(392bn) Democratizing Experimental Design: A User-Friendly Doe Software for Experimental Information Analysis

Design of experiments (DoE) is an important methodology used in scientific research that optimizes the exploration of the experimental design space and consequently enhances resources allocation, minimizes waste, and generates valuable insights about the system under analysis. The DoE framework has become widely used because of its reliability and its ability to return designs without requiring extensive computational resources (Montgomery et al., 2017). However, a significant drawback is that this methodology does not leverage potential mechanistic modelling knowledge on the system, thereby inevitably losing valuable information that could be extracted from the underlying model structure. Many methodologies have been developed to overcome this limitation, including Model-Based Design of Experiments (MBDoE) (Franceschini et al., 2008), or the Fisher Information Matrix (FIM)-driven approach (Friso et al., 2024). The first method exploits fundamental knowledge of the system under analysis expressed by mathematical models to design optimal experiments, incorporating prior knowledge about the process mechanisms to maximize the predicted information gain and increase the precision on model parameters. MBDoE requires the solution of a complex nonlinear optimization problem, where a metric of FIM or of the variance-covariance matrix of model parameters) is the objective function. Meanwhile, the FIM-driven approach utilises the FIM to quantify the expected information content from a set of candidate experiments (potentially designed through conventional DoE methods) without requiring full optimization procedures, allowing for rapid quantification of expected experimental information and experimental selection based on the sensitivity matrix, Q, and the uncertainty on measurement errors, σ, while maintaining computational efficiency. In Equation 1 (see attached picture), the expression of the FIM is reported, where is the total number of performed experiments, and is the number of measured responses (Franceschini et al., 2008).

Where and represent the sensitivity matrices for the responses r and s in the j-th experiment, and is the measurement error covariance between responses r and s in the j-th experiment. The major drawback of MBDoE and FIM-driven methodologies is that they require an in-depth understanding of their underlying statistical principles to be implemented correctly. This statistical complexity creates a significant barrier to entry for many researchers who lack specialised training in experimental design methods, limiting the widespread adoption of these powerful approaches across different research fields. This work introduces XOpt, a software solution designed to democratize access to DoE methodologies and MBDoE methods by simplifying experimental design while maintaining key analytical capabilities. XOpt features an intuitive Graphical User Interface (GUI) that guides users with limited statistical and mathematical background through the experimental design process, from defining criteria and design spaces to selecting optimal experiments based on the desired goal.

Most importantly, the software allows users to easily incorporate both algebraic and differential models and to integrate DoE techniques with information analysis using the knowledge given by the mathematical model employed to describe the system under analysis. This analysis allows optimization of the experimental selection methodologies while retaining an explorative part in order not to be constrained to a local optimum. The software also offers the possibility to apply standard model-free methodologies, such as Latin Hypercube Sampling, without having to implement them from zero using software such as Python or MATLAB.

The software supports model discrimination through comparing multiple candidate model structures and quantifying their fitting performance and model complexity, uncertainty propagation, and FIM-driven experimental ranking (Galvanin et al., 2016; Galvanin et al., 2017), making advanced statistical tools accessible to researchers with limited statistical and mathematical backgrounds. The implementation enables efficient comparison of candidate model structures, and it identifies experiments that maximize the expected information gain. This approach streamlines the experimental selection process for model discrimination, parameter identification, and output uncertainty reduction making it fast, simple, and accessible without compromising analytical rigor. Future developments in the software will include integration with autonomous model identification platforms capabilities and implementation of robust MBDoE approaches.

References

Montgomery, D., C., “Design and Analysis of Experiments”, Jhon Wiley & Sons, Incorporated, 2017

Franceschini, G., Macchietto, S., “Model-based design of experiments for parameter precision: State of the art”, Chemical Engineering Science, Volume 63, Issue 19, 2008

Friso A., Galvanin F., “An optimization-free Fisher information driven approach for online design of experiments”, Computers & Chemical Engineering, Volume 187, 2024

Galvanin F., Cao E., Al-Rifai N., Gavriilidis A., Dua V., “A joint model-based experimental design approach for the identification of kinetic models in continuous flow laboratory reactors”, Computers & Chemical Engineering, Volume 95, 2016

Galvanin F., Psyrraki C., Morris T., Gavriilidis A., “Development of a kinetic model of ethylene methoxycarbonylation with homogeneous Pd catalyst using a capillary microreactor”, Chemical Engineering Journal, Volume 329, 2017,