Deep Optimal Experimental Design for Parameter Estimation Problems

TL;DR

This paper introduces a deep learning-based experimental design method that simplifies parameter estimation in nonlinear systems by replacing traditional optimization with likelihood-free neural network training, demonstrated on ODE systems.

Contribution

It proposes a novel deep learning approach for optimal experimental design that replaces complex bi-level optimization with likelihood-free estimation, improving efficiency and accuracy.

Findings

Deep design simplifies the experimental setup process.

The method enhances parameter recovery quality.

Successful application to two ODE systems.

Abstract

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.