Congratulations to Chinmay Kulkarni, a Ph.D candidate in the MSEAS group, for being awarded the 2020 MathWorks prize for outstanding doctoral research! The MathWorks prize is awarded by the MIT Center of Computational Science and Engineering. All the best to Chinmay!

Congratulations to Jing Lin on his graduation! Jing received an SM from Mechanical Engineering for his research on “Minimum-Correction Second-Moment Matching: Theory, Algorithms and Applications” with our MSEAS group at MIT.

We address the problem of finding the closest matrix Ũ to a given U under the constraint that a prescribed second-moment matrix P̃ must be matched, i.e. Ũ^TŨ=P̃. We obtain a closed-form formula for the unique global optimizer Ũ for the full-rank case, which is related to U by an SPD (symmetric positive definite) linear transform. This result is generalized to rank-deficient cases as well as to infinite dimensions. We highlight the geometric intuition behind the theory and study the problem’s rich connections to minimum congruence transform, generalized polar decomposition, optimal transport, and rank-deficient data assimilation. In the special case of P̃=I, minimum-correction second-moment matching reduces to the well-studied optimal orthonormalization problem. We investigate the general strategies for numerically computing the optimizer, analyze existing polar decomposition and matrix square root algorithms. More importantly, we modify and stabilize two Newton iterations previously deemed unstable for computing the matrix square root, which can now be used to efficiently compute both the orthogonal polar factor and the SPD square root. We then verify the higher performance of the various new algorithms using benchmark cases with randomly generated matrices. Lastly, we complete two applications for the stochastic Lorenz-96 dynamical system in a chaotic regime. In reduced subspace tracking using dynamically orthogonal equations, we maintain the numerical orthonormality and continuity of time-varying base vectors. In ensemble square root filtering for data assimilation, the prior samples are transformed into posterior ones by matching the covariance given by the Kalman update while also minimizing the corrections to the prior samples.

This cruise aimed to identify transport pathways from the surface into the interior ocean during the late winter in the Alborán sea between the Strait of Gibraltar (5°40’W) and the prime meridian. Theory and previous observations indicated that these pathways likely originated at strong fronts, such as the one that separates salty Mediterranean water and the fresher water inflowing from the Atlantic. Our goal was to map such pathways and quantify their transport. Since the outcropping isopycnals at the front extend to the deepest depths during the late winter, we planned the cruise at the end of the Spring, prior to the onset of thermal stratification of the surface mixed layer.

Congratulations to Manan Doshi for successfully clearing the MIT Mechanical Engineering Ph.D Qualifying Exams. Manan now begins his journey towards an outstanding Ph.D thesis. All the best!