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Applied Mathematics Symposium

Applied Mathematics Symposium: Artificial Intelligence meets Fluid Dynamics



The Departments of Mathematics at IIT Guwahati, IIT Hyderabad and VIT Vellore are jointly organizing an online symposium titled “Applied Mathematics Symposium: Artificial Intelligence meets Fluid Dynamics” on July 07, 2023 (Friday) during 09:00-16:40 IST. The symposium will be held online via Microsoft Teams.

Date: July 07, 2023 (Friday)

Mode: Online Platform (Microsoft Teams)

Microsoft Teams Link: Click here to join the meeting

About the symposium: Our aim is to bring together researchers working in the broad field of applied mathematics, particularly at the interface of artificial intelligence (AI) and fluid dynamics (FD). The present symposium focuses on discussing recent progress in application of AI in fluid dynamics and other related areas. Invited speakers to this event include both early-career and senior researchers from within and outside India. The targeted audience are researchers at all levels, not necessarily experts in the thematic area of the symposium, but also those who aspire to work in this area.

Speakers


  • Nathan Kutz, University of Washington, USA (Plenary speaker)

  • Chirodeep Bakli, IIT Kharagpur, India (Invited speaker)

  • Francesco Romano, ENSAM Lille, France (Invited speaker)

  • Koji Fukagata, Keio University, Japan (Invited speaker)

  • Tapan Kumar Hota, SRM Amravati (Invited speaker)

  • Aniruddha Bora, Brown University (Invited speaker)

    • Program Schedule


    09:00-09:10 IST                                Welcome Address

    09:10-10:10 IST                                Plenary Talk

    Speaker: Nathan Kutz, University of Washington, USA

    Title: The future of governing equations

    Abstract: A major challenge in the study of dynamical systems is that of model discovery: turning data into reduced order models that are not just predictive, but provide insight into the nature of the underlying dynamical system that generated the data. We introduce a number of data-driven strategies for discovering nonlinear multiscale dynamical systems and their embeddings from data. We consider two canonical cases: (i) systems for which we have full measurements of the governing variables, and (ii) systems for which we have incomplete measurements. For systems with full state measurements, we show that the recent sparse identification of nonlinear dynamical systems (SINDy) method can discover governing equations with relatively little data and introduce a sampling method that allows SINDy to scale efficiently to problems with multiple time scales, noise and parametric dependencies. For systems with incomplete observations, we show that the Hankel alternative view of Koopman (HAVOK) method, based on time-delay embedding coordinates and the dynamic mode decomposition, can be used to obtain a linear models and Koopman invariant measurement systems that nearly perfectly captures the dynamics of nonlinear quasiperiodic systems. Neural networks are used in targeted ways to aid in the model reduction process. Together, these approaches provide a suite of mathematical strategies for reducing the data required to discover and model nonlinear multiscale systems.

    10:10-10:30 IST                                Break

    10:30-11:15 IST                                Invited Talk 1

    Speaker: Koji Fukagata, Keio University, Japan

    Title: Applications of convolutional neural networks to fluid flows: toward machine-learning-assisted flow control

    Abstract: Application of machine learning is currently one of the hottest topics in the fluid mechanics field. In this presentation, we will introduce some of our recent attempts on regeneration of flow fields using convolutional neural network (CNN). We will also introduce the applications of CNN for super-resolution analysis and reduced order modeling. We also introduce our attempts to interpret the nonlinear modes extracted by CNN autoencoder and to use them for an advanced design of flow control, as well as an attempt for uncertainty quantification and applications to experimental data.

    11:15-12:00 IST                                Invited Talk 2

    Speaker: Chirodeep Bakli, IIT Kharagpur, India

    Title: Applications of Machine Learning to Link Interfaces to Bulk in Confined Fluids

    Abstract: Device miniaturization and 2-D materials are extremely popular today for designing smart devices, achieving super-sleek equipment with smart thermal management, or, in general, systems that are ‘flexible’ in every sense of the word. Engineering these applications involves tweaking the fluid-solid interface and designing fluids that behave quite differently from the traditional behavior. To elaborate, water as a coolant would have not only high thermal conductivity but also high specific heat; oils would have high surface tension to create self-cleaning and self-healing surfaces; ice freezing and anti-freezing behavior obtained with the click of a switch, and so on. These fluid engineering applications are an offshoot of reduced dimensional attributes which impart a behavior to the system that is usually explained by terms like the failure of the continuum, slip boundary condition, etc. Usually, molecular dynamics simulation tries to give a perspective to the behavior of the fluid between the bulk and interfaces; however, the output is in the form of huge trajectory files, which come after rigorous simulations with a lot of computational expense. Moreover, each case is to be simulated separately, consuming a lot of time and resources. With machine learning techniques, the fluid behavior from the trajectory files can be decoded towards a unified theory to explain the deviations obtained with confinement. Machine learning algorithms come as a tool to analyze the fluid behavior at bulk and interfaces machine and try to decrypt the code a substrate uses to make the fluid realize its presence. Classical fluid mechanics may codify this as viscosity, thermal conductivity, diffusion coefficient, etc. We here try to crack the molecular code using machine learning to unify fluid orientation, lattice structure, van der Waals forces, and hydrogen bonding with some easily measurable parameters and use the same to predict bulk properties.

    12:00-12:45 IST                                Invited Talk 3

    Speaker: Tapan Kumar Hota, SRM Amravati

    Title: Some Recent Development of Dynamic Modes in Interfacial Instability

    Abstract: Understanding complex fluid movement is now accessible than ever thanks to new techniques and methodology. Nonetheless, many researchers prefer the traditional eigenmode-based methods. Using the eigenmodes, many insights into the evolution of small and finite amplitude perturbations can be gained, namely from the growth rate of perturbation can be determined from the leading eigenmodes obtained after linearizing the non-linear governing equations. P. Schmid [J. Fluid Mech., 2010, vol. 656] recently developed a novel technique for doing spectral analysis of a fluid flow that is purely based on snapshot sequences from numerical simulations or experimental data. The fundamental idea behind this method is to investigate the retrieved dominating frequencies and wavenumbers, as well as dynamic modes that represent the associated flow structures. The mathematical foundations of this decomposition are linked to the Koopman operator, which offers a nonlinear dynamical system a linear representation. The dynamic modes for linearized problems reduce to global linear eigenmodes, but for nonlinear periodic problems, they reduce to Fourier modes. This method will be illustrated in relation to viscous fingering, a type of hydrodynamic stability.

    12:45-15:00 IST                                Break

    15:00-15:45 IST                                Invited Talk 4

    Speaker: Francesco Romano, ENSAM Lille, France

    Title: Machine learning for optimal flow control in an axial compressor

    Abstract: The effectiveness of using air jets for active flow control in axial compressors to delay stall phenomenon has been demonstrated in the literature. In this research, a combination of machine learning and genetic algorithms is employed to determine the optimal parameters of air jets for controlling rotating stall in the axial compressor CME2. Three control parameters are examined: the absolute injection angle, the number of injector pairs, and the injection velocity. By utilizing an experimental dataset, the impact of the air jet parameters on surge margin improvement and power balance is modelled using two neural networks. The parameters of the air jets are then optimized using a genetic algorithm for three rotational velocities (Ω = 3200 RPM, 4500 RPM, and 6000 RPM). Initially, the focus is on maximizing surge margin improvement and power balance separately. Subsequently, a bi-objective optimization problem is formulated to explore the trade-off between these two competing objectives. Based on the Pareto front, the results indicate that an optimal set of parameters can be achieved globally within a velocity ratio range (defined as the ratio of the injection velocity to the rotor tip speed) of 1.1 to 1.6 and an injection angle attack varying from 1° to 11°. These findings, together with their physical interpretation, suggest the potential generalizability of the control strategy to other compressors.

    15:45-16:30 IST                                Invited Talk 5

    Speaker: Aniruddha Bora, Brown University

    Title: Learning bias corrections for climate models using neural operator framework

    Abstract: Numerical simulation for climate modeling resolving all important scales is a computationally taxing process. Therefore, to circumvent this issue a low-resolution simulation is performed, which is subsequently corrected for bias using reanalyzed data (ERA5), known as nudging tendency or correction. The existing implementation for nudging correction uses a relaxation-based method for the algebraic difference between low resolution and ERA5 data. In this study, we replace the bias correction process with a surrogate model based on the Deep Operator Network (DeepONet). DeepONet (Deep Operator Neural Network) learns the mapping from the low resolution (a functional) to the nudging tendency (another functional). The accuracy of the DeepONet model is tested against the nudging tendency obtained from the E3SMv2 (Energy Exascale Earth System Model) and shows good agreement. The overarching goal of this work is to deploy the DeepONet model in an online setting and replace the nudging module in the E3SM loop for better efficiency and accuracy.

    16:30-16:40 IST:                                Vote of Thanks