Mathematics faculty and graduate students are invited to attend the PhD Defense of Mats Johnson.

Join us in person or on Zoom:

Join Zoom Meeting:  https://zoom.us/j/92380404824?pwd=JnbFyOUATN5ukwt7pMrDCHZx8zoAkI.1

Meeting ID: 923 8040 4824

Passcode: 413060

Advisor:  Dr. David Aristoff

Committee:  Dr. Olivier Pinaud, Dr. Margaret Cheney, Dr. Diego Krapf

Title:  Data-Driven Methods for Compact Modeling of Stochastic Processes

Abstract:  Accurately representing the committor function is a common problem in computational chemistry, physics and biology as it encodes many important statistical properties of a stochastic system. However,  due to high-dimensionality and metastability, solutions are often difficult to compute.  We build upon recent developments in machine learning and randomized linear algebra to construct the ‘fast committor machine’ (FCM).  From simulated trajectory data, the FCM efficiently learns a kernel-based estimation of the committor using iterative refinements of a linear mapping of the data.  The coefficients are estimated using a block version of randomly pivoted Cholesky which grants linear scaling and significantly outperforms standard kernel ridge regression on large datasets.  The training speed of the FCM is demonstrated numerically on the triple-well potential and alanine dipeptide where it outperforms a basic neural network.  In addition to the committor approximation, the FCM also yields the subspace that best describes the variance of the function.