Bio

Cody Trevillian is an Applied & Computational Physics Ph.D. student at Oakland University’s Department of Physics, in Rochester Hills, MI, USA, where he currently holds a Master’s degree in Physics awarded in 2019. In 2016 he obtained a Physics B.A. from Michigan Technological University. He has studied under Professor Andrei Slavin since January 2018 & Dr. Vasyl Tyberkevych since April 2018, investigating Magnetism & Spin Dynamics in nano-elements through the simulation of unexplained experimental results using numerical methods. He presented this work at the American Physical Society’s March Meeting and will submit expansions of his research to the Annual Conference on Magnetism and Magnetic Materials in November 2019. He enjoys time with his friends and family, who support his scientific ventures with their encouragement, fascination, patience & understanding, and their dogs. His personal scientific goals range from the expansion of accessibility options for individuals with disabilities to the development & implementation of novel neuromorphic computing paradigms and can be as far reaching as discovering the fundamental origins of existence & the simple structures that lie beneath the complexity of our natural world. Though the study of physics is his passion & pursuit of life, he finds enjoyment in tabletop games such as Dungeons and Dragons, camping & exploring the outdoors, traveling to new locations, dancing, playing & listening to live music, laughing at live comedy, and finding every opportunity for which to enjoy life & the universe.

Computational Essay: What is Chirality? How do we encounter it in our everyday, and not-so-everyday lives?

Project: DifferentialEquationNet: Real physical networks of time-dependent neurons

Goal

In this project, coupled sets of time-dependent 2nd order ordinary differential equations (DifferentialEquationNet) describing the spiking behavior of certain orientations of materials forming a physical neuron network are simulated based on their given material parameters. These DifferentialEquationNets are trained through an iterative stochastic-gradient-descent-like method. Implemented functions: DifferentialEquationNet, *NetSim, *NetTrain, *NetPlotRate, and *NetPlotState. In the investigated case, DifferentialEquationNet dictates the behavior of a bilayer of an antiferromagnet (AFM) and a normal metal (NM) using a Differential Equation ((Khymyn, Oct. 2018), (Sulymenko, July 2018)).

Summary of Results

We find that AND, OR and XOR gates can be efficiently simulated using the NDSolve framework, with over 200 iterative computations of networks consisting of several coupled neurons having little impact on the required computation time, occurring in under three seconds. This shows that the application and training of similar networks to the classification of larger systems like the MNIST database, which are still comparatively smaller in size, in reality, will not be temporally expensive to perform. These expedient results thus provide impetus to the continued development of this project for generalized time-dependent differential equation nets.

Future Work

Continued generalizations will occur as the program is made more user friendly for the definition of alternative controlling differential equations. Look for these (sooner than later!) on the Wolfram Function Repository!