Sohrab Towfighi | Searcharxiv

arXiv2019

Symbolic regression by uniform random global search

Symbolic regression (SR) is a data analysis problem where we search for the mathematical expression that best fits a numerical dataset. It is a global optimization problem. The most popular approach to SR is by genetic programming (SRGP). It is a common paradigm to compare an algorithm's performance to that of random search, but the data comparing SRGP to random search is lacking. We describe a novel algorithm for SR, namely SR by uniform random global search (SRURGS), also known as pure random search. We conduct experiments comparing SRURGS with SRGP using 100 randomly generated equations. Our results suggest that a SRGP is faster than SRURGS in producing equations with good R^2 for simple problems. However, our experiments suggest that SRURGS is more robust than SRGP, able to produce good output in more challenging problems. As SRURGS is arguably the simplest global search algorithm, we believe it should serve as a control algorithm against which other symbolic regression algorithms are compared. SRURGS has only one tuning parameter, and is conceptually very simple, making it a useful tool in solving SR problems. The method produces random equations, which is useful for the generation of symbolic regression benchmark problems. We have released well documented and open-source python code, currently under formal peer-review, so that interested researchers can deploy the tool in practice.

cs.NE↗

arXiv2018

Cahn-Hilliard diffuse interface simulations of bubble-wall collisions

The collision of a rising bubble with a superhydrophilic horizontal surface is studied numerically using the Cahn-Hilliard diffuse-interface method. For the studied systems, the Bond number, $Bo=ρR^2 g/σ$, varies between 0.25 to 1.5, and the Galileo number, $Ga=ρ(R^3 g)^{1/2}/μ$, changes between 8.5 to 50. We assume that the viscosity and density of the bubble are negligible compared to the surrounding medium. We show that our computations reproduce experimentally observed dynamics for the collision of a bubble with a solid surface. Furthermore, for the studied range of parameters, the bubble-wall collision is mainly in the inertial regime. Our simulations show that even in the absence of substantial viscous dissipation, the ratio of rebound-to-collision velocity, the so-called coefficient of restitution, is much smaller than one for the studied systems. More importantly, the coefficient of restitution best scales with the Froude number, $Fr=U_{t}/\sqrt{g R}$, the ratio of inertial to gravitational forces.

physics.flu-dyn↗