Sarswati Shah

Mailing address:
Center for Mathematics and Artificial Intelligence (CMAI)
Department of Mathematical Sciences
George Mason University, Fairfax
Virginia 22030, United States
Email: sshah66@gmu.edu

Welcome to my webpage! Currently, I am working as a postdoctoral research fellow in the Department of Mathematical Sciences , at the George Mason University, with Prof. Harbir Antil. Prior to that, I was working as a DGAPA postdoctoral research fellow in the Institute of Mathematics (IM), at the National Autonomous University of Mexico (UNAM), with Prof. Gerardo Hernandez Dueñas. I obtained my Ph.D. degree from the Department of Mathematics, at the University of Delhi, under the supervision of Prof. Randheer Singh. My research focuses on mathematical modeling and structure-preserving scientific computing for nonlinear transport. I develop methods for hyperbolic conservation laws, transport-aware reduced-order modeling, PDE-constrained optimization, and physics-constrained generative modeling, with applications ranging from multiphase and geophysical flows to energy systems and nonlinear optics.

Research Interests

Hyperbolic Conservation Laws and Nonlinear PDE Systems
Structure-Preserving Numerical Methods and Scientific Computing
Transport-Aware Reduced-Order Modeling, Optimal Transport, and PDE-Constrained Optimization
Physics-Constrained Generative Modeling and Scientific Machine Learning
Applications in Multiphase and Geophysical Flows, Energy Systems, and Nonlinear Optics

Education

Ph.D. in Applied Mathematics

University of Delhi, India (Oct, 2016 -- March, 2021)
Thesis: EVOLUTION OF NONLINEAR WAVES IN QUASILINEAR HYPERBOLIC SYSTEMS
Advisor: Prof. Randheer Singh

M.Sc. in Mathematics

Deen Dayal Upadhyay Gorakhpur University, India (Aug, 2013 -- Jul, 2015)

B.Sc. in Mathematics & Physics

Deen Dayal Upadhyay Gorakhpur University, India (Aug, 2010 -- Jul, 2013)

Employment

Current Affiliation

Postdoctoral Research Fellow at the Department of Mathematical Sciences, George Mason University, United States, 2025.

Prof. Harbir Antil

Previous Affiliations

DGAPA Postdoctoral Fellow at the Institute of Mathematics (IM), National Autonomous University of Mexico, Mexico, 2022 -- 2024.

Prof. Gerardo Hernández Dueñas

Assistant Professor at the Department of Applied Sciences, The NorthCap University, Haryana, India, 2021 -- 2022.

Publications

Preprints and Submitted Manuscripts

Harbir Antil, Alex Kaltenbach, and Sarswati Shah, QH-GEM: Quantum-Hydrodynamic Generative Modeling, submitted, 2026. [arXiv]
Harbir Antil, Rocío Díaz Martín, Ivan V. Medri, Kristofor Pas, Gustavo K. Rohde, Aryan Saxena, and Sarswati Shah, Reduced Order Modeling of One-Dimensional Conservative PDEs via the Cumulative Distribution Transform, submitted, 2026. [arXiv]
Harbir Antil, Rainald Löhner, and Sarswati Shah, Polarization-Induced Beam Bending: Mathematical Model, Discretization, and Algorithm, submitted, 2026. [arXiv]
Sarswati Shah and Gerardo Hernández-Dueñas, A New Model for Two-Layer Liquid-Gas Stratified Flows in Pipes with General Cross Sections, submitted, 2026. [arXiv]

Peer-Reviewed Scientific Articles

Sarswati Shah, The Riemann Problem for the Flow Pattern in Deviated Pipes Carrying Isentropic Two-Phase Flows, Studies in Applied Mathematics, 154, e70003, 2025. [link]
Sarswati Shah and Gerardo Hernández Dueñas, Weakly Compressible Two-Layer Shallow-Water Flows Along Channels, Journal of Scientific Computing, 100, 61, 2024. [link]
Bipin Kumar Chaudhary, Randheer Singh, and Sarswati Shah, Delta Shocks and Vacuums in the Aw–Rascle Model with Anti van der Waals Chaplygin Gas under the Flux Approximation, Physics of Fluids, 36, 016144, 2024. [link]
Sarswati Shah, Randheer Singh, Bipin Kumar Chaudhary, and Jasobanta Jena, The Riemann Problem for Real Isothermal Gases with Dust Particles, International Journal of Applied and Computational Mathematics, 9, 1–15, 2023. [link]
Sarswati Shah, Randheer Singh, and Jasobanta Jena, Interaction of Acceleration Wave with a Blast Wave in Two-Phase Chaplygin Flow Driven by Source Term, Acta Applicandae Mathematicae, 186, 2, 2023. [link]
Randheer Singh, Sarswati Shah, and Jasobanta Jena, On Kinematics of One-Dimensional Radially Symmetric Shocks in Non-Ideal Reacting Gases, Mathematical Methods in the Applied Sciences, 47, 1735–1749, 2023. [link]
Sarswati Shah, Randheer Singh, and Bipin Kumar Chaudhary, Concentration and Cavitation of Riemann Solutions to Two-Phase Chaplygin Flows under Vanishing Pressure and Flux Approximation, Communications in Nonlinear Science and Numerical Simulation, 118, 107065, 2023. [link]
Sarswati Shah, Randheer Singh, and Jasobanta Jena, Steepened Wave in Two-Phase Chaplygin Flows Comprising a Source Term, Applied Mathematics and Computation, 413, 126656, 2022. [link]
Sarswati Shah and Randheer Singh, Lie Symmetries for Analyzing Interaction of a Characteristic Shock and a Singular Surface in a Non-Ideal Reacting Gas with Dust Particles, Mathematical Methods in the Applied Sciences, 44, 3804–3818, 2020. [link]
Sarswati Shah and Randheer Singh, Imploding Shocks in Real Reacting Gases with Dust Particles, Journal of Mathematical Physics, 61, 033506, 2020. [link]
Sarswati Shah and Randheer Singh, Propagation of Non-Planar Weak and Strong Shocks in a Non-Ideal Relaxing Gas, Ricerche di Matematica, 70, 371–393, 2019. [link]
Sarswati Shah and Randheer Singh, Collision of a Steepened Wave with a Blast Wave in Dusty Real Reacting Gases, Physics of Fluids, 31, 076103, 2019. [link]
Sarswati Shah and Randheer Singh, Evolution of Singular Surface and Interaction with a Strong Shock in Reacting Polytropic Gases Using Lie Group Theory, International Journal of Non-Linear Mechanics, 116, 173–180, 2019. [link]

Scholastic Achievements

DGAPA Postdoctoral Fellowship by CTIC, Govt. of Mexico. March, 2022.
National Postdoctoral Fellowship (N-PDF) by SERB, Govt. of India. (Not availed), Dec, 2021.
Qualified CSIR- NET (JRF) with AIR-20, June, 2016.
Qualified GATE with AIR-268, Feb, 2016.
Awarded Gold medal for securing the first position in M.Sc. Mathematics, Aug, 2015.

Teaching Experience

As an Instructor

Hyperbolic Conservation Laws (postgraduate), Institute of Mathematics, UNAM, Mexico, Spring, 2024. [Syllabus]
Partial Differential Equations (postgraduate), Institute of Mathematics, UNAM, Mexico, Fall, 2023. [Syllabus]
Ordinary Differential Equations (postgraduate), Institute of Mathematics, UNAM, Mexico, Spring, 2023. [Syllabus]
Metric Spaces (undergraduate), Department of Applied Sciences, The NorthCap University, India, Fall, 2021.
Engineering Math I (undergraduate), Department of Applied Sciences, The NorthCap University, India, Fall, 2021.
Mathematical Modelling and Simulation (undergraduate), Department of Applied Sciences, The NorthCap University, India, Spring, 2021.
Engineering Math II (undergraduate), Department of Applied Sciences, The NorthCap University, India, Spring, 2021.

As a tutor

Fluid Dynamics (postgraduate), Department of Mathematics, University of Delhi, India, Spring, 2018 and 2019
Method of Applied Mathematics (postgraduate), Department of Mathematics, University of Delhi, India, Fall, 2018 and 2019
Module Theory (postgraduate), Department of Mathematics, University of Delhi, India, Spring, 2017

Conferences & Talks

Conferences & Workshops

International Congress of Mathematicians (ICM 2026), Pennsylvania Convention Center, Philadelphia, PA, United States, July 23-30, 2026. (Talk: Modeling and Numerical Approximation of Bilayer Water and Gas Flows in Pipelines)
Finite Element Circus Fall 2025, George Mason University, Arlington, VA, United States, October 17-18, 2025. (Talk: Reduced-Order Modeling of Conservation Laws)
SIAM NWCS24: SIAM Conference on Nonlinear Waves and Coherent Structures, Lord Baltimore Hotel, Baltimore, MD, United States, June 24-27, 2024. (Talk: Path-Conservative Central Upwind Schemes for Weakly Compressible Two-Layer Shallow Water Flow)
Workshop on Theoretical and Practical Perspectives in Geophysical Fluid Dynamics, International Center for Theoretical Sciences, Bengaluru, India, May 20-31, 2024. (Poster: Path-conservative central-upwind schemes for weakly compressible two-layer shallow water flow)
Hot Topics: Recent Progress in Deterministic and Stochastic Fluid-Structure Interaction, Simons Laufer Mathematical Sciences Institute (MSRI), University of California, Berkeley, United States, Dec 04-08, 2023. (Attended)
Workshop on Modern Applied and Computational Analysis, Institute for Computational & Experimental Research in Mathematics (ICERM), Brown University, United States, Jun 26-30, 2023. (Poster: Central-Upwind Schemes for Weakly Compressible Two-layer Shallow-Water Flows)
ENOAN XXXI: Escuela Nacional de Optimización y Análisis Numérico, Instituto de Matemáticas UNAM Cuernavaca & Universidad Autónoma del Estado de Morelos, Morelos, México,(online) Jun 26-30, 2023. (Talk: Delta shock wave solution to the Riemann problem for two-phase generalized Chaplygin flows)
FoCM 2023: Foundations of Computational Mathematics, Sorbonne University, Paris, France Jun 12-21, 2023. (Poster: Central-Upwind Schemes for Weakly Compressible Two-layer Shallow-Water Flows)
Summer School: Horizons in Non-Linear PDEs, Ulm University, Ulm, Germany, Sep 26-30, 2022. (Talk: Weakly compressible two-layer shallow-water flows)
MultiMat 2022: 10^th International Conference on Numerical Methods for Multi-Material Fluid Flow, Universität Zürich (Irchel Campus), Zürich, Switzerland, Aug 22-26, 2022. (Poster: Weakly compressible two-layer shallow-water flows in general channels)
HYP 2022: XVIII International Conference on Hyperbolic Problems; Theory, Numerics, Applications, University of Málaga, Málaga, Spain Jun 20-24, 2022. (Talk: Weakly compressible two-layer shallow-water flows with friction and entrainment along channels)
Annual meeting of the SIAM Mexico section, Universidad Autonoma de Coahuila, Saltillo, Coahuila, Mexico Jun 08-10, 2022. (Talk: Weakly compressible two-layer shallow-water flows in general channels)
Workshop on Advances and Challenges in Hyperbolic Conservation Laws, Institute for Computational & Experimental Research in Mathematics (ICERM), Brown University, United States (online) May 17-21, 2021. (Attended)
48^th Annual Conference of Odisha Mathematical Society, Institute of Mathematics and Applications, Bhubaneswar, Odisha, India, Apr 10-11, 2021. (Talk: Evolution of singular surface in the drift flux equations of two-phase flows)
Online Webinar on An Introductory Course on Fluid Dynamics, Department of Mathematics, CHRIST(Deemed to be University), Bangalore, India, Aug 17-20 & Aug 24-28, 2020. (Attended)
64^th Congress of ISTAM, Indian Institute of Technology Bhubaneswar, Odisha, India, Dec 09-12, 2019 (Talk: Propagation of shock wave in a non-ideal reacting gas)
National Conference on Recent Trends in Mathematical Sciences, Department of Mathematics & Statistics, DDU Gorakhpur University, Gorakhpur, U.P., India, Nov 24-25, 2018. (Talk: Converging shocks on non-planar flow of reacting gas)
'Advanced Instructional School’ on “Differential Equations", School of Mathematics, University of Hyderabad, Hyderabad, India, Jun 04-23, 2018. (Attended)
'Science Academics Lecture Workshop’ on “Essence of Partial Differential Equation”, School of Basic Science, Indian Institute of Technology Mandi, H.P., India, Apr 02-04, 2018. (Attended)
Research Scholar Seminar & Annual Conference of the Society of Mathematical Sciences, Department of Mathematics, University of Delhi, Delhi, India, May 01-02, 2017. (Attended)

Invited Talks

Potomac Region PDE Day, Virginia Commonwealth University (VCU), Richmond, Virginia, USA, November 14, 2026. (Talk: QH-GEM: Quantum Hydrodynamic Generative Modeling)
Colloquium Talk, Center for Mathematics and Artificial Intelligence (CMAI), George Mason University, Fairfax, Virginia, USA, September 18, 2026. (Talk: QH-GEM: Quantum Hydrodynamic Generative Modeling)
Minisymposium, ILAS 2026, Virginia Tech, Blacksburg, Virginia, USA, May 18-22, 2026. (Talk: Reduced Order Modeling of Conservation Laws via CDT)
Colloquium Talk, Center for Mathematics and Artificial Intelligence (CMAI), George Mason University, Fairfax, Virginia, USA, February 27, 2026. (Talk: Polarization-Induced Beam Bending: Mathematical Model and Numerical Algorithm)
AMS Special Session on Advances and Challenges in Hyperbolic Conservation Laws, 2025 Virtual Fall Eastern Sectional Meeting, USA, October 25-26, 2025. (Talk: A Central Upwind Scheme for Two-Layer Stratified Flow in Pipes with General Channels)
Minisymposium, Mathematical Congress of the Americas 2025, Miami, Florida, USA, July 21-26, 2025. (Talk: Two-Layer Stratified Flow in Pipes with General Channels)
Henes Workshop on Computational and Applied Mathematics, Michigan Technological University, Michigan, USA, May 22-23, 2025. (Talk: Weakly Compressible Two-Layer Shallow-Water Flows with Friction Along Channels)
Seminar Talk, Department of Mathematics and Statistics, Georgetown University, Washington, DC, USA, March 12, 2025. (Talk: Two-Layer Shallow-Water Flows Along Channels: Modelling and Computational Approach)
Colloquium Talk, Department of Mathematical Sciences, George Mason University, Fairfax, Virginia, USA, February 28, 2025. (Talk: Two-Layer Shallow-Water Flows Along Channels: Modelling and Computational Approach)
Seminar Talk, TIFR - Centre for Applicable Mathematics, Bengaluru, India, June 06, 2024. (Talk: Theoretical modelling and numerical simulation of hyperbolic balance laws)
Minisymposium, in the conference '56^th National Congress of the Mexican Mathematical Society', Universidad Autónoma de San Luis Potosí (UASLP), México, Oct 23-27, 2023. (Talk: Central-Upwind Schemes for Weakly Compressible Two-layer Shallow-Water Flows)
Colloquium, Instituto de Matemáticas, Universidad Nacional Autónoma de México (UNAM), México, May 26, 2023. (Talk: Theoretical modelling and numerical simulation of hyperbolic balance laws)
Colloquium, Facultad de Ingeniería, Universidad Autónoma de Querétaro (UAQ), México, Mar 09, 2023. (Talk: Models and methods for two-layer compressible fluid flows; gas-gas flows and liquid-liquid flows)
Two lectures, in the workshop 'Numerical Analysis of Ordinary & Fractional Partial Differential Equations (NAOFPDE-2022)' sponsored by MPHEQIP Bhopal at the Department of Mathematics, Govt. Tilak P.G. College, Katni, India, Dec 27-31, 2022. (Talk: Introduction of Hyperbolic Partial Differential Equations and some of its example to real world application)

Research Visits

One-week research visit
Invited by: Prof. Jim Thomas
TIFR - Centre for Applicable Mathematics, Bengaluru, Karnataka, India, June 03-07, 2024.

Two-week research visit
Invited by: Prof. M. Pascale Lelong
NorthWest Research Associates (NWRA), Seattle, Washington, USA, Nov 07-19, 2022.

Professional Services

Referee for the following journals:
Physics of Fluids
Ricerche di Matematica
The European Physical Journal Plus
Journal of Engineering Mathematics

Skills

Be familiar with LaTeX, MATLAB, C, C++, Python