Michael P. Brenner - Machine Learning for Partial Differential Equations

When Newton's laws are applied in every point in space we arrive at a set of nonlinear partial differential equations describing the world.  We often marvel at the complexity of the solutions, but we know very well that the phenomena that occur can be described by a finite dimensional dynamical system -- we just have difficulty finding or describing it accurately, especially as the solutions become more and more complex.   I will describe here several ongoing research efforts that aim to use recent advances in machine learning  to unravel this problem -- learning underlying patterns implied by the equations to develop more efficient ways of solving the equations of motion,  finding more efficient ways of interpreting experimental measurements, and finding ways of represent of better representing and ultimately understand solutions of equations that obey the laws of physics.