| Abstract | The approximation and emulation of first principles based deterministic models are important problems in science, engineering, industrial processes, design, digital twining and other tasks. Usually these are complex systems described by partial differential/integral equations, with a broad range of initial and boundary conditions. Finding solutions is often computationally costly and time consuming. Surrogate models have been useful for constructing approximations that effectively replace the complex and costly original models. Statistical and computational intelligence based techniques have been effective for creating surrogate models, such as neural networks, support vector machines and boosted trees (labeled black box techniques). This paper approaches the problem of finding surrogate models aimed at solving inverse problems for deterministic systems described by a partial differential equation. This situation, often intractable when using first principles methods, is illustrated with a case study of heat transfer in a rectangular space. Unsupervised methods are used for gaining insight into the properties of the input/output state spaces and supervised approaches, composed of white (explainable), black box modeling methods and ensembles, explore the feasibility of retrieving the input from the system's outputs. For most input variables accurate inverse models were obtained, demonstrating the effectiveness of machine learning approaches for this problem. |
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