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Physics-based optimization problems are generally very time-consuming,especially due to the computational complexity associated with the forwardmodel. Recent works have demonstrated that physics-modelling can beapproximated with neural networks. However, there is always a certain degree oferror associated with this learning, and we study this aspect in this paper. Wedemonstrate through experiments on popular mathematical benchmarks, that neuralnetwork approximations (NN-proxies) of such functions when plugged into theoptimization framework, can lead to erroneous results. In particular, we studythe behavior of particle swarm optimization and genetic algorithm methods andanalyze their stability when coupled with NN-proxies. The correctness of theapproximate model depends on the extent of sampling conducted in the parameterspace, and through numerical experiments, we demonstrate that caution needs tobe taken when constructing this landscape with neural networks. Further, theNN-proxies are hard to train for higher dimensional functions, and we presentour insights for 4D and 10D problems. The error is higher for such cases, andwe demonstrate that it is sensitive to the choice of the sampling scheme usedto build the NN-proxy. The code is available athttps://github.com/Fa-ti-ma/NN-proxy-in-optimization.

On Using Deep Learning Proxies as Forward Models in Deep Learning Problems