A computer-implemented method, a computer program product, and a computer system for optimally balancing deployment of a deep learning based surrogate model and a physics based mathematical model in simulating a complex problem. One or more computing devices or servers compare results of running the deep learning based surrogate model with results of partially running the physics based mathematical model or with observations. One or more computing devices or severs output the results of running the deep learning based surrogate model as system outputs of simulating the complex problem, in response to determining that the deep learning based surrogate model is reliable. One or more computing devices or servers output results of running the physics based mathematical model as the system outputs of simulating the complex problem, in response to determining that the deep learning based surrogate model is not reliable.