Enforcing Conservation Laws in Neural Operators for Earth System Modeling

Neural operators are transforming computationally intensive scientific disciplines such as weather forecasting and climate modeling, accelerating simulations by several orders of magnitude. However, they often fail to respect fundamental physical principles, such as conservation laws, during long autoregressive rollouts. We introduce an efficient correction layer that enforces global conservation constraints in neural operators. For initial conditions approximately satisfying the constraints, we prove that conservation can be guaranteed while only moderately increasing the total runtime. In a number of fluid dynamics experiments, our method produces physically realistic simulations while maintaining the computational advantages of neural operators. Our results enable the development of reliable and efficient climate model emulators by ensuring that crucial physical balance equations, such as mass and energy, are preserved during extended simulations.