**Team:** 1003

**School:** Los Alamos High

**Area of Science:** Computational Physics

**Interim:** **Problem Definition**

Neural networks are useful tools for creating models of problems for which a model is not already known. For example, in the case of recognizing handwritten digits, no equation is already known that can produce an accurate result from an input image of a digit. On the other hand, differential equations are the essence of known models. For applications such as computational physics, a set of differential equations only needs to be found or derived to create a model. For cases in between, that is some mechanics of the system are known but some are not, neural networks and differential equations can be woven together to create a model. The differential equations set the basic known mechanics of the system, and the rest the neural nets learns to model.

The Lotka-Volterra equations have been implemented to create a computational model to model s predator/prey population dynamic. The parameters of the system were successfully "trained" using automatic differentiation to create a stable system with set parameters. Models of a simple harmonic oscillator and a pendulum were constructed. A neural net was constructed and trained to match the solution to the pendulum system.

A neural net-differential equation hybrid will be created. It will use the simple harmonic oscillator equations and a neural net jointly. The result will be trained to match the solution of the pendulum equation set. If successful, this will prove such an algorithm can be used to learn more complex mechanics of a system, already knowing simple mechanics of it. This will be applied to more cases, and perhaps used to create a model of systems that are not fully known or comprehended.

**Team Members:**

**Sponsoring Teacher:** NA