Residual Loss

INFO

Quantifies the error in governing equations, used in physics-informed neural networks (PINNs).

How It Works

$$\text{Residual Loss}=\frac{1}{n}\sum _{i=1}^n{\left|\mathcal{N}(u_i)-f_i\right|}^2$$

• $\mathcal{N}(u_i)$: Differential operator applied to predicted solution
• $f_i$: Known forcing term or target
• $n$: Number of collocation points

This measures how well the model satisfies the underlying PDEs.

What to Look For

• Lower residual = better physics compliance
• Use alongside data loss for balanced training
• Can be decomposed by equation type (e.g., momentum, continuity)

Application Models

• pinns
• pde-solvers