CILAMCE 2018 CONGRESS 11-14 NOVEMBER 2018, PARIS/COMPIÈGNE,F RANCE D EEP NEURAL NETWORK FOR V ECTOR F IELD T OPOLOGY R ECOGNITION WITH APPLICATIONS TO F LUID F LOW S UMMARIZATION Eliaquim Monteiro Ramos 1 , Leandro Tavares da Silva 2 , Jaime Santos Cardoso 3 , Gilson Antonio Giraldi 4 1 National Laboratory for Scientific Computing, Petrópolis, Brazil, eliaquimgauss@hotmail.com 2 Federal Center of Technology Education Celso Suckow da Fonseca, Petrópolis, Brazil, leandrots@gmail.com 3 University of Porto and INESC, Porto, Portugal, jaime.cardoso@inesctec.pt 4 National Laboratory for Scientific Computing, Petrópolis, Brazil, gilson@lncc.br In the past decades, concepts in vector field topology have been used for fluid flow analysis and visualiza- tion [1, 2]. On the other hand, recent works have applied techniques from video summarization to yield a synthetic and useful visual abstraction of the flow evolution in computational fluid dynamics (CFD) sim- ulations [3, 4]. Moreover, deep learning methods are currently the state-of-the-art for pattern recognition and classification tasks [5]. In this paper we apply an encoder-decoder deep neural network architecture [6] for learning a metric in the space of vector fields associated with the simulation. Such metric can be used to compare vector fields and discriminate between different topologies. Henceforth, starting from the assumption that we can partition the flow simulation according to the topology of the velocity fields therein, we apply the obtained metric as a component of a fluid flow summarization methodology. Specifically, let D ⊂ R 2 be the rectangular simulation domain and L the space of smooth real vector fields v : D → E 2 in D, where E 2 is the two-dimensional Euclidean space. For numerical computations, each vector field v is represented by a matrix V ∈ R n×m×2 , using a regular n × m grid over D, which allows to obtain the space b L , named in this work the source space. On the other hand, let H be the space of velocity fields related to the simulation setup, named the target space, whose discrete version generated through the n × m grid is denoted by b H . In this scenario, the training set χ s = ( V si , l si ) ; i = 1, 2,..., N s  in the source space b L is composed by vector fields V si with known topologies labeled by l si . We can build this set considering periodic orbits, hyperbolic and non-hyperbolic topologies of vector fields in E 2 as well as their combinations [7]. On the other hand, the unlabeled training set χ t =  V ti ; i = 1, 2,..., N t  , in the target space b H , contains velocity fields with unknown topologies and it is tailored by a specific simulation. Given a sequence of numerical frames generated through a CFD simulation, the pipeline firstly performs a coarse temporal stream flow segmentation using a simple similarity measure combined with an interval tree for subsequent analysis. For each obtained segment, some keyframes are selected [4]. The corresponding velocity fields, with unknown topologies, are used to build the set χ t ⊂ b H . Next, the encoder-decoder architecture is trained using the sets χ s and χ t and the learnt metric d t : b H → R + is used to compute a X-means clustering algorithm [8] to complete the summarization. We demonstrate the methodology using 2D fluid simulations of the N-roll mill apparatus where N symmetrically placed rollers, that rotate at constant angular velocities, are surrounding by a fluid. In this paper, we simulate the N-roll mill flows, for N = 4, 6 using the SPH technique [9]. We compare the CFD summarization technique proposed with counterpart ones and show that the clusters generated by our algorithm captures a compact but detailed picture of important segments of the fluid which allows to build a summary useful for scientific visualization purposes. 1