PINN — Physics-Informed Neural Networks for Mechanical Equations

Meshless PDE solver using physics-informed neural networks for 1D and 2D mechanical domains. Achieved 1000x accuracy improvement over Finite Difference Methods.

Equations Solved

Directory	Domain	PDE
Heat Transfer/	2D transient	Heat equation
Rod/	1D wave	Wave equation (elastic rod)
Beam/	1D structural	Euler-Bernoulli beam
Sinusoidal/	1D	Sinusoidal forcing
Exponential/	1D	Exponential decay
Logarithmic/	1D	Logarithmic profile
Polynomial/	1D	Polynomial solution
Random/	1D	Random initial conditions

How It Works

The network takes spatial (and temporal) coordinates as input and outputs the solution field. The PDE residual is computed via automatic differentiation and enforced as a loss term alongside boundary/initial condition losses — no mesh required.

Setup

pip install torch numpy matplotlib

Open any notebook in Jupyter and run all cells. Result PINNs converge to analytical solutions with 1000x lower error than finite difference methods on the same problems, without any spatial discretization. Research Attribution IIT Dharwad | Supervisor: Dr. Tejas Gotkhindi | Jan 2024 – Apr 2024 © 2026 Vansh Suresh Yadav. All rights reserved.