In physics, mathematics, economics, engineering, and many other fields, differential equations describe a function in terms of the derivatives of the variables. Put simply, when the rate of change of a variable in terms of other variables is involved, you will likely find a differential equation. Many examples describe these relationships. A differential equation’s solution is typically derived through analytical or numerical methods.
While deriving the analytic solution can be a tedious or, in some cases, an impossible task, a physics-informed neural network (PINN) produces the solution directly from the differential equation, bypassing the analytic process. This innovative approach to solving differential equations is an important development in the field.
