The next seminar “Modelling of materials theory, model reduction and efficient numerical methods” will take place on Wednesday from 9:00 in lecture room K3 and will also be streamed on Zoom. The first seminar “Modelling of materials – theory, model reduction and efficient numerical methods” will take place on Wednesday from 9:00 till 10:00 in the room K3. The talk will be given by Martin Šípka. Please see the details below.
Speaker: Martin Šípka
Title: Path integral optimization with differentiable simulations
Abstract: The optimization of path-dependent quantities is a common problem emerging in many applications across science and technology. Since the discovery and development of the calculus of variations, we know how to find the corresponding Euler-Lagrange equations and analytically evaluate the minimizer function. However, for complicated integrands, the arising equations are often very complex or even impossible to derive or solve, especially for high-dimensional problems.
In this talk, we will introduce simulations that are differentiable through every operation performed while evaluating the solution. By such construction, we can simulate the entire path, evaluate the integral and calculate the gradient of the resulting cost function with respect to any optimizable parameter. First, we very briefly introduce the computational frameworks and libraries developed recently, allowing us to write differentiable code quickly, and we illustrate the differentiable simulations approach on a famous brachistochrone problem that has a well known analytical solution. In the second part of the talk, we explore the path integral formulation of chemical reaction exploration and investigate a much more real-world application of differentiable simulations. In this case, we also explore the numerical properties of the gradients and talk about the convergence of the method.
We will conclude the talk with some other ideas where the differentiable simulations can be useful, such as dimensionality reduction in physics and control theory, and we will welcome suggestions for further areas of usefulness from the audience.