Topic of Research Seminar: Physics- Informed Neural Networks for Forward and Inverse Problems in Nonlinear Differential Equations
Abstract: This seminar presents Physics-Informed Neural Networks (PINNs) as a modern approach for solving forward and inverse problems in nonlinear differential equations. Traditional numerical methods, such as finite difference schemes and Runge–Kutta methods, require mesh generation and time stepping, and their accuracy depends strongly on discretization size. In contrast, PINNs combine neural networks with physical laws by directly embedding differential equations into the training process.
The seminar first explains the basic idea of artificial neural networks and how physics is added into the loss function to guide learning. The methodology is demonstrated on three nonlinear systems: the Lotka–Volterra predator–prey model, the viscous Burgers’ equation, and the two-dimensional Navier–Stokes equations.
For forward problems, PINNs successfully reproduce accurate solutions without using traditional time-marching schemes. For inverse problems, unknown physical parameters such as viscosity and flow coefficients are treated as trainable variables and are recovered from sparse and even noisy data. In the Navier–Stokes example, the network reconstructs the pressure field without being given any pressure data. The results show that PINNs provide a flexible, mesh-free and physics-consistent framework for solving complex nonlinear differential equations while also identifying unknown parameters. This demonstrates their potential for scientific computing and real-world engineering applications.
Subject Field of Topic: Applied Mathematics (Scientific Machine Learning)
Name of Speaker: Ms. Khansa Hanif
Professorial Rank of Speaker: PhD Scholar (Mathematics Dpt.) SNS
Email of Speaker: [email protected]
Affiliation of Speaker: School of Natural Sciences (SNS – NUST)
Date and Venue: (Wednesday) 18 February, 2026, 03:30 pm, C-Room # 403 Old Building, School of Natural Sciences (SNS), NUST Islamabad