Reimagining Fisher’s Equation via Physics-Informed Neural Networks

Purpose: We implement a modern Physics-Informed Neural Networks (PINNs) algorithm that markedly enhances the computational execution of classical and generalized Fisher equations by easily integrating physical governing laws into supervised learning structures. \textbf{Methods:} We are using the Physics-Informed Neural Network framework to minimize the loss function using different optimization algorithms. This improves the accuracy of complex spatio-temporal dynamics by combining data-driven optimization with conservation principles. Results: Rigorous validation across multiple Fisher equation variants exhibits computational precision, with optimum estimates that achieve error magnitudes of 10 ^-6 while demonstrating outstanding numerical stability and convergence features. A full performance analysis shows that our method is better at predicting than existing finite-difference and spectral methods, especially in areas with steep gradients and nonlinear transition zones. Conclusion: We deploy a mesh-independent Physics-Informed Neural Network (PINN) framework that overcomes the limits of existing solvers, assuring computational efficiency and scalability. The technique yields correct solutions for complex reaction–diffusion systems and demonstrates substantial potential for simulating biological and physical phenomena, including pattern creation and population dynamics. By eliminating the necessity for mesh-based methods, this framework offers a viable alternative for solving nonlinear PDEs, especially in tough cases where standard approaches fall short.