A new formulation for symbolic regression to identify physico-chemical laws from experimental data

Abstract

A modification to the mixed-integer nonlinear programming (MINLP) formulation for symbolic regression was proposed with the aim of identification of physical models from noisy experimental data. In the proposed formulation, a binary tree in which equations are represented as directed, acyclic graphs, is fully constructed for a pre-defined number of layers. The introduced modification results in the reduction in the number of required binary variables and removal of redundancy due to possible symmetry of the tree formulation. The formulation was tested using numerical models and was found to be more efficient than the previous literature example with respect to the numbers of predictor variables and training data points. The globally optimal search was extended to identify physical models and to cope with noise in the experimental data predictor variable. The methodology was proven to be successful in identifying the correct physical models describing the relationship between shear stress and shear rate for both Newtonian and non-Newtonian fluids, and simple kinetic laws of chemical reactions. Future work will focus on addressing the limitations of the present formulation and solver to enable extension of target problems to larger, more complex physical models.

Automated robotic platforms in design and development of formulations

“…54,63 However, in all the presented solutions, temperature control is not ensured and, in some cases, mixing appears to be far from ideal, stressing the need for standard 48 and Houben et al 13 The most common adopted techniques for reactive systems are UPLC and HPLC, 10,49,53,[101][102][103][104][105][106][107][108][109][110][111][112][113] GC, 113,114 MS, 37,40,46,50,52,55,57,106,115 IR, 53,59,113,115,116 Raman, 53 and UV spectrophotometry. 114,117,118 However, according to the theoretical framework outlined by Bernardo et al, 41 For formulated liquid products, the main general desired properties can be identified as: stability, aspect (color and turbidity), viscosity, surface tension, pH, conductivity, zeta potential, and droplets size distribution, in the case of emulsions. Therefore, more complex, analytical sensors need to be identified and integrated in the robotic platforms to acquire data about different properties at the same time.…”

“…This approach has been successfully applied mainly for the identification of predictive kinetic models in the field of reaction engineering and chemical reaction development. 118 Moreover, the current state of art focused on the problems of model selection out of a library of pre-derived models [162][163][164][165] and parameter estimation, 163,166 recently been published, such as measurements of gas solubility in liquids. 167 Also, several pioneering works 55,61,168 have shown advances in both the hardware and the software for the exploration of physicscontrolled phenomena in microfluidics, for example, multiphase droplets generation.…”

“…Once again, most of the analytics automated in the literature has been used for reaction development. Thorough reviews can be found in Mateos et al 48 and Houben et al 13 The most common adopted techniques for reactive systems are UPLC and HPLC, 10,49,53,101‐113 GC, 113,114 MS, 37,40,46,50,52,55,57,106,115 IR, 53,59,113,115,116 Raman, 53 and UV spectrophotometry 114,117,118 . However, according to the theoretical framework outlined by Bernardo et al, 41 formulation design is a cycle of inversion and evaluation of quality, property, and process functions.…”

“…More recently, some successful examples of application to experimental noisy data have been proposed. Specifically, Neumann and co-workers used this approach to derive simple kinetic laws and constitutive rheology equations for Newtonian and non-Newtonian fluids, showing the potential and the limitations of the present formulation of the algorithm 118. Despite the promising results, this methodology is still at its early stage and future research will be needed to reduce the computational time required to derive physical models from noisy data in the presence of a large number of variables and operators, allowing the data-driven search for complex physical models.The challenge of discovery and scale-up are intimately interconnected and of fundamental importance for speeding up product design and development under the constraints of the fast-changing market.…”

Optimal Life-Cycle Resilience Enhancement of Aging Power Distribution Systems: A MINLP-Based Preventive Maintenance Planning

“…As reported by Neumann et al [32], several global solvers are available to deterministically solve non-convex MINLP problems. These solvers include ANTIGONE [33], BARON [34], Couenne [35], LINDO [36], and SCIP [37].…”