Multi-Architecture Coupled Ensemble Physics-Informed Neural Networks.

Reaction-diffusion equations describe how patterns form and spread across physics, chemistry, and biology, from chemical fronts to biological morphogenesis. They are normally solved with slow numerical methods. This thesis trains a neural network to learn those solutions directly from the governing equations, and makes that approach work for the stiff, coupled systems where standard physics-informed neural networks break down.

• Parallel subnetworks. A dedicated network for each coupled field, trained jointly under one physics-informed loss, which removes the gradient interference that degrades single-network PINNs.
• Fourier feature embeddings. A 64-dimensional random-feature lift of the (x, y, t) inputs that overcomes spectral bias and lets the model resolve sharp, high-frequency pattern structure.
• Gradient-norm adaptive loss weighting. Per-term weights set from running gradient magnitudes, automatically balancing the initial-condition, residual, and data objectives for stable convergence.

40 to 60 percent lower relative L2 error than single-network PINN baselines, consistently across both systems.

Implemented from scratch in JAX and Flax. Evaluated across four benchmark variations spanning the Gray-Scott and Ginzburg-Landau systems, each measured as relative L2 error against a reference numerical solution.