Adding a soft mass-conservation penalty to PINNs for the 1D advection-diffusion equation reduces long-term relative L2 error by 9–67× and mass error by 15–215× compared to vanilla PINNs across Peclet numbers 0.01–20.
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Mass-Conserving Physics-Informed Neural Networks For The One-Dimensional Advection-Diffusion Equation
Adding a soft mass-conservation penalty to PINNs for the 1D advection-diffusion equation reduces long-term relative L2 error by 9–67× and mass error by 15–215× compared to vanilla PINNs across Peclet numbers 0.01–20.