An algorithm for modelling differential processes utilising a ratio‐coupled loss

Abstract We present an algorithm for training predictive surrogate models using a loss function that combines two sources of similar data. The method jointly optimises surrogate model weights and a hyperparameter that controls the relative influence of each source, encouraging convergence toward mappings that represent their respective signals best. A differentiable loss function leverages gradient‐based optimisation to achieve this task. The resulting model can achieve higher quality results when unknown errors distort the signal from either source. Using the proposed methodology, experimental case studies are conducted to train a surrogate model to produce representations of the simple diffusion equation, the nonlinear Schrödinger equation, and the circular rotating shallow‐water equations. Thus, surrogates trained with the ratio‐coupled loss are shown to approximate linear and nonlinear partial differential equations for any number of prediction variables and under varying noise conditions.