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UID:130@cds.iisc.ac.in
DTSTART;TZID=Asia/Kolkata:20250619T153000
DTEND;TZID=Asia/Kolkata:20250619T163000
DTSTAMP:20250616T133215Z
URL:https://cds.iisc.ac.in/events/ph-d-thesis-colloquium-cds-hybrid-june-1
 9-2025-structure-preserving-physics-informed-neural-networks-for-modelling
 -flow-in-anisotropic-porous-media-with-pressure-dependent-viscosity/
SUMMARY:Ph.D. Thesis {Colloquium}: CDS: Hybrid: June 19\, 2025: "Structure-
 Preserving Physics-Informed Neural Networks for Modelling Flow in Anisotro
 pic Porous Media with Pressure-Dependent Viscosity.".
DESCRIPTION:DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES\nPh.D. Thesis Col
 loquium\n\n\n\nSpeaker                 : Nischal Karthik Mapakshi
 \nS.R. Number        : 06-18-00-10-12-19-1-17456\nTitle          
                 : "Structure-Preserving Physics-Informed Neural Ne
 tworks for Modelling Flow in Anisotropic Porous Media with Pressure-Depend
 ent Viscosity."\nResearch Supervisor:  Prof. Soumyendu Raha\nDate &amp\; 
 Time         : June 19\, 2025 (Thursday) at 03:30 PM\nVenue       
                : The Thesis Colloquium will be held on HYBRID 
 Mode\n# 102 CDS Seminar Hall /MICROSOFT TEAMS.\nPlease click on the follow
 ing link to join the Thesis Colloquium:\nMS Teams link\n\n\n\nABSTRACT\n\
 nThis work presents a comprehensive Physics-Informed Neural Network (PINN)
  framework to model subsurface flow through anisotropic porous media with 
 pressure-dependent viscosity. The study begins with a strong-form PINN imp
 lementation\, where the governing PDEs are directly encoded using automati
 c differentiation in TensorFlow. This avoids numerical quadrature and allo
 ws exact enforcement of physics through the strong form. To preserve physi
 cal realism—particularly non-negative pressures and the discrete maximum
  principle (DMP)—a custom sigmoid-based output transformation was introd
 uced. This hard constraint mechanism enabled the network to achieve 0.0\\%
  DMP violations across benchmark problems.\n\nA key highlight of this stud
 y is the use of realistic physical parameters (permeability\, viscosity\, 
 pressure) that span several orders of magnitude—something not commonly d
 one in existing PINN literature due to conditioning issues. This is addres
 sed using a robust non-dimensionalization strategy\, which improves traini
 ng stability and enhances the model’s applicability to real-world engine
 ering problems.\n\nBenchmarking against manufactured solutions and scaling
  studies revealed that while increasing collocation points improves accura
 cy up to a point\, performance plateaus beyond a threshold\, indicating li
 mited returns. The effect of anisotropy and nonlinearity was also explored
 : while pressure-dependent viscosity had a mild effect on constraint satis
 faction\, directional anisotropy significantly increased the risk of DMP v
 iolations if constraints were not strongly enforced.\n\nTo address complex
  geometries such as annular domains\, the study transitions to a Galerkin 
 PINNs formulation\, where the PDE is reformulated in weak form using test 
 functions. This variational approach enhances stability\, particularly in 
 irregular geometries. Two constraint strategies were explored:\n\n(1) Hard
  constraints using sigmoid or ReLU output transformations\, and\n\n(2) Sof
 t constraints using interior-penalized loss terms to bound the pressure fi
 eld.\n\nThe hard constraint formulation continued to deliver strict DMP pr
 eservation even in highly anisotropic regimes\, while the soft version exh
 ibited small\, localized violations. A systematic sweep over the anisotrop
 y parameter $\\varepsilon$ was performed for both formulations. Results de
 monstrated a clear correlation between increasing $\\varepsilon$ and DMP v
 iolation percentage. However\, hard-constrained models consistently suppre
 ssed violations to near-zero levels. All pressure results were reported in
  dimensional units (Pa)\, and pressure and velocity fields were saved sepa
 rately for each $\\varepsilon$\, ensuring transparency and reproducibility
 .\n\nHyperparameter optimization was also conducted using Bayesian methods
 . Results showed that increasing the number of layers or learning rate imp
 roves convergence up to a point\, beyond which performance deteriorates du
 e to overfitting or instability. Learning curves and error trends confirme
 d the presence of optimal regimes that balance accuracy and training effic
 iency.\n\nFollowing the Galerkin formulation\, the study now advances towa
 rd a Variational Multiscale (VMS) PINNs formulation. While traditionally u
 sed to separate coarse and fine scales\, in this work VMS serves to enrich
  the variational residual by adding stabilizing terms on both sides\, offe
 ring an alternative means of improving solution stability. As with the Gal
 erkin formulation\, both hard and soft constraint strategies will be explo
 red for VMS\, with an $\\varepsilon$-sweep used to evaluate DMP adherence.
 \n\nThis unified PINN framework—spanning strong-form\, Galerkin\, and VM
 S formulations—demonstrates the ability to model nonlinear\, anisotropic
  flow with high physical fidelity. By enforcing maximum principles and inc
 orporating realistic parameter scales\, the approach is well-suited for su
 bsurface flow modeling in geophysics\, petroleum recovery\, and groundwate
 r applications.\n\n\n\nALL ARE WELCOME
CATEGORIES:Events,Ph.D. Thesis Colloquium
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