prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What are the datasets used in this community for research?

Read the following text and answer briefly.

Context 1: \section{Introduction}
Underwater robot picking is to use the robot to automatically capture sea creatures like holothurian, echinus, scallop, or starfish in an open-sea farm where underwater object detection is the key technology for locating creatures  Until now, the datasets used in this community are released by the Underwater Robot Professional Contest (URPC$\protect\footnote{Underwater Robot Professional Contest: {\bf http://en cnurpc org} }$) beginning from 2017, in which URPC2017 and URPC2018 are most often used for research  Unfortunately, as the information listed in Table \ref{Info}, URPC series datasets do not provide the annotation file of the test set and cannot be downloaded after the contest  
Therefore, researchers \cite{2020arXiv200511552C,2019arXiv191103029L} first have to divide the training data into two subsets, including a new subset of training data and a new subset of testing data, and then train their proposed method and other \emph{SOTA} methods  On the one hand, training other methods results in a significant increase in workload  On the other hand, different researchers divide different datasets in different ways, 
\begin{table}[t]
\renewcommand\tabcolsep{3 5pt}
\caption{Information about all the collected datasets  * denotes the test set's annotations are not available  \emph{3} in Class means three types of creatures are labeled, \emph{i e ,} holothurian, echinus, and scallop  \emph{4} means four types of creatures are labeled (starfish added)  Retention represents the proportion of images that retain after similar images have been removed }
\centering 
\begin{tabular}{|l|c|c|c|c|c|}
\hline
Dataset&Train&Test&Class&Retention&Year \\ 
\hline 
URPC2017&17,655&985*&3&15\%&2017 \\
\hline
URPC2018&2,901&800*&4&99\%&2018 \\
\hline
URPC2019&4,757&1,029*&4&86\%&2019 \\
\hline
URPC2020$_{ZJ}$&5,543&2,000*&4&82\%&2020 \\
\hline
URPC2020$_{DL}$&6,575&2,400*&4&80\%&2020 \\
\hline
UDD&1,827&400&3&84\%&2020 \\
\hline 

\end{tabular}
\label{Info}
\end{table}
\begin{figure*}[htbp]
\begin{center}
\includegraphics[width=1\linewidth]{example pdf}
\end{center}
   \caption{Examples in DUO, which show a variety of scenarios in underwater environments }
\label{exam}
\end{figure*}
causing there is no unified benchmark to compare the performance of different algorithms 
In terms of the content of the dataset images, there are a large number of similar or duplicate images in the URPC datasets  URPC2017 only retains 15\% images after removing similar images compared to other datasets  Thus the detector trained on URPC2017 is easy to overfit and cannot reflect the real performance 
For other URPC datasets, the latter also includes images from the former, \emph{e g }, URPC2019 adds 2,000 new images compared to URPC2018; compared with URPC2019, URPC2020$_{ZJ}$ adds 800 new images  The URPC2020$_{DL}$ adds 1,000 new images compared to the URPC2020$_{ZJ}$  It is worth mentioning that the annotation of all datasets is incomplete; some datasets lack the starfish labels and it is easy to find error or missing labels  \cite{DBLP:conf/iclr/ZhangBHRV17} pointed out that although the CNN model has a strong fitting ability for any dataset, the existence of dirty data will significantly weaken its robustness 
Therefore, a reasonable dataset (containing a small number of similar images as well as an accurate annotation) and a corresponding recognized benchmark are urgently needed to promote community development 


To address these issues, we introduce a dataset called Detecting Underwater Objects (DUO) by collecting and re-annotating all the available underwater datasets  It contains 7,782 underwater images after deleting overly similar images and has a more accurate annotation with four types of classes (\emph{i e ,} holothurian, echinus, scallop, and starfish)  
Besides, based on the MMDetection$\protect\footnote{MMDetection is an open source object detection toolbox based on PyTorch  {\bf https://github com/open-mmlab/mmdetection}}$ \cite{chen2019mmdetection} framework, we also provide a \emph{SOTA} detector benchmark containing efficiency and accuracy indicators, providing a reference for both academic research and industrial applications  It is worth noting that JETSON AGX XAVIER$\protect\footnote{JETSON AGX XAVIER is an embedded development board produced by NVIDIA which could be deployed in an underwater robot  Please refer {\bf https://developer nvidia com/embedded/jetson-agx-xavier-developer-kit} for more information }$ was used to assess all the detectors in the efficiency test in order to simulate robot-embedded environment  DUO will be released in https://github com/chongweiliu soon 

In summary, the contributions of this paper can be listed as follows 

  $\bullet$ By collecting and re-annotating all relevant datasets, we introduce a dataset called DUO with more reasonable annotations as well as a variety of underwater scenes 

  $\bullet$ We provide a corresponding benchmark of \emph{SOTA} detectors on DUO including efficiency and accuracy indicators which could be a reference for both academic research and industrial applications  


\pagestyle{empty}
\section{Background}
In the year of 2017, underwater object detection for open-sea farming is first proposed in the target recognition track of Underwater Robot Picking Contest 2017$\protect\footnote{From 2020, the name has been changed into Underwater Robot Professional Contest which is also short for URPC }$ (URPC2017) which aims to promote the development of theory, technology, and industry of the underwater agile robot and fill the blank of the grabbing task of the underwater agile robot  The competition sets up a target recognition track, a fixed-point grasping track, and an autonomous grasping track  The target recognition track concentrates on finding the {\bf high accuracy and efficiency} algorithm which could be used in an underwater robot for automatically grasping 

The datasets we used to generate the DUO are listed below  The detailed information has been shown in Table \ref{Info} 

  {\bf URPC2017}: It contains 17,655 images for training and 985 images for testing and the resolution of all the images is 720$\times$405  All the images are taken from 6 videos at an interval of 10 frames  However, all the videos were filmed in an artificial simulated environment and pictures from the same video look almost identical  
  
   {\bf URPC2018}: It contains 2,901 images for training and 800 images for testing and the resolutions of the images are 586$\times$480, 704$\times$576, 720$\times$405, and 1,920$\times$1,080  The test set's annotations are not available  Besides, some images were also collected from an artificial underwater environment 
  
  {\bf URPC2019}: It contains 4,757 images for training and 1029 images for testing and the highest resolution of the images is 3,840$\times$2,160 captured by a GOPro camera  The test set's annotations are also not available and it contains images from the former contests 
  
  {\bf URPC2020$_{ZJ}$}: From 2020, the URPC will be held twice a year  It was held first in Zhanjiang, China, in April and then in Dalian, China, in August  URPC2020$_{ZJ}$ means the dataset released in the first URPC2020 and URPC2020$_{DL}$ means the dataset released in the second URPC2020  This dataset contains 5,543 images for training and 2,000 images for testing and the highest resolution of the images is 3,840$\times$2,160  The test set's annotations are also not available 
  
  {\bf URPC2020$_{DL}$}: This dataset contains 6,575 images for training and 2,400 images for testing and the highest resolution of the images is 3,840$\times$2,160  The test set's annotations are also not available 
  
  {\bf UDD \cite{2020arXiv200301446W}}: This dataset contains 1,827 images for training and 400 images for testing and the highest resolution of the images is 3,840$\times$2,160  All the images are captured by a diver and a robot in a real open-sea farm 

\begin{figure}[t]
\begin{center}
\includegraphics[width=1\linewidth]{pie pdf}
\end{center}
   \caption{The proportion distribution of the objects in DUO }
\label{pie}
\end{figure}



\begin{figure*}
  \centering
  \subfigure[]{\includegraphics[width=3 45in]{imagesize pdf}}
  \subfigure[]{\includegraphics[width=3 45in]{numInstance pdf}}
  \caption{(a) The distribution of instance sizes for DUO; (b) The number of categories per image }
  \label{sum}
\end{figure*}
\section{Proposed Dataset}

\subsection{Image Deduplicating}
As we explained in Section 1, there are a large number of similar or repeated images in the series of URPC datasets  Therefore, it is important to delete duplicate or overly similar images and keep a variety of underwater scenarios when we merge these datasets together  Here we employ the Perceptual Hash algorithm (PHash) to remove those images  PHash has the special property that the hash value is dependent on the image content, and it remains approximately the same if the content is not significantly modified  Thus we can easily distinguish different scenarios and delete duplicate images within one scenario  

After deduplicating, we obtain 7,782 images (6,671 images for training; 1,111 for testing)  The retention rate of the new dataset is 95\%, which means that there are only a few similar images in the new dataset  Figure \ref{exam} shows that our dataset also retains various underwater scenes 

\subsection{Image Re-annotation}
Due to the small size of objects and the blur underwater environment, there are always missing or wrong labels in the existing annotation files  In addition, some test sets' annotation files are not available and some datasets do not have the starfish annotation  In order to address these issues, we follow the next process which combines a CNN model and manual annotation to re-annotate these images  Specifically, we first train a detector (\emph{i e ,} GFL \cite{li2020generalized}) with the originally labeled images  After that, the trained detector predicts all the 7,782 images  We treat the prediction as the groundtruth and use it to train the GFL again  We get the final GFL prediction called {\bf the coarse annotation}  Next, we use manual correction to get the final annotation called {\bf the fine annotation}  Notably, we adopt the COCO \cite{Belongie2014} annotation form as the final format 
\subsection{Dataset Statistics}
{\bf The proportion of classes}: The total number of objects is 74,515  Holothurian, echinus, scallop, and starfish are 7,887, 50,156, 1,924, and 14,548, respectively  Figure \ref{pie} shows the proportion of each creatures where echinus accounts for 67 3\% of the total  The whole data distribution shows an obvious long-tail distribution because the different economic benefits of different seafoods determine the different breed quantities 

{\bf The distribution of instance sizes}: Figure \ref{sum}(a) shows an instance size distribution of DUO  \emph{Percent of image size} represents the ratio of object area to image area, and \emph{Percent of instance} represents the ratio of the corresponding number of objects to the total number of objects  Because of these small creatures and high-resolution images, the vast majority of objects occupy 0 3\% to 1 5\% of the image area 

{\bf The instance number per image}: Figure \ref{sum}(b) illustrates the number of categories per image for DUO  \emph{Number of instances} represents the number of objects one image has, and \emph{ Percentage of images} represents the ratio of the corresponding number of images to the total number of images  Most images contain between 5 and 15 instances, with an average of 9 57 instances per image 

{\bf Summary}:
In general, smaller objects are harder to detect  For PASCAL VOC \cite{Everingham2007The} or COCO \cite{Belongie2014}, roughly 50\% of all objects occupy no more than 10\% of the image itself, and others evenly occupy from 10\% to 100\%  
In the aspect of instances number per image, COCO contains 7 7 instances per image and VOC contains 3  In comparison, DUO has 9 57 instances per image and most instances less than 1 5\% of the image size 
Therefore, DUO contains almost exclusively massive small instances and has the long-tail distribution at the same time, which means it is promising to design a detector to deal with massive small objects and stay high efficiency at the same time for underwater robot picking 

\section{Benchmark}
Because the aim of underwater object detection for robot picking is to find {\bf the high accuracy and efficiency} algorithm, we consider both the accuracy and efficiency evaluations in the benchmark as shown in Table \ref{ben} 

\subsection{Evaluation Metrics}
Here we adopt the standard COCO metrics (mean average precision, \emph{i e ,} mAP) for the accuracy evaluation and also provide the mAP of each class due to the long-tail distribution 

{\bf AP} -- mAP at IoU=0 50:0 05:0 95 

{\bf AP$_{50}$} --  mAP at IoU=0 50 

{\bf AP$_{75}$} --  mAP at IoU=0 75  

{\bf AP$_{S}$} --   {\bf AP} for small objects of area smaller than 32$^{2}$ 

{\bf AP$_{M}$} --   {\bf AP} for objects of area between 32$^{2}$ and 96$^{2}$ 

{\bf AP$_{L}$} --   {\bf AP} for large objects of area bigger than 96$^{2}$ 

{\bf AP$_{Ho}$} --  {\bf AP} in holothurian 

{\bf AP$_{Ec}$} --  {\bf AP} in echinus 

{\bf AP$_{Sc}$} --  {\bf AP} in scallop 

{\bf AP$_{St}$} --  {\bf AP} in starfish 


For the efficiency evaluation, we provide three metrics:

{\bf Param } --  The parameters of a detector 

{\bf FLOPs} --  Floating-point operations per second 

{\bf FPS} --  Frames per second 

Notably, {\bf FLOPs} is calculated under the 512$\times$512 input image size and {\bf FPS} is tested on a JETSON AGX XAVIER under MODE$\_$30W$\_$ALL  

\subsection{Standard Training Configuration}
We follow a widely used open-source toolbox, \emph{i e ,} MMDetection (V2 5 0) to produce up our benchmark  During the training, the standard configurations are as follows:

  $\bullet$ We initialize the backbone models (\emph{e g ,} ResNet50) with pre-trained parameters on ImageNet \cite{Deng2009ImageNet} 

  $\bullet$ We resize each image into 512 $\times$ 512 pixels both in training and testing  Each image is flipped horizontally with 0 5 probability during training 

  $\bullet$ We normalize RGB channels by subtracting 123 675, 116 28, 103 53 and dividing by 58 395, 57 12, 57 375, respectively 

  $\bullet$ SGD method is adopted to optimize the model  The initial learning rate is set to be 0 005 in a single GTX 1080Ti with batchsize 4 and is decreased by 0 1 at the 8th and 11th epoch, respectively  WarmUp \cite{2019arXiv190307071L} is also employed in the first 500 iterations  Totally there are 12 training epochs 

  $\bullet$ Testing time augmentation (\emph{i e ,} flipping test or multi-scale testing) is not employed 



\subsection{Benchmark Analysis}
Table \ref{ben} shows the benchmark for the \emph{SOTA} methods  Multi- and one- stage detectors with three kinds of backbones (\emph{i e ,} ResNet18, 50, 101) give a comprehensive assessment on DUO  We also deploy all the methods to AGX to assess efficiency 

In general, the multi-stage (Cascade R-CNN) detectors have high accuracy and low efficiency, while the one-stage (RetinaNet) detectors have low accuracy and high efficiency  However, due to recent studies \cite{zhang2019bridging} on the allocation of more reasonable positive and negative samples in training, one-stage detectors (ATSS or GFL) can achieve both high accuracy and high efficiency 

\begin{table*}[htbp]
\renewcommand\tabcolsep{3 0pt}

\begin{center}
\caption{Benchmark of \emph{SOTA} detectors (single-model and single-scale results) on DUO  FPS is measured on the same machine with a JETSON AGX XAVIER under the same MMDetection framework, using a batch size of 1 whenever possible  R: ResNet } 
\label{ben}
\begin{tabular}{|l|l|c|c|c|ccc|ccc|cccc|}
\hline
Method&Backbone&Param &FLOPs&FPS&AP&AP$_{50}$&AP$_{75}$&AP$_{S}$&AP$_{M}$&AP$_{L}$&AP$_{Ho}$&AP$_{Ec}$&AP$_{Sc}$&AP$_{St}$ \\ 
\hline 
\emph{multi-stage:} &&&&&&&&&&&&&& \\

\multirow{3}{*}{Faster R-CNN \cite{Ren2015Faster}}
&R-18&28 14M&49 75G&5 7&50 1&72 6&57 8&42 9&51 9&48 7&49 1&60 1&31 6&59 7\\
&R-50&41 14M&63 26G&4 7&54 8&75 9&63 1&53 0&56 2&53 8&55 5&62 4&38 7&62 5\\
&R-101&60 13M&82 74G&3 7&53 8&75 4&61 6&39 0&55 2&52 8&54 3&62 0&38 5&60 4\\
\hline

\multirow{3}{*}{Cascade R-CNN \cite{Cai_2019}}
&R-18&55 93M&77 54G&3 4&52 7&73 4&60 3&\bf 49 0&54 7&50 9&51 4&62 3&34 9&62 3\\
&R-50&68 94M&91 06G&3 0&55 6&75 5&63 8&44 9&57 4&54 4&56 8&63 6&38 7&63 5\\
&R-101&87 93M&110 53G&2 6&56 0&76 1&63 6&51 2&57 5&54 7&56 2&63 9&41 3&62 6\\
\hline

\multirow{3}{*}{Grid R-CNN \cite{lu2019grid}}
&R-18&51 24M&163 15G&3 9&51 9&72 1&59 2&40 4&54 2&50 1&50 7&61 8&33 3&61 9\\
&R-50&64 24M&176 67G&3 4&55 9&75 8&64 3&40 9&57 5&54 8&56 7&62 9&39 5&64 4\\
&R-101&83 24M&196 14G&2 8&55 6&75 6&62 9&45 6&57 1&54 5&55 5&62 9&41 0&62 9\\
\hline

\multirow{3}{*}{RepPoints \cite{yang2019reppoints}}
&R-18&20 11M&\bf 35 60G&5 6&51 7&76 9&57 8&43 8&54 0&49 7&50 8&63 3&33 6&59 2\\
&R-50&36 60M&48 54G&4 8&56 0&80 2&63 1&40 8&58 5&53 7&56 7&65 7&39 3&62 3\\
&R-101&55 60M&68 02G&3 8&55 4&79 0&62 6&42 2&57 3&53 9&56 0&65 8&39 0&60 9\\
\hline 
\hline 
\emph{one-stage:} &&&&&&&&&&&&&& \\
\multirow{3}{*}{RetinaNet \cite{Lin2017Focal}}
&R-18&19 68M&39 68G&7 1&44 7&66 3&50 7&29 3&47 6&42 5&46 9&54 2&23 9&53 8\\
&R-50&36 17M&52 62G&5 9&49 3&70 3&55 4&36 5&51 9&47 6&54 4&56 6&27 8&58 3\\
&R-101&55 16M&72 10G&4 5&50 4&71 7&57 3&34 6&52 8&49 0&54 6&57 0&33 7&56 3\\
\hline 

\multirow{3}{*}{FreeAnchor \cite{2019arXiv190902466Z}}
&R-18&19 68M&39 68G&6 8&49 0&71 9&55 3&38 6&51 7&46 7&47 2&62 8&28 6&57 6\\
&R-50&36 17M&52 62G&5 8&54 4&76 6&62 5&38 1&55 7&53 4&55 3&65 2&35 3&61 8\\
&R-101&55 16M&72 10G&4 4&54 6&76 9&62 9&36 5&56 5&52 9&54 0&65 1&38 4&60 7\\
\hline 

\multirow{3}{*}{FoveaBox \cite{DBLP:journals/corr/abs-1904-03797}}
&R-18&21 20M&44 75G&6 7&51 6&74 9&57 4&40 0&53 6&49 8&51 0&61 9&34 6&59 1\\
&R-50&37 69M&57 69G&5 5&55 3&77 8&62 3&44 7&57 4&53 4&57 9&64 2&36 4&62 8\\
&R-101&56 68M&77 16G&4 2&54 7&77 3&62 3&37 7&57 1&52 4&55 3&63 6&38 9&60 8\\
\hline 

\multirow{3}{*}{PAA \cite{2020arXiv200708103K}}
&R-18&\bf 18 94M&38 84G&3 0&52 6&75 3&58 8&41 3&55 1&50 2&49 9&64 6&35 6&60 5\\
&R-50&31 89M&51 55G&2 9&56 8&79 0&63 8&38 9&58 9&54 9&56 5&66 9&39 9&64 0\\
&R-101&50 89M&71 03G&2 4&56 5&78 5&63 7&40 9&58 7&54 5&55 8&66 5&42 0&61 6\\
\hline 

\multirow{3}{*}{FSAF \cite{zhu2019feature}}
&R-18&19 53M&38 88G&\bf 7 4&49 6&74 3&55 1&43 4&51 8&47 5&45 5&63 5&30 3&58 9\\
&R-50&36 02M&51 82G&6 0&54 9&79 3&62 1&46 2&56 7&53 3&53 7&66 4&36 8&62 5\\
&R-101&55 01M&55 01G&4 5&54 6&78 7&61 9&46 0&57 1&52 2&53 0&66 3&38 2&61 1\\
\hline 

\multirow{3}{*}{FCOS \cite{DBLP:journals/corr/abs-1904-01355}}
&R-18&\bf 18 94M&38 84G&6 5&48 4&72 8&53 7&30 7&50 9&46 3&46 5&61 5&29 1&56 6\\
&R-50&31 84M&50 34G&5 4&53 0&77 1&59 9&39 7&55 6&50 5&52 3&64 5&35 2&60 0\\
&R-101&50 78M&69 81G&4 2&53 2&77 3&60 1&43 4&55 4&51 2&51 7&64 1&38 5&58 5\\
\hline 

\multirow{3}{*}{ATSS \cite{zhang2019bridging}}
&R-18&\bf 18 94M&38 84G&6 0&54 0&76 5&60 9&44 1&56 6&51 4&52 6&65 5&35 8&61 9\\
&R-50&31 89M&51 55G&5 2&58 2&\bf 80 1&66 5&43 9&60 6&55 9&\bf 58 6&67 6&41 8&64 6\\
&R-101&50 89M&71 03G&3 8&57 6&79 4&65 3&46 5&60 3&55 0&57 7&67 2&42 6&62 9\\
\hline 

\multirow{3}{*}{GFL \cite{li2020generalized}}
&R-18&19 09M&39 63G&6 3&54 4&75 5&61 9&35 0&57 1&51 8&51 8&66 9&36 5&62 5\\
&R-50&32 04M&52 35G&5 5&\bf 58 6&79 3&\bf 66 7&46 5&\bf 61 6&55 6&\bf 58 6&\bf 69 1&41 3&\bf 65 3\\
&R-101&51 03M&71 82G&4 1&58 3&79 3&65 5&45 1&60 5&\bf 56 3&57 0&\bf 69 1&\bf 43 0&64 0\\


\hline 
\end{tabular}
\end{center}
\end{table*}
Therefore, in terms of accuracy, the accuracy difference between the multi- and the one- stage methods in AP is not obvious, and the AP$_{S}$ of different methods is always the lowest among the three size AP  For class AP, AP$_{Sc}$ lags significantly behind the other three classes because it has the smallest number of instances  In terms of efficiency, large parameters and FLOPs result in low FPS on AGX, with a maximum FPS of 7 4, which is hardly deployable on underwater robot  Finally, we also found that ResNet101 was not significantly improved over ResNet50, which means that a very deep network may not be useful for detecting small creatures in underwater scenarios  

Consequently, the design of high accuracy and high efficiency detector is still the main direction in this field and there is still large space to improve the performance 
In order to achieve this goal, a shallow backbone with strong multi-scale feature fusion ability can be proposed to extract the discriminant features of small scale aquatic organisms; a specially designed training strategy may overcome the DUO's long-tail distribution, such as a more reasonable positive/negative label sampling mechanism or a class-balanced image allocation strategy within a training batch 

\section{Conclusion}
In this paper, we introduce a dataset (DUO) and a corresponding benchmark to fill in the gaps in the community  DUO contains a variety of underwater scenes and more reasonable annotations  Benchmark includes efficiency and accuracy indicators to conduct a comprehensive evaluation of the \emph{SOTA} decoders  The two contributions could serve as a reference for academic research and industrial applications, as well as promote community development 
\bibliographystyle{IEEEbib}

Context 2: Paper Info

Title: Interpretable reduced-order modeling with time-scale separation Interpretable reduced-order modeling with time-scale separation
Publish Date: 7 March 2023
Author List: Sebastian Kaltenbach (from CSE-Lab, ETH Zurich, Harvard SEAS), Phaedon-Stelios Koutsourelakis (from CSE-Lab, ETH Zurich, Harvard SEAS), Petros Koumoutsakos (from CSE-Lab, ETH Zurich, Harvard SEAS), Harvard Seas (from CSE-Lab, ETH Zurich, Harvard SEAS)

Figure

FIG  5  Comparison between the phase-space of the reference solution (left) and the phase-space of the predictions
FIG  7  Comparison between predictions and reference solutions for a new initial condition fort = 1 25, 3 75, 7 5, 12 5, 20, 30  (from left to right and top to down) We note that with longer prediction time the uncertainty bounds increases Despite the chaotic nature of the KS equation, the predictive posterior mean is close to the reference solution for t ≤ 12 5

abstract

Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering  However, finding solutions for these PDEs can be computationally expensive, making model-order reduction crucial  We propose such a data-driven scheme that automates the identification of the time-scales involved and, can produce stable predictions forward in time as well as under different initial conditions not included in the training data 
To this end, we combine a non-linear autoencoder architecture with a time-continuous model for the latent dynamics in the complex space  It readily allows for the inclusion of sparse and irregularly sampled training data  The learned, latent dynamics are interpretable and reveal the different temporal scales involved 
We show that this data-driven scheme can automatically learn the independent processes that decompose a system of linear ODEs along the eigenvectors of the system's matrix  Apart from this, we demonstrate the applicability of the proposed framework in a hidden Markov Model and the (discretized) Kuramoto-Shivashinsky (KS) equation 
Additionally, we propose a probabilistic version, which captures predictive uncertainties and further improves upon the results of the deterministic framework 

INTRODUCTION

High-fidelity simulations of critical phenomena such as ocean dynamics and epidemics have become essential for decision-making  They are based on physically-motivated PDEs expressing system dynamics that span multiple spatiotemporal scales and which necessitate cumbersome computations   In recent years there is increased attention to the development of data-driven models that can accelerate the solution of these PDEs as well as reveal salient, lower-dimensional features that control the long-term evolution 
In most cases, data-driven reduced-order models are not interpretable  In particular, models based on neural networks despite good predictive capabilities , they offer a black-box description of the system dynamics  A possible remedy is applying a symbolic regression to the learned neural network representation , but this adds additional computational cost due to the two-step procedure 
A number of frameworks such as SINDy allows to learn interpretable dynamics but it relies on the a-priori availability of lower-dimensional descriptors and of time-derivatives which can be very noisy for both simulation and experimental data  Other frameworks are tailored to specific problems such as molecular dynamics  
Here, we present a framework that only needs the value of the observables, and not their derivatives, as training data and is capable of identifying interpretable latent dynamics  The deployment of interpretable latent dynamics ensures that conservation of important properties of that are reflected in the reduced-order model  
The present method is related to approaches based on the Koopman-operator extended Dynamic Mode Decomposition (eDMD) but uses continuous complex-valued latent space dynamics and only requires one scalar variable per latent dimension to describe the latent space dynamics  Therefore we do not have to enforce any parametrizations on the Koopman matrix  
The time-continuous formulation moreover allows to incorporate sparse and irregularly sampled training data and fast generation of predictions after the training phase  By using a complex-valued latent space we can also incorporate harmonic effects and reduce the number of latent variables needed  Linear and non-linear autoencoders are used to map the observed, high-dimensional time-series to the lower-dimensional, latent representation and we identify simultaneously the autoencoder as well as the latent dynamics by optimizing a combined loss function 
Hence the to tasks of dimensionality reduction and discovery of the reduced dynamics are unified while other frameworks treat the two parts separately   Apart from using an architecture based on autoencoders to identify the latent space, projection-based methods could also be employed   We are also proposing a probabilistic version of our algorithm ) that makes use of probabilistic Slow Feature Analysis  
This allows for a latent representation that arart from being time-continuous, can quantify the predictive uncertainty and hierarchically decompose the dynamics into their pertinent scales while promoting the discovery of slow processes that control the system's evolution over long time horizons  The rest of the paper is structured as follows: We introduce the methodological framework as well as algorithmic details in section II 
Particular focus is paid on the interpretability of the inferred lower-dimensional dynamics  In section III we present three numerical illustrations, i e  a system of linear ODEs, a hidden Markov Model and the discretized KS-equation  We then present in section IV the probabilistic extension of the framework and apply it to the KS-equation 
We conclude with a summary and a short discussion about possible next steps  We introduce the autoencoders deployed in this work, followed by the interpretable latent space dynamic and discuss the training process  We consider data from high-dimensional time series x n ∈ R f with n = 1,    , T   We remark that the intervals between the different states do not need to be uniformly spaced 

Autoencoder

A core assumption of the method is that each high-dimensional state x n can be compressed to a lower-dimensional representation z n ∈ C c with c << f   We identify this lower-dimensional representation by an autoencoder consisiting of a parameterized encoder and decoder  The encoder maps the high-dimensional representation to the latent space as:
The latent space is complex-valued  The decoder reconstructs the high-dimensional representation based on the latent variables as: We denote the parameters of the encoder as well as the decoder by θ  As discussed later in Section II C, both set of parameters are optimized simultaneously during training and therefore there is no need for differentiating them 

Interpretable Latent Space Dynamics

We employ a propagator in the latent space to capture the reduced-order dynamics of the system  In contrast to other time-extended variational autoencoder frameworks, our representation uses complex valued latent variables  In addition the latent variables are treated independently  The latter feature enables us to have an interpretable latent dynamics as well as a model that is especially suitable for being trained in the Small Data regime due to the small number of required parameters 
This is in contrast to temporal propagators such as LSTMs   For each dimension i of the latent variable z we are using the following continuous ODE in the complex plane: By solving this ODE, we can define the operator: Interpretable reduced-order modeling with time-scale separation Here, λ is a vector containing all the individual λ's and ∆t n indicates the time-step between the latent states 
The symbol is used to indicate a component-wise multiplication  We remark that the latent variables and the parameter governing the temporal evolution are complex numbers and their role in describing the system dynamics is similar to that of an eigenvalue  The real part is associated with growth and decay whereas the imaginary part is representing the periodic component 
This approach has similarities with the Koopman-operator based methods and the extended dynamic mode decomposition   In contrast to the methods mentioned before we are using a continuous formulation in the latent space that allows us to incorporate scarce and irregularly sampled training data and directly rely on complex numbers in the latent space 

Training and Predictions

We optimize a loss function that combines both a reconstruction loss as well as a loss associated with the error of our learned propagator in the latent space: (5) We note that we could directly incorporate mini-batch training by only taking the summation over a subset of the N available training data 
For new predictions of unseen states, we use the encoder to generate a latent representations which is then advanced in time by the learned propagator  At a designated time step we are using the decoder to reconstruct the high-dimensional solution  We applied our algorithm to three systems  First, we show that the algorithm is capable of exactly reproducing the solution of a linear ODE and to identify its eigenvalues 
Afterwards we are applying the framework to a high-dimensional process generated by a complex latent dynamics, which is correctly identified  As a final test case, we are applying the algorithm to a Kuramoto Shivashinski (KS) equation  Interpretable reduced-order modeling with time-scale separation

Linear ODE

We are considering a two-dimensional ODE system for x = y 1 y 2 : Based on the obtained training data we run our algorithm using a linear encoder and decoder structure as well as two latent variables z
Context 3: CNN com - Transcripts
Tensions Boil Over possible government shutdown; New trouble targeting Gadhafi; Libyan Rebels in Panicked Retreat; Should U S  Recognize the Rebels?; Meeting With Gadhafi; Washington, D C  to Feel Burden of Shutdown; Religious Leaders Fast to Protests Cuts for Poor
WOLF BLITZER, HOST: Don, thanks very much 
Happening now, the top U S  general in charge of the military mission in Libya now expressing doubts that the opposition has the manpower to topple Moammar Gadhafi, as deadly new air strikes force rebel fighters into another retreat  This hour, I'll speak with a former Republican Congressman who's in Tripoli right now trying to get Gadhafi to step down 
Also, growing outrage across the United States, amidst new signs tomorrow's potential government shutdown may -- repeat may be unavoidable  Why one lawmaker is telling Congress -- and I'm quoting right now -- "go straight to hell "
And possible presidential hopeful, Donald Trump, on a mission to tell President Obama, "you're fired " We're fact checking his controversial investigation into the president's birth 
Up first, the political showdown over the budget, as tensions reach a boiling point about 31 hours until impending government shutdown  Just hours from now, President Obama will meet with Republican House speaker, John Boehner, and the Democratic Senate majority leader, Harry Reid, for further negotiations  Those talks scheduled to begin 7:00 p m  Eastern 
Hundreds of thousands of people across the country will be impacted by the shutdown  And we'll be bringing you examples throughout the next two hours 
One place it would be felt heavily is right here in Congress' backyard, the city of Washington  Washington, DC -- its spending is tied to the federal budget  And this major metropolitan area could lose millions of dollars while a number of critical services, like trash collection, for example, would be suspended for at least a week 
Today, an enraged Eleanor Holmes, the delegate representing Washington, DC, lit into Congress over the stalemate 
(BEGIN VIDEO CLIP) ELEANOR HOLMES NORTON (D), D C  DELEGATE: It's one thing to beat up on the District of Columbia  It's another thing drop a bomb on the city  And that's what this Congressional -- C R  does  It takes the route of authoritarian governments and dictatorships by dictating to a local government how it may spend its local funds  And it may force the District of Columbia government to shut down, although our government had a balanced budget 
BLITZER: And get this -- the members of Congress charged with reaching a deal, they'll still be receiving a paycheck if there's a shutdown, despite the hundreds of thousands of government employees who won't be receiving any paychecks  The current Congressional salary, by the way, $174,000 a year 
Our CNN senior Congressional correspondent, Dana Bash, is up on Capitol Hill with the latest developments -- Dana, specifically, where are the sticking points right now?
DANA BASH, CNN SENIOR CONGRESSIONAL CORRESPONDENT:
Well, look, Wolf, this is effectively a bill to fund the government  And the sticking points certainly are about how much spending to cut  That's what this whole issue has been about 
However -- however, one of the main issues, I am told, that were just -- that was discussed at the White House meeting this afternoon with the president, the House speaker and the Senate majority leader, was over not necessarily spending measures, but over lightning rod issues like regulating greenhouse gases and abortion 
BASH (voice-over): One of the biggest disagreements is not over government spending, but policy 
REP  JOHN BOEHNER (R-OH), SPEAKER OF THE HOUSE: Some 40 or 50 policy restrictions that were attached to -- to our bill 
BASH: So-called policy riders Republicans call essential and Democrats call nonstarters  The most divisive is over abortion  A GOP plan to cut all federal funding for Planned Parenthood, which provides abortion procedures in addition other women's health services 
SEN  HARRY REID (D-NV), MAJORITY LEADER: This is a budget  This is to keep our country running  This is not a woman's health bill 
BASH: Planned Parenthood staged a rally outside the Capitol to protest 
CECILE RICHARDS, CEO, PLANNED PARENTHOOD: They don't want to allow Planned Parenthood to serve the three million women that we see every single year  Ninety-seven percent of the services Planned Parenthood provides are preventive care 
UNIDENTIFIED MALE: I certainly don't think that taxpayers should subsidize abortions  It's -- if a woman chooses to have an abortion, it's legal to do that in this country  But I don't think taxpayers should be put in a position to have to pay for those abortions 
BASH: Another major sticking point -- how much spending to cut  A Democratic source tells CNN they have finally tentative agreement on slashing $34 5 billion from the rest of this year's budget  But a Republican source says there's no deal 
BOEHNER: There is no agreement on the number  There are no agreement on the policy issues that are contained with it 
BASH: Then there's the critical issue of what programs and agencies to cut  Democrats say they're trying to find spending cuts with the least impact on those who need it most  So they're pushing for things like temporary one year cuts in programs  Some examples, cuts in wetlands protection and Pell grants for summer school and graduate students 
Republicans call that smoke and mirrors 
BOEHNER: And our goal is to make real spending cuts 
BASH: Some examples of what Republicans want to cut -- money for food inspectors, Head Start education programs and funding for housing 
BASH: This afternoon, House Republicans did pass a bill to keep the government running for one week past tomorrow's midnight deadline  It has $12 billion in cuts  It would fund the Defense Department for the rest of the year  But Democrats, including the president of the United States, call it a distraction and they say that they really want to keep the focus on what they're negotiating, which is a bill that would keep the government open -- keep the government functioning and funded for the rest of the year 
BLITZER: And the president's playing hardball  He's saying he'll veto that legislation --
BASH: He was, yes 
BLITZER: -- if it were to pass the Senate and come to his desk  I hear, Dana, that some employees already are getting furloughing notices 
BASH: It's true  This is just preventive  But all across the Capitol here today, people in offices and -- and -- well, really, everywhere -- were told whether or not, if, in fact, it does come to a government shutdown, if they're going to be here or not  And this is an example  We obtained one of the furlough notices  And I'll just read you a line  This -- imagine if this came across your desk  It says: "Because your services are not needed for the orderly suspension of operations and you're not engaged in one of the accepted functions, you're being placed on furlough effective Saturday, April 9, 2011 "
Now, again, of course, this is just protective  The government is still open  But interesting that they're already getting ready for a government shutdown and telling people who will come to work and not 
One more note  Even people who are here, who are called essential, they're not going to get paid, either 
BLITZER: All right, Dana 
Don't go too far away 
We'll be in close touch 
The impact of the potential government shutdown is even being felt on the front lines of combat in Afghanistan  And Iraq  The Defense secretary, Robert Gates, is in Iraq right now  And he's telling U S  troops they will feel a pinch 
ROBERT GATES, SECRETARY OF DEFENSE: I hope they didn't have you standing out here in the sun too long
If -- if the government shutdown starts on the 8th and goes for a week, you'd get a half a check  If it goes from the 15th to the 30th, you wouldn't get a paycheck on the 30th but you would be back paid for all of it  So that's -- that's the deal 
BLITZER: Not great deal 
Gates also told the troops this would likely be his last trip to the country as Defense secretary and he wanted to say thank you 
He's expected to retire later this year 
Now to the deadly stalemate in Libya  New signs the military operation in the region is facing some tough new challenges 
Our Pentagon correspondent, Barbara Starr is here 
She's watching the story 
She's got more 
What are you learning? BARBARA STARR, CNN PENTAGON CORRESPONDENT: Well, Wolf, there was very dramatic, very hard-nosed testimony today on Capitol Hill from the top U S  commander responsible for the U S  involvement in Libya, saying that Gadhafi forces are becoming increasingly difficult to target, as they are using civilian vehicles, mixing in with local populations, moving next to mosques, schools, hospitals -- all the same tactics we saw for years in Iraq 
And now, all of this today leading to a very dramatic exchange between General Carter Ham and one of the most vocal administration critics, Senator John McCain 
SEN  JOHN MCCAIN (R), ARIZONA: Hearing your testimony, General Ham, is almost an Orwellian experience for me  The fact is that if we had imposed the no-fly zone three weeks, four weeks ago, Gadhafi would not be in power today 
The fact is that the situation on the ground is basically a stalemate 
Would you say that the situation on the ground is a stalemate or an emerging stalemate?
GEN  CARTER HAM, COMMANDER, U S  AFRICA COMMAND: Senator, I -- I would agree with that if present on the ground 
MCCAIN: So the goal -- our policy objective of the removal of Gadhafi is further from being achieved than it was three or four weeks ago 
HAM: Senator, I -- I don't know that I would agree with that  What I -- because that, again, was not a military mission  The military mission of protecting, I think, was not wholly achieved, but achieved in large part 
STARR: General Ham also acknowledging another problem -- a key U S  aircraft, the AC-130, that flies low and slow to target on the ground, is facing what he called "a significant threat" from surface to air missiles, which he said remain effective and operational in some cases 
And, Wolf, get this  General Ham says there were about 20,000 of those surface to air missiles when the campaign started and they are concerned that an awful lot of them are still out there -- Wolf 
BLITZER: Barbara, thanks very much for that report 
Panicked rebels are once again on the retreat from Gadhafi's forces  Just today, at least three people were killed, another 10 injured, in new air strikes  And there are mounting questions about whether NATO could be responsible for the attack 
Our senior international correspondent, Ben Wedeman, is joining us now from Benghazi 
Ben's watching all of this closely 
You just heard General Ham, who is the commander of the U S  military's Africa Command  He was in charge of the mission before handing over complete control to NATO  You just heard him say there could be a stalemate out there 
What's the sense on the ground?
BEN WEDEMAN, CNN SENIOR INTERNATIONAL CORRESPONDENT: Well, the sense was a few days ago that it was, indeed, a stalemate -- sort of a seesaw battle that went back and forth between Ajdabiya and Brega 
But what we saw today was that that seesaw was tipped over  And it was a general retreat by the opposition forces from somewhere near Brega to almost the other side of Ajdabiya  This, after this air strike, which almost everybody on the ground believes to be NATO leaving not three, but four people dead  And many others are still unaccounted for 
That set off this general retreat whereby we saw all their heavy -- all of the opposition forces' heavy equipment -- multiple rocket launchers, tens and tens of these pickup trucks mounted with heavy machine guns streaming through Ajdabiya to the other side, the far side of the city  Some of them going all the way back to Benghazi, according to the head of the rebel forces in the eastern part of the country, Abdul Fatah Younis  He says that the Gadhafi forces were approaching Ajdabiya from three different directions 
I would not call that a stalemate -- Wolf 
BLITZER: Ben, you got a close-up look at some of the casualties today out on the front lines 
WEDEMAN: It's very bad, very bad  I mean it wasn't just fighters  It was also medics who had gone to the scene of this reported air strike, which then got hit again  So one of them was a doctor, one of them was a medic  And we were in the hospital  And there was real anger at NATO, anger at the fact that when they needed those air strikes on the Gadhafi forces, they weren't getting them  And now, for the second time in a week, there's been another strike  Now, of course, we must stress that NATO says that they -- because they don't have enough boots on the ground, they can neither confirm nor deny this was a NATO strike  But certainly, speaking to eyewitnesses in the hospital, it certainly sounded like an air strike  And there are no other planes in the skies of Libya other than NATO planes -- Wolf



ground_truth: URPC2017, URPC2018, URPC2019, URPC2020_ZJ and URPC2020_DL.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How does the framework capture the reduced-order dynamics?

Read the following text and answer briefly.

Context 2:  The loss function was optimized using the Adam algorithm   As we consider a linear ODE we can analytically compute the eigenvalues involved and compare it with the parameters λ identified by our algorithm 
We observe in Figure that the algorithm was able to recover the correct values, i e  the eigenvalues 7 and 3 of the given linear ODE  The system does not have a periodic component and the two imaginary parts correctly go to zero, whereas the real parts converge to the reference value  Moreover we are also able to identify for the linear mapping between our latent variables z and the training data a matrix consisting of a multiple of the eigenvectors (1,1) and (1,-1) and thus the correct solution 
This example was chosen to show that the algorithm is able to quickly identify the exact solution of a linear ODE in terms of its linearly independent components 

Hidden multiscale dynamics

We consider eight-dimensional synthetic time series data produced by an underlying twodimensional complex valued process  In particular, the data points x are generated by first solving for the temporal evolution for the two complex-valued processes p 1 and p 2 and than mapping to the eight-dimensional space by using a randomly sampled linear mapping W  
One of the two processes used to generate the data is chosen to be much slower than the other one and both processes have a periodic component  dp 2 dt = (−0 9 + 1 5i)p 2 (8) As training data we consider 40 time series with 150 data points each, obtained by simulating the described processes for a maximum of t = 15 s and then sampling from the obtained data points 
Hence the training data consists of: • 40 time-series • with each consisting 150 observations of the x at a uniform time-step ∆t = 0 0025 The autoencoder obtained consists of one linear layer for both the decoder as well as the encoder  The model is trained for 5000 iterations using the Adam optimizer and a learning rate of 10 −3  
The results for the convergence of the parameters λ 1 and λ 2 can be found in Figure   We note that the process which is slower decaying and thus more responsible for the long-term evolution of the system has a higher convergence rate than the faster process  With the obtained parameters λ as well as the trained autoencoder, we compute predictions based on the last time step used for training, i e  we apply the encoder to obtain our latent representation and than use the latent dynamics to advance the latent representation in time 
Afterwards, we employ the decoder to reconstruct the full high-dimensional system  The results can be found in Figure and show very good agreement between predictions and reference data  This example shows that our model is successfully able to carry out dimensionality reduction and moreover indicates that the convergence rate between latent processes can be different 
The latter is relevant when training models as for accurate predictions all latent processes and their dynamics should be converged 

Kuramoto-Sivashinsky

Finally, we applied our algorithm to the KS equation and aim to identify a reduced-order model for the solution u(y, t): We employed periodic boundary conditions, µ = 1 and a domain size y ∈ [0, 22]  For this domain-size, the KS-equation exhibits a structurally stable chaotic attractor as discussed in The black lines divides the area for which training data was given from the area without raining data 
;   The equation is discretized in space using a discretization step of 22 64 resulting in a state vector x of dimension 64 and a nonlinear system of coupled ODEs  This is solved using a stiff fourth-order solver  We employed a non-linear encoder and decoder with four fully-connected layers each and ReLU-activation functions as well as Dropout Layers between the fully-connected layers 
We trained the model for 200000 iterations using Adam and a learning rate of 5 • 10 4 and assuming a five-dimensional latent space  We obtained the λ's in Figure   Four latent variables have λ's close to zero and thus a slow temporal dynamic that is responsible for the long-term evolution whereas one latent variable is quickly decaying 
Based on the obtained parameters, we do predictions based on an unseen initial condition not contained in the training data  We are able to reconstruct the correct phase space based on our predictions despite only using a very limited amount of training data  The results for the phase space can be seen in Figure  
Although the small-scale fluctuations in the temporal dynamics are not well captured, the model identifies the correct manifold which has a good accuracy compared to the reference solution  All phase-spaces were obtained by using a finite-difference operator on the data or predictions  These results are in accordance Interpretable reduced-order modeling with time-scale separation with whose LSTM-based temporal dynamic model was also able to find the correct phase space but not to track the actual dynamics for long-term predictions 
Our model is not able to account for noise in the temporal evolution and thus dealing with chaotic, small-scale fluctuations is challenging  We believe that a probabilistic version of our algorithm could be advantageous here  This section contains a fully probabilistic formulation for the deterministic model discussed before 
We replace the Autoencoder with a Variational Autoencoder and the ODE in the latent space with a SDE  The loss function which we optimize is the Evidence-Lower Bound (ELBO) 

Model Structure

We postulate the following relations for our probabilistic model using an Ornstein-Uhlenbeck (OU) for each dimension i of the latent space and a Wiener process W t in the latent space: We again assume that the latent variables z t are complex-valued and a priori independent  Complex variables were chosen as their evolution includes a harmonic components which are observed in many physical systems 
We assume an initial conditions z 0,i ∼ CN (0, σ 2 0,i )  The total parameters associated with the latent space dynamics of our model are thus {σ 2 0,i , σ 2 i , λ i } c i=1 and will be denoted by θ together with all parameters responsible for the decoder mapping G (see next section)  These parameters along with the state variables z t have to be inferred from the data x t  
Based on probabilistic Slow Feature Analysis (SFA) , we set σ 2 i = 2; (λ j ) and σ 2 0,i = 1  As a consequence, a priori, the latent dynamics are stationary  A derivation and reasoning for this choice can be found in Appendix A  Hence the only independent parameters are the λ i , the imaginary part of which can account for periodic effects in the latent dynamics 

Variational Autoencoder

We employ a variational autoencoder to account for a probabilistic mappings from the lower-dimensional representation z n to the high-dimensional system x n   In particular we are employing a probabilistic decoder The encoder is used to infer the state variables z based on the given data and thus defined in the inference and learning section 

Inference and Learning

Given the probabilistic relations , our goal is to infer the latent variables z 0:T as well as all model parameters θ  We follow a hybrid Bayesian approach in which the posterior of the state variables is approximated using amortized Variational Inference and Maximum-A-Posteriori (MAP) point-estimates for θ are computed 
The application of Bayes' rule for each data sequence x 0:T leads to the following posterior: where p(θ) denotes the prior on the model parameters  In the context of variational inference, we use the following factorization of the approximate posterior i e  we infer only the mean µ and variance σ for each state variable based on the given data points 
This conditional density used for inference is the encoder-counterpart to the probabilistic decoder defined in the section before  It can be readily shown that the optimal parameter values are found by maximizing the Evidence Lower Bound (ELBO) F(q φ (z 0:T ), θ) which is derived in Appendix B  We compute Monte Carlo estimates of the gradient of the ELBO with respect to φ and θ with the help of the reparametrization trick and carry out stochastic optimization with the ADAM algorithm  

Results for the probabilistic extension

We applied our probabilistic version to the KS-equation  We used the same settings as for the deterministic approach but considered up to 10 complex latent variables  The obtained λ's are in Figure   The probabilistic model allows us to quantify the uncertainty in predictions  In Figure predictions for various time-steps and the respective uncertainty bounds are shown for an unseen initial condition 
Due to the chaotic nature of the KS-equation and the small amount of training data, the underlying linear dynamic of our model is only able to capture the full dynamics for a limited time horizon  Fortunately, due to the probabilistic approach the model is capable of capturing chaotic fluctuations with increasingly wide uncertainty bounds 
We also computed the phase space representation for the KS-equation based on the predictions obtained by our model and compare it with the reference solution  The probabilistic model identifies the correct manifold with a better accuracy than the deterministic model  As some of the small-scale fluctuations are accounted as noise, the resulting manifold is more concentrated at the origin and the obtained values are slightly smaller than the reference manifold although their shape is very similar 
Context 3: 
BLITZER: Ben Wedeman in Benghazi for us 
The U S  says Moammar Gadhafi is no longer the legitimate leader of Libya 
So why not recognize the rebels?
Why one U S  official says it raises serious concerns 
And a former U S  Congressman in Libya armed with a message for the Libyan dictator 
Will he get to meet with him face-to-face?
My interview with Curt Weldon, that Republican former Congressman -- that's coming up, as well 
BLITZER: Let's get right to Jack 
He's got some nuclear concerns on his mind with The Cafferty File -- Jack 
JACK CAFFERTY, THE CAFFERTY FILE: Well, they had another little temblor in Japan -- a 7 1 magnitude earthquake hit Northeastern Japan today, the strongest aftershock since that massive 9 0 quake and tsunami that followed devastated that nation four weeks ago  And this one today was in roughly the same area 
One of the big concerns, of course, is possible further damage to the Fukushima Daiichi nuclear power plant  The Tokyo Electric Power Company, TEPCO, which operates the plant -- or what's left of it -- said there were no serious incidents as a result of today's aftershock 
So they say  Radioactivity from that plant has poisoned the surrounding land, air and ocean  Millions of people have been exposed  Millions more could be, as radioactivity has been picked up in food and drinking water and detected in faraway places, like California 
This week, workers plugged a crack in the plant that had been gushing contaminated water into the ocean for weeks  As a result, TEPCO says now radiation levels in the ocean waters off the coast there have dropped dramatically 
Yesterday, the head of the United Nations' scientific committee on the effects of atomic radiation said the Fukushima accident is not expected to have any serious impact on the health of the Japanese people  He said, quote: "We have seen traces of iodine in the air all over the world, but they are much, much, much lower than traces we have seen at similar distances following Chernobyl," unquote 
Well, not everybody is convinced  In South Korea, more than 130 primary schools and kindergartens ordered closed today outside of Seoul  People there were worried that windy, rainy weather could be carrying radioactive material from Japan 
North Korea aired warnings on television for its people to stay indoors during that rain storm and to take a full shower if they were caught outside in the storm 
Even here in the United States, some chefs are now using sensors to test levels of radiation in the fish they plan to serve in restaurants 
Here's the question -- do you think you're being told the truth about the nuclear accident in Japan?
If your -- if your trout is he glowing, Wolf --
BLITZER: Yes?
CAFFERTY: -- you might want to send it back and get a ham sandwich 
BLITZER: You want it well done, but not necessarily that well done 
CAFFERTY: No 
BLITZER: All right, Jack 
Not a laughing matter 
BLITZER: Serious stuff 
CAFFERTY: Right 
BLITZER: See you in a few moments 
New questions this hour about the capabilities of the rebels in Libya and whether they have the power to overthrow Moammar Gadhafi 
Should the United States -- should the United States have a hand in helping arm the rebels?
Let's bring in our foreign affairs correspondent, Jill Dougherty, with this part of the story 
What are you hearing over at the State Department -- Jill  JILL DOUGHERTY, CNN FOREIGN AFFAIRS CORRESPONDENT: Well, you know, Wolf, other countries have done it, other countries like France and Italy have done it -- recognizing the opposition  And supporters say now, with the rebels in retreat, the U S  shouldn't wait 
But what would it really change anything?
DOUGHERTY (voice-over): The U S  says Moammar Gadhafi is no longer the legitimate leader of Libya 
Secretary of State Hillary Clinton is full of praise for them 
HILLARY RODHAM CLINTON, SECRETARY OF STATE: These were not soldiers  These were not trained military forces  They were doctors and lawyers and university professors and economists and, you know, young men who were students  And they are being attacked by mercenaries, by ruthless forces that Gadhafi is utilizing to show no mercy against his people  And they are courageous  They are moving as fast as they can to try to form themselves into a military operation 
DOUGHERTY: Clinton has met with the rebel leaders personally, but the administration still is cautious  The president authorized the CIA to send in agents to learn about the rebels and assess their needs  Clinton's special representative, the State Department's Christopher Stevens, seen here in 2008 in Tripoli, is on the ground in Benghazi, scoping them out 
MARK TONER, U S  STATE DEPARTMENT SPOKESMAN: We sent somebody in to get that kind of on the ground assessment of the -- of -- of their identity, of their leadership structure, to talk with them firsthand and to see what direction we think they're moving in  We've seen some positive signals 
DOUGHERTY: Recognizing the rebels, a senior official tells CNN, raises serious issues  It would acknowledge that Libya is now a divided country 
And could the U S  be sure the group represents the whole opposition movement?
It's a bit early, this official says  Maybe they turn out not to be the right folks 
But Secretary Clinton knows the timing is urgent 
CLINTON: What NATO is doing is buying time, buying space 
DOUGHERTY: So far, the U S  is providing what's called non- lethal humanitarian aid  The administration hasn't yet decided to arm them or provide financial assistance 
DOUGHERTY: But a senior U S  official tells CNN there's a lot the United States could be doing right now without going so far as to recognize the rebels, pointing out that the U S  funds political groups and other organizations around the world  But this official says you want to be careful about who they are 
So, so far, caution seems to be winning out over urgency -- Wolf 
Jill is at the State Department 
The House speaker, John Boehner, may be doing double duty if the government shuts down this weekend  You're going to find out why he could be cleaning up a lot of trash in his own backyard 
And a former U S  Congressman now on a mission to meet with Moammar Gadhafi in Tripoli in person  Curt Weldon, he's here  He'll join us in THE SITUATION ROOM from Tripoli  You're going to find out who he says would be a good replacement for the embattled Libyan leader 
BLITZER: Military leaders have a message for Congress about "don't ask/don't tell "
Well, military leaders say preparations for repealing "don't ask/don't tell" are going better than they expected  They testified before a House committee today about getting rid of the policy that bars openly gay service members  They caution, though, that it will take time and training to implement the repeal  And it must still be certified by President Obama, the Defense secretary and the chairman of the Joint Chiefs of Staff 
Well, your Smartphone just got a little smarter  The FCC is requiring that wireless carriers provide access to the mobile Internet anywhere it's available, even when it's offered by a competing provider  And that could be a huge -- make a huge difference to smaller carriers, who told the FCC they just can't compete otherwise against industry heavyweights like Verizon and AT&T 
New York City school chancellor, Cathie Black, is stepping down after only three months on the job  Mayor Michael Bloomberg says her short stint just didn't work out as either of them had expected or hoped  Her approval rating has plunged to 17 percent 
Black chaired "First" magazine before overseeing the nation's largest school system  Deputy Mayor Dennis Walcott will replace her 
And a war of words is erupting between an emerging Republican star, New Jersey Governor Chris Christie, and his state's largest teachers' union  In a network TV interview, Christie called the union leaders, quote, "political thugs " He blames them for teacher lay-offs that he says could have been avoided if they had not opposed salary freezes  The New Jersey Education Association is firing back, accusing Christie of name-calling -- Wolf 
BLITZER: Sticks and stones will break many bones 
SYLVESTER: Sticks and stones may break my bones --
SYLVESTER: But words never hurt me 
A former U S  Congressman is in Tripoli, Libya right now  His goal -- to talk to Moammar Gadhafi  His message -- we'll talk about that  My interview with Curt Weldon coming up next 
Plus, we showed it to you earlier -- a member of Congress telling colleagues to, quote, "go to hell "
Now she's is joining us live here in THE SITUATION ROOM to explain 
HOLMES NORTON: -- of Columbia  It's another thing to drop a bomb on a city  And that's what this --
BLITZER: Former Congressman Curt Weldon is in a -- Weldon is on a mission to Libya right now to try to meet with the embattled leader, Moammar Gadhafi  But that may be easier said than done 
Joining us now from Tripoli, former Republican Congressman Curt Weldon of Pennsylvania  Congressman, thanks very much for coming in 
And joining us now from Tripoli, former Republican Congressman Curt Weldon of Pennsylvania 
CURT WELDON, FORMER U S  CONGRESSMAN: My pleasure, Wolf 
BLITZER: Let's talk about your meeting with Moammar Gadhafi  I take it it has not yet happened 
Do you expect to meet with the Libyan leader? WELDON: Absolutely  The invitation that was sent to me was from his chief of staff, Bashir Salah, who I've met on all three of my official visits here in 2004 and 2005  And the letter specifically says we want you to come over and meet with the leader and our senior leadership 
And I said it's worth me coming over to support the administration and to try to let the leader know face to face that this is facing -- it's very grave timing in the situation and they have to have some movement fairly quickly or they're not going to be happy with the -- with the alternatives 
BLITZER: What's taking so long?
Why haven't you been able to meet with Gadhafi yet?
WELDON: Well, it -- that's not unusual  I mean all three of the delegation trips that I led here in 2003 and 2004 -- or, actually, 2004 and 2005 -- they always make you wait until 30 minutes before the meeting and then you go  And some of those meetings were at 10:00 at night, some were at 5:00 in the afternoon 
As you know from the excellent reporting being done by your folks here, there's a lot of security concerns, and they are very concerned where Gadhafi is at any given moment  That's one of the issues, but we have been making ourselves available 
We have been doing a lot of back-channel meetings with friends and associates that I have here, and we have met with the chief of staff and one of the sons, and today with the prime minister, a very lengthy meeting for two hours  So, we're going to give them until tomorrow  We're not going to stay beyond that  And we have given them some suggestions, and we expect a response by midday tomorrow  And if we don't, we will done exit conversation with your people and let you know our feelings 
BLITZER: What's the major headline that you got out of these meetings with other leaders? I take it you met with Saif Al-Islam Gadhafi, one of the sons of Moammar Gadhafi  What are they saying to you?
WELDON: Well, we actually didn't meet with Saif  I have met with Saif probably 10 times over the past seven years, both in America and here in Libya  I have not yet met with Saif  I have offered, if he is available 
I have met with Saadi  And the general thrust is obviously that they want peace and they want to find a way out of this  But as I have explained to them, there's certain things that have to be done according to our president and our secretary of state, who I'm here to support 
We don't have a different agenda  There's no compromise on our part  Our only mission here is to talk face to face with them and say this is reality and this is a grave situation, and you need to do certain things that we suggest that we think will get our administration to respond to your actions  And again, we're not doing any negotiating 
They know me, they have seen my efforts  I have not taken anything from their country in the way of financial benefits, and I'm here only because I want to avoid war  I don't want to see American soldiers killed, and I don't want to see more innocence Libyans killed 
BLITZER: You wrote an op-ed in "The New York Times" this week saying that once you meet face to face with Moammar Gadhafi, you will tell him to step down  Is that still your intention?
WELDON: Absolutely, Wolf  I wrote the op-ed before the trip was planned  And I wrote it, Wolf, because back in 2004, when I led the first delegation of Americans to sit down with him in the tent in Tripoli, he said to me, "Congressman, why did it take 30 years for someone from your country to come and sit with me and tell me to my face that you believe that I'm a criminal and a terrorist



ground_truth: By using a propagator in the latent space.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the sticking point in the political showdown over the budget?

Read the following text and answer briefly.

Context 3:  And then if you didn't believe me, bomb me?"
And I said, "Leader, I can't explain that " So I said now it's time for someone to sit in a tent face to face with Colonel Gadhafi and let him know how grave this situation is 
And I'm willing to do that  And I think I'm probably the best person because I have met with him three times, and because I sat in that tent in 2004 and listened to him tell me that  So, in effect, that's why I'm here 
BLITZER: You wrote also in "The New York Times" this -- you wrote, "Colonel Gadhafi's son, Saif, a powerful businessman, a politician, could play a constructive role as a member of the committee to devise a new government structure or constitution "
You know, a lot of people, including the opposition, the rebels, as they're called, they think Saif Al-Islam Gadhafi is just as much a killer or thug as his father is, and they say they have no interest in dealing with him either 
What do you say to that criticism?
WELDON: Well, what I said, I'm not endorsing anything anyone for any office here  What I am hoping for is what the president wants, which is a free and fair election to take place, hopefully sooner rather than later 
But having been involved with Libya for seven years, I was a witness to the work that Saif did in the Lockerbie case, the La Bella nightclub bombing  I personally witnessed through the Gadhafi Foundation the work that Saif did to free up the Bulgarian nurses who were sentenced to death twice, along with a Palestinian doctor 
I have seen the work that Saif and Dr  Salani (ph) at the foundation have done in dealing with chemical weapons destruction and with the elimination of landmines and humanitarian efforts worldwide  I have been out to (INAUDIBLE), the chemical weapons plant, and I have actually seen visibly how they have removed the chemical weapons production materials  He was behind all of that 
Believe me, Wolf, I'm not happy with some of the statements and the actions that he's made over the past month, and he knows I'm not happy  But I think in a fair election, up until now, he should be given the opportunity to seek office where he can run against other candidates, perhaps, for the presidency  And so I would at this time think that he should be allowed that opportunity 
That's not to say I condone anything that he said or his actions  He will have to be accountable for those on his own 
BLITZER: Because you make him sound like he's a decent guy when so many people think he is a killer, a murderer, especially given the statements that he recently made, that if he goes into Benghazi, if he finds these rebels, he will go and kill them all  You make it sound like he's a decent guy 
WELDON: Well, I -- you know, I haven't been with him on a continual basis  I have met with him a number of times, both in the U S  and here, under some very stressful situations, especially when it came to resolving the Lockerbie case and the La Bella nightclub  And despite what Sarkozy said about resolving the issues of the Bulgarian nurses when they were sentenced to death twice, it was Saif who played a very critical role against some very powerful forces in this country that wanted to kill those people 
You know, I don't know of any incidences where I, first hand, have seen evidence of him committing human rights violations, and if he did, he has to be held accountable like everyone else  And I have said that publicly and I will say that privately 
So my judgment is just based upon my experience with him, the fact that he is a knowledgeable person, he understands the need to interact and interface with the West  I think he could be a viable candidate  But ultimately, my opinion is hopefully going to be the opinion of the Libyan people 
BLITZER: Because you probably have seen all of the articles, the reports over the past month, month and a half, of mass murder, of killings, not only by Saif Al-Islam, but some of his brothers that have gone on, the atrocities that have been so widely reported  I hear what you're saying about his role over the recent years when the Bush administration, and later the Obama administration, was trying to improve relations with Libya, but over the past several weeks, based on all of the international reporting we have seen, it's been a brutal record that he has accomplished 
WELDON: Well, again, I don't have firsthand evidence of that  I just got here two days ago  And I fully support an international tribunal to look at human rights violations on everyone in this country  That's necessary  And if they find evidence that he has been involved in that, then he should suffer the consequences of his actions 
(END VIDEOTAPE) BLITZER: In our next hour, part two of the interview with former congressman Curt Weldon  There have been some questions raised about his motive  Is he in all of this for the money? You're going to find out his answer to that and more  Stand by 
Also, Washington, D C 's congressional delegate is telling colleagues -- and I'm quoting her now -- "Go to hell " She is joining us live in THE SITUATION ROOM to tell us why 
Plus, no budget deal, no food -- the extreme tens of thousands of people are going to as a government shutdown looms 
BLITZER: Let's get back to the outrage boiling over on Capitol Hill, only hours before a potential government shutdown 
Joining us now, the Democratic delegate representing the city of Washington, D C , Eleanor Holmes Norton 
ELEANOR HOLMES NORTON (D), D C  DELEGATE: Of course, Wolf 
BLITZER: I think it's fair to say that Washington, D C , a city of a population of about 600,000 people, the only major metropolitan -- the only major city in the United States that's going to foal the direct impact of a federal government shutdown so dramatically, so powerfully, because it is a federal district 
Give me an example of what's going to happen if there's a government shutdown 
NORTON: Absolutely, although your viewers will be shocked by what they are about to hear 
They know a little bit about taxation without representation -- we pay our taxes, then we have full representation in the House and the Senate  But I bet they didn't know that our local budget, without a dime of federal money in it -- and we support ourselves almost entirely -- has to be sent to the masters in the Congress to sign off on it before we can spend our own local money 
Well, listen to this, Wolf  We passed our budget in -- last spring  The appropriators signed off on it last summer 
So, why are we in a federal budget fight over their money when it is our money I am talking about? I have put forward amendments that said the district can spend its own local funds 
BLITZER: What's going to happen in the District of Columbia Saturday, Sunday, Monday, if there is a government shutdown? Give me an example or two 
NORTON: I will give you some dramatic ones  How about the shutdown of the D C  government itself? Because since the final gavel hasn't fallen on all the federal appropriations, then the district government has now prepared to shut down on Saturday morning just because the federal government is shutting down 
We are at the height of the tourist season, the Cherry Blossom Festival  That has been severely curtailed because of the federal shutdown  That's going to -- three million people come here just in one month for the cherry blossoms  Our mayor has had to put out a list of agencies that will be open and a list of agencies that won't be open 
BLITZER: Trash collection -- will there be any trash collection in the District of Columbia?
NORTON: No trash collection, and some residents have started up a Facebook page that says if they close down the District of Columbia, we're carrying our trash to Speaker Boehner's House 
BLITZER: You don't support that do you?
NORTON: I do not 
NORTON: And let me just say right here, I do not  But let me tell you, I am only expressing a little of the rage that the taxpaying residents of the District of Columbia are feeling 
BLITZER: But let me ask you this, Congresswoman, because the Democrats were in control, they had a large majority in the House all of last year; in the Senate, a significant majority  They failed to pass a budget  Don't the Democrats deserve a lot of the blame for this current impasse?
NORTON: Absolutely not, because the Democrats would never have held our budget up here 
LISA BLOOM, CNN LEGAL ANALYST: Why didn't they pass the budget?
NORTON: Well, that doesn't have anything to do with us  This is our local money 
All it would take is -- the Democrats in the Senate are ready to agree  The president is ready to sign an amendment --
BLITZER: But they could have done this any time last year 
NORTON: Wait a minute, Wolf  Wait a minute -- an amendment that said while we're fighting it out on the federal budget, we will let the district spend its own local funds 
So that's all I'm asking  I'm not in this fight, so don't ask me why the Democrats didn't pass the Democratic budget 
I passed -- we passed our budget  Our budget is balanced  The only issue before the Senate and the House is, can we spend our local money? It doesn't have anything to do with their budget 
They can go on from now until Timbuktu  Let us spend our money and don't close down our city because the federal government can't get its act together 
BLITZER: I'm with you there  This is an outrage, the fact that there is -- if there is going to be shutdown  I'm still hoping there won't be a shutdown, but it's --
NORTON: I think there may not be 
BLITZER: -- ridiculous when you think about it, when you think about how close they are  It would be a horrible, horrible tragedy, because 800,000 people directly are going to start losing their paychecks  And the District of Columbia, which is, as you point out correctly, taxation without representation, is going to suffer a great deal more than any other city in the United States 
Good luck, Congresswoman  Thanks very much 
NORTON: Thank you, Wolf 
BLITZER: I feel your pain 
Concerns within military families over a government shutdown  Also, why they are downright scared they won't be able to put food on the table 
And tens of thousands of people on a hunger strike, including some members of Congress  We'll explain why 
CAFFERTY: The question this hour is: Do you believe you're being told the truth about the nuclear accident in January?
Fred writes, "You want the truth? You can't handle the truth "
"Just how should a government balance our right to know the truth with the perceived need to not create a panic and thus a larger problem? Can you really evacuate a million people? To where? Yes, without the truth, how can anyone try to act reasonably?"
"In the end, we do have a right to know the truth  Honesty is the best policy "
Paul in Ohio writes, "Jack, I believe they're telling what they think they know with certainty  It is most certain that they don't know everything "
Jeremy in California, "So I'm confused  Is the current California radiation level 'harmless to human health,' 'not immediately harmful to human health,' not permanently harmful to people outside the region,' or no more than an apples-to-oranges transcontinental flight?"
Craig writes, "Perspective  In Japan, they have had yet another earthquake and have lived in fear and chaos for over a month  And yet, their government hasn't shut down  Nuclear disaster, natural disaster, absolute destruction hasn't kept their elected officials from doing their duty to the people 
"Yet, in America, we get Harry Reid, John Boehner and a White House who are more concerned with the 2012 election campaign  It's times like these when we see just how far off the mark we really are "
Louis writes, "No  Just too many things going wrong  They say that the seafood will be safe  I ask this: Do fish migrate or do they set up housekeeping in one spot and then stay there? And if so, why don't I catch fish in the same place every day?"
And Jim in Colorado, "The nuclear industry telling the truth? The unicorn, garden gnome and I were talking this over just the other day, and we all agreed it could happen  Why not?"
If you want to read more about the unicorn and the garden gnome, go to CNN com/CaffertyFile 
BLITZER: We will, for sure, Jack  Thank you  See you in a few moments 
Several sticking points in the ongoing budget negotiations, but will the government shutdown come down to money or social issues?
Plus, Donald Trump, he's making allegations about President Obama's birthplace  Does Donald Trump have any grounds for any of that? We're digging deeper for answers 
BLITZER: The growing outrage over the budget crisis isn't just about Congress' failure to reach a deal, it's also about some of the cuts that are being proposed 
Lets bring in our own Lisa Sylvester once again  She has the details -- Lisa 
Well, as congressional leaders hammer away on a budget compromise, a group of religious leaders have been fasting and praying to raise awareness of cuts in the budget that they say will harm the poor 
JIM WALLIS, PRESIDENT, SOJOURNERS: Orange juice never tasted so good 
SYLVESTER (voice-over): It's been 10 days since Jim Wallis last had solid food  The president of Sojourners, a Christian group that advocates for the underprivileged, is leading the charge among faith groups on a hunger fast to protest proposed cuts in the federal budget for the poor 
WALLIS: We're saying a budget is a moral document  And whether at your kitchen table, as a family, or a church or a nation, you make choices  What's important, what's not?
SYLVESTER: Wallis said in the last 10 days, more than 30,000 people around the country have joined in the fast in their own way  He says they have become a bit like God's lobbyists for the poor, putting a theological and moral spin on the cuts  Wallis said he is all for deficit reduction but --
WALLIS: I don't think doing this at the expense of the poorest people is a good choice, or hurting those who are already hurting the most is moral or even is smart 
SYLVESTER: Fiscal conservatives have suggested cuts in food stamps, foreign aid, and preschool programs for low-income families, that private groups can and should provide for the needy  But David Beckman of Bread for the World, who used to work at the World Bank, says the private sector can't fill the gap 
DAVID BECKMAN, PRESIDENT, BREAD FOR THE WORLD: All the private charitable feeding in the country amounts to about six percent of the food that poor people get from the national programs  So if you slash food stamps, as the House Republicans are proposing to do, there is no way that churches and charities and charitable people can make up for that 
SYLVESTER: Tony Hall was a member of Congress for years  As part of the fast, he is urging his former colleagues to reconsider cuts 
TONY HALL, ALLIANCE TO END HUNGER: When you make decisions about people's lives, be careful  You don't cut the poorest of the poor, because they didn't get you here  They didn't cause this mess 
SYLVESTER: On Wednesday, members of Congress began signing up for the fast 
REP  BARBARA LEE (D), CALIFORNIA: Several members of Congress today will be joining you in this fast 
SYLVESTER: Now, Sheila Jackson Lee, Keith Ellison and Jim McGovern are among 28 congressional Democrats who have signed on so far to join the hunger fast, and they will be doing a relay, with each taking one day to fast and then passing on the fast to their colleagues 
Wallis and Hall, they're doing it a little differently  They're fasting all the way through Easter Sunday  But they say for them, this fight for the poor is larger than just the specific budget battle -- Wolf 
BLITZER: These are committed, committed people to try to help 
We're going back to Libya in just a few moments  Rebel forces, furious with NATO right now, the R-rated message they are sending through our own Ben Wedeman 



ground_truth: The sticking point in the political showdown over the budget is how much spending to cut.