Deep Optimal Experimental Design for Parameter Estimation Problems
This addresses the problem of computational inefficiency in experimental design for researchers using deep learning in parameter estimation, though it appears incremental as it adapts existing concepts to new methods.
The paper tackles the challenge of adapting optimal experimental design to deep learning-based parameter estimation by introducing a deep learning methodology that simplifies the design process and improves recovery quality, as demonstrated on two Ordinary Differential Equation systems.
Optimal experimental design is a well studied field in applied science and engineering. Techniques for estimating such a design are commonly used within the framework of parameter estimation. Nonetheless, in recent years parameter estimation techniques are changing rapidly with the introduction of deep learning techniques to replace traditional estimation methods. This in turn requires the adaptation of optimal experimental design that is associated with these new techniques. In this paper we investigate a new experimental design methodology that uses deep learning. We show that the training of a network as a Likelihood Free Estimator can be used to significantly simplify the design process and circumvent the need for the computationally expensive bi-level optimization problem that is inherent in optimal experimental design for non-linear systems. Furthermore, deep design improves the quality of the recovery process for parameter estimation problems. As proof of concept we apply our methodology to two different systems of Ordinary Differential Equations.