A machine learning based approach for phononic crystal property discovery

Abstract

Phononic crystals are artificially structured materials that can possess special vibrational properties that enable advanced manipulations of sound and heat transport. These special properties originate from the formation of a bandgap that prevents the excitation of entire frequency ranges in the phononic band diagram. Unfortunately, identifying phononic crystals with useful bandgaps is a problematic process because not all phononic crystals have bandgaps. Predicting if a phononic crystal structure has a bandgap, and if so, the gap's center frequency and width is a computationally expensive process. Herein, we explore machine learning as a rapid screening tool for expedited discovery of phononic bandgap presence, center frequency, and width. We test three different machine learning algorithms (logistic/linear regression, artificial neural network, and random forests) and show that random forests performs the best. For example, we show that a random phononic crystal selection has only a 17% probability of having a bandgap, whereas after incorporating rapid screening with the random forests model, this probability increases to 89%. When predicting the bandgap center frequency and width, this model achieves coefficient of determinations of 0.66 and 0.85, respectively. If the model has a priori knowledge that a bandgap exists, the coefficients of determination for center and width improve to 0.97 and 0.85, respectively. We show that most of the model's performance gains are achieved for training datasets as small as ∼5000 samples. Training the model with just 500 samples led to reduced performance but still yielded algorithms with predictive values.

Tailoring Structure‐Borne Sound through Bandgap Engineering in Phononic Crystals and Metamaterials: A Comprehensive Review

“…This has led to inverse-design based studies that start with the desired BG configuration or functionality and employ optimization approaches to arrive at the geometry and material that is required to achieve them. Most of these efforts largely rely on topology optimization, [56,57, genetic algorithms, [215,432,437,438] or machine learning-based approaches [439][440][441][442][443][444][445][446] and have unveiled unusual and hence previously inconceivable geometries that enable materials with enhanced BG characteristics. While these efforts are now burgeoning thanks to modern computational power, one of the earliest fruitful strides in this direction for elastic waves, can be attributed to the works of Sigmund and Søndergaard Jensen [411] in the early 2000s, who first put forward a theoretical framework showing that phononic BGs could be considerably enlarged by opening the design space of the unit cell geometry, while enforcing the boundary conditions as constraints-in other words, via topology optimization.…”

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