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UID:4@cds.iisc.ac.in
DTSTART;TZID=Asia/Kolkata:20230731T113000
DTEND;TZID=Asia/Kolkata:20230731T123000
DTSTAMP:20231007T192554Z
URL:https://cds.iisc.ac.in/events/ph-d-thesis-colloquium-cds-sparsificatio
 n-of-reaction-diffusion-dynamical-systems-in-complex-networks/
SUMMARY:Ph.D. Thesis {Colloquium}: CDS : “Sparsification of Reaction-Diff
 usion Dynamical Systems in Complex Networks.”
DESCRIPTION:Speaker : Mr. Abhishek Ajayakumar\n\nS.R. Number : 06-18-01-10-
 12-18-1-16176\n\nTitle : “Sparsification of Reaction-Diffusion Dynamical
  Systems in Complex Networks.”\n\nResearch Supervisor: Prof. Soumyendu R
 aha\n\nDate &amp\; Time : July 31\, 2023 (Monday) at 11:30 AM\n\nVenue : T
 he Thesis Colloquium will be held on HYBRID Mode # 102 CDS Seminar Hall /M
 ICROSOFT TEAMS.\n\nPlease click on the following link to join the Thesis C
 olloquium:\n\nMS Teams link:\n\nhttps://teams.microsoft.com/l/meetup-join/
 19%3ameeting_MDFmNDdlYWYtOTI0ZC00Njg5LWEwZjUtNzZhZjNiY2I0MDhm%40thread.v2/
 0?context=%7b%22Tid%22%3a%226f15cd97-f6a7-41e3-b2c5-ad4193976476%22%2c%22O
 id%22%3a%22f67fa1e8-f789-4048-bb53-c2880088cc5d%22%7d\n\n_________________
 _________________________________________________________________________\
 nAbstract\nGraph sparsification is an area of interest in computer science
  and applied mathematics. Sparsification of a graph\, in general\, aims to
  reduce the number of edges in the network while preserving specific prope
 rties of the graph\, like cuts and subgraph counts. Modern deep learning f
 rameworks\, which utilize recurrent neural network decoders and convolutio
 nal neural networks\, are characterized by a significant number of paramet
 ers. Pruning redundant edges in such networks and rescaling the weights ca
 n be useful. Computing the sparsest cuts of a graph is known to be NP-hard
 \, and sparsification routines exist for generating linear sized sparsifie
 rs in almost quadratic running time. The complexity of this task varies\, 
 and it is closely linked to the level of sparsity we desire to achieve. In
  our study\, we extend the concept of sparsification to the realm of react
 ion-diffusion complex systems. We aim to address the challenge of reducing
  the number of edges in the network while preserving the underlying flow d
 ynamics.\n\nSparsification of such complex networks is approached as an in
 verse problem guided by data representing flows in the network\, where we 
 adopt a relaxed approach considering only a subset of trajectories. We map
  the network sparsification problem to a data assimilation problem on a Re
 duced Order Model (ROM) space with constraints targeted at preserving the 
 eigenmodes of the Laplacian matrix under perturbations. The Laplacian matr
 ix is the difference between the diagonal matrix of degrees and the graph
 ’s adjacency matrix. We propose approximations to the eigenvalues and ei
 genvectors of the Laplacian matrix subject to perturbations for computatio
 nal feasibility and include a custom function based on these approximation
 s as a constraint on the data assimilation framework.\n\nIn the latter pha
 se of the study\, we developed a framework to enhance POD-based model redu
 ction techniques inreaction-diffusion complex systems. This framework inco
 rporates techniques from stochastic filtering theory and pattern recogniti
 on.\n\nGetting optimal state estimates from a noisy model and noisy measur
 ements forms the core of the filtering problem. By integrating the particl
 e filtering technique\, we generate the reaction-diffusion state vector at
  various time steps\, utilizing noisy measurements obtained from ROM. To e
 nsure the framework’s effectiveness\, we make intermittent updates to th
 e system variables during the particle filtering step\, employing the care
 fully crafted sparse graph. The framework is utilized for experimentation\
 , and results are presented on random graphs\, considering the diffusion e
 quation on the graph and the chemical Brusselator model as the dynamical s
 ystems embedded in the graph. We discuss the method’s limitations\, and 
 the proposed framework is evaluated by comparing its performance against t
 he Neural ODE-based approach\, which serves as a compelling reference due 
 to its demonstrated robustness in specific applications.\n\n==============
 =================================================================\n\nALL A
 RE WELCOME
CATEGORIES:Ph.D. Thesis Colloquium
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