FFT {low_specx.size(1)} is less than the cut frequency {self.dominance_freq}. "
+            f"Please check the input sequence length, or decrease the cut frequency."
+        )
+        low_specx[:, self.dominance_freq :] = 0  # LPF
+        low_specx = low_specx[:, 0 : self.dominance_freq, :]  # LPF
+
+        if self.individual:
+            low_specxy_ = torch.zeros(
+                [low_specx.size(0), int(self.dominance_freq * self.length_ratio), low_specx.size(2)],
+                dtype=low_specx.dtype,
+            ).to(low_specx.device)
+            for i in range(self.n_features):
+                low_specxy_[:, :, i] = self.freq_upsampler[i](low_specx[:, :, i].permute(0, 1)).permute(0, 1)
+        else:
+            low_specxy_ = self.freq_upsampler(low_specx.permute(0, 2, 1)).permute(0, 2, 1)
+
+        low_specxy = torch.zeros(
+            [low_specxy_.size(0), int((self.n_steps + self.n_pred_steps) / 2 + 1), low_specxy_.size(2)],
+            dtype=low_specxy_.dtype,
+        ).to(low_specxy_.device)
+        low_specxy[:, 0 : low_specxy_.size(1), :] = low_specxy_  # zero padding
+        low_xy = torch.fft.irfft(low_specxy, dim=1)
+        low_xy = low_xy * self.length_ratio  # energy compensation for the length change
+
+        return low_xy


Test patch:
diff --git a/tests/imputation/fits.py b/tests/imputation/fits.py
new file mode 100644
index 00000000..c35c942e
--- /dev/null
+++ b/tests/imputation/fits.py
@@ -0,0 +1,117 @@
+"""
+Test cases for FITS imputation model.
+"""
+
+# Created by Wenjie Du <wenjay.du@gmail.com>
+# License: BSD-3-Clause
+
+
+import os.path
+import unittest
+
+import numpy as np
+import pytest
+
+from pypots.imputation.fits import FITS
+from pypots.optim import Adam
+from pypots.utils.logging import logger
+from pypots.utils.metrics import calc_mse
+from tests.global_test_config import (
+    DATA,
+    EPOCHS,
+    DEVICE,
+    TRAIN_SET,
+    VAL_SET,
+    TEST_SET,
+    GENERAL_H5_TRAIN_SET_PATH,
+    GENERAL_H5_VAL_SET_PATH,
+    GENERAL_H5_TEST_SET_PATH,
+    RESULT_SAVING_DIR_FOR_IMPUTATION,
+    check_tb_and_model_checkpoints_existence,
+)
+
+
+class TestFITS(unittest.TestCase):
+    logger.info("Running tests for an imputation model FITS...")
+
+    # set the log and model saving path
+    saving_path = os.path.join(RESULT_SAVING_DIR_FOR_IMPUTATION, "FITS")
+    model_save_name = "saved_fits_model.pypots"
+
+    # initialize an Adam optimizer
+    optimizer = Adam(lr=0.001, weight_decay=1e-5)
+
+    # initialize a FITS model
+    fits = FITS(
+        DATA["n_steps"],
+        DATA["n_features"],
+        individual=False,
+        cut_freq=5,
+        epochs=EPOCHS,
+        saving_path=saving_path,
+        optimizer=optimizer,
+        device=DEVICE,
+    )
+
+    @pytest.mark.xdist_group(name="imputation-fits")
+    def test_0_fit(self):
+        self.fits.fit(TRAIN_SET, VAL_SET)
+
+    @pytest.mark.xdist_group(name="imputation-fits")
+    def test_1_impute(self):
+        imputation_results = self.fits.predict(TEST_SET)
+        assert not np.isnan(
+            imputation_results["imputation"]
+        ).any(), "Output still has missing values after running impute()."
+
+        test_MSE = calc_mse(
+            imputation_results["imputation"],
+            DATA["test_X_ori"],
+            DATA["test_X_indicating_mask"],
+        )
+        logger.info(f"FITS test_MSE: {test_MSE}")
+
+    @pytest.mark.xdist_group(name="imputation-fits")
+    def test_2_parameters(self):
+        assert hasattr(self.fits, "model") and self.fits.model is not None
+
+        assert hasattr(self.fits, "optimizer") and self.fits.optimizer is not None
+
+        assert hasattr(self.fits, "best_loss")
+        self.assertNotEqual(self.fits.best_loss, float("inf"))
+
+        assert hasattr(self.fits, "best_model_dict") and self.fits.best_model_dict is not None
+
+    @pytest.mark.xdist_group(name="imputation-fits")
+    def test_3_saving_path(self):
+        # whether the root saving dir exists, which should be created by save_log_into_tb_file
+        assert os.path.exists(self.saving_path), f"file {self.saving_path} does not exist"
+
+        # check if the tensorboard file and model checkpoints exist
+        check_tb_and_model_checkpoints_existence(self.fits)
+
+        # save the trained model into file, and check if the path exists
+        saved_model_path = os.path.join(self.saving_path, self.model_save_name)
+        self.fits.save(saved_model_path)
+
+        # test loading the saved model, not necessary, but need to test
+        self.fits.load(saved_model_path)
+
+    @pytest.mark.xdist_group(name="imputation-fits")
+    def test_4_lazy_loading(self):
+        self.fits.fit(GENERAL_H5_TRAIN_SET_PATH, GENERAL_H5_VAL_SET_PATH)
+        imputation_results = self.fits.predict(GENERAL_H5_TEST_SET_PATH)
+        assert not np.isnan(
+            imputation_results["imputation"]
+        ).any(), "Output still has missing values after running impute()."
+
+        test_MSE = calc_mse(
+            imputation_results["imputation"],
+            DATA["test_X_ori"],
+            DATA["test_X_indicating_mask"],
+        )
+        logger.info(f"Lazy-loading FITS test_MSE: {test_MSE}")
+
+
+if __name__ == "__main__":
+    unittest.main()