Analysis and Robustness of Sparse Identification of Nonlinear Dynamical Systems on systems exhibiting chaotic behaviour
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Advisor: Anubhab Roy, Applied Mechanics
This thesis extends the analysis of sparse identification of nonlinear dynamical systems (SINDy) to complex systems governed by higher order differential equations. The Lorenz system and Duffing oscillator were used to evaluate the effectiveness of the model, with results showing accurate identification of the underlying equations. The robustness of SINDy is also tested on data generated in a wave simulation lab. These findings provide insight into the potential of SINDy to accurately identify the governing equations of complex systems, even in the presence of noise.
Thesis
Placement: American Express
Change detection is a crucial task in remote sensing for monitoring the effects of various natural and man-made phenomena over a given area. Urban planning, environmental monitoring and disaster management are a few fields where change detection plays a crucial role. The process involves comparing aerial images of the target area captured at two different times. This study aims to use various Convolutional Neural Network (CNN) architectures to achieve state-of-the-art results on publicly available change detection datasets. We also want to achieve these results without drastically increasing the computational time of the algorithm.
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Placement: American Express
Multivariable Causal Analysis using CCM
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Advisor: Arun Tangirala, Chemical Engineering
Convergent Cross Mapping (CCM) is a model-free approach used to infer causal relationships in non-linear dynamical systems. However, CCM has limitations in dealing with noisy data, synchrony, particular periodic oscillations and distinguishing between direct and indirect causal links. The research aims to propose and refine extensions to Convergent Cross Mapping, using multivariate state space reconstruction, to address some of these limitations and distinguish between direct and indirect causal links.
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Placement: McKinsey & Company
User confirmation using voice data recorded by a hot wire anemometer
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Advisor: Mahesh Panchagnula, Applied Mechanics
We know that there are various voice identification/confirmation softwares made where the samples/data were taken with the help of a microphone. My experiment basically tests if we can build a voice confirmation system with the help of data recorded with the help of a hot wire anemometer.
Thesis
Placement: Accenture Japan, Tokyo
Dynamic Mode Decomposition (DMD) is a mathematical technique used to extract spatiotemporal patterns from high-dimensional data. It is a data-driven approach that identifies the underlying dynamic modes of a system by analyzing its time series data. DMD is particularly useful in fields such as fluid dynamics, climate modeling, and neuroscience, where the data is often high-dimensional and complex. One common application of DMD in fluid mechanics is to study the dynamics of vortices and other coherent structures in a fluid flow. Using DMD, it is possible to extract the dominant modes of the flow and identify the frequencies and spatial structures associated with vortex shedding, turbulent fluctuations, and other dynamic features. In this Thesis , I will be exploring the limitations of a types of DMD Algorithms that can be used to study the complex Flows around Biomimetic Devices.
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Placement: Shell
Modelling of Climate Subsystems
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Advisor: Sayan Gupta, Applied Mechanics
Climate is a collection of subsystems that interact with each other- such as the atmosphere, hydrosphere, biosphere etc. Traditionally Global Climate Models(GCMs) which solve mass, momentum & energy equations across the globe. But it is difficult to separate subsystems and isolate the interactions between them in this method. Through this paper, we are trying to propose new methods-stochastic modelling and ML methods, to model these subsystems interactions and validate it with the existing data. The subsystems we will be focusing on in this paper are the Indian Ocean Dipole & the El-Nino Southern Oscillation.
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Placement: Indus Insights
Comprehensive generative model of sleep EEG across all stages
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Advisor: Srinivas Chakravarthy, Biotechnology
The work aims at replicating the human brain during its various sleep stages of NREM and REM, through an extension of Complex-Valued Oscillatory Neural Networks. We further aim to observe and duplicate the transition between the sleep stages. Right now, a switching based approach is considered to pass inputs through variables of wakefulness, sleep, REM and NREM stage after having replicated the sleep-wake and REM-NREM flip flop models to fully reproduce the transition stages.
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Placement: Target Corporation
Dynamical systems are usually understood by their evolution equations and visualized by integrating them forward in time. However, with real-life dynamical systems, evolution equations are not always available; these are primarily nonlinear, and predicting them becomes increasingly difficult with increasing nonlinearity. Chaotic dynamical systems are systems where small changes in the initial state of the system lead to drastic changes in its final state, making them difficult to predict. This calls for data-driven methods to predict the dynamics of such systems. This project takes the help of Koopman operator theory and delay embedding to do the same.
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Placement: Inito
Multi-task Floorplan Recognition using Bidirectional Graph Reasoning Network
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Advisor: Srinivas Chakravarthy, Biotechnology
This research aims to propose a new approach to recognising elements in floor plan layouts. Besides walls and rooms, we aim to recognise diverse floor plan elements, such as doors, windows and different types of rooms and their dimensions, furniture etc. This can be achieved by proposing a Bidirectional Graph Reasoning Network (BGRNet), a deep multi-task neural network architecture, where each task aims to recognise, extract and interpret different floor plan layout elements separately. The proposed network incorporates a Graph Connection Module that mines the intra-modular and inter-modular relations between each task in the network, thus enhancing the prediction accuracy of each task.
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Placement: Zomato