Applied Math
PhD Seminar

2026 Fall

The seminar of this semester is organized by Zihao Li and He Wang, and co-organized by the graduate student union in the School of Mathematical Sciences at Fudan. This section is partially sponsored by Shanghai Key Laboratory for Contemporary Applied Mathematics.

2026-09-24 16:10:00 - 17:00:00 @ Rm 1801, Guanghua East Tower [poster]

Abstract: Click to expand In this paper, we study the problem of optimizing Markov processes that interpolate between two prescribed probability distributions while minimizing a given cost. The main computational challenge is the curse of dimensionality: in high-dimensional state spaces, representing the full distribution is intractable. To address this, we reformulate the problem in terms of sequential couplings and develop convex relaxations based on local marginals and cluster moments. These relaxations exploit locality and sparse interaction structure, provide computable lower bounds, and recover low-order statistics of the intermediate laws. We identify dynamic optimal transport as a special case of our Markov process optimization problem and develop a procedure for recovering the underlying Benamou--Brenier dynamics from the relaxed solution. We also show that the procedure extends to more general Markov processes and illustrate it with a constrained process between Ising models.

Past Presentations

2026-09-10 16:10:00 - 17:00:00 @ Rm 1801, Guanghua East Tower [poster]

Abstract: Click to expand This work considers stepsize schedules for gradient descent on smooth convex objectives. We extend the existing literature and propose a unified technique for constructing stepsizes with analytic bounds for an arbitrary number of iterations. This technique constructs new stepsize schedules by concatenating two stepsize schedules with fewer steps. Using this approach, we introduce two new families of stepsize schedules, achieving a convergence rate of $O(n^{-\log_2{(\sqrt 2+1)}})$ with state-of-the-art constants for the objective value and gradient norm of the last iterate, respectively. Furthermore, our analytically derived stepsize schedules either match or surpass the existing best numerically computed stepsize schedules.

2026-09-17 16:10:00 - 17:00:00 @ Rm 1801, Guanghua East Tower [poster]

Abstract: Click to expand Variational Monte Carlo (VMC) with neural network wavefunctions is a powerful approach to ground-state calculations, but its performance depends critically on wavefunction optimization. In this talk, we will introduce VMC and focus on geometry-aware optimization methods for neural network wavefunctions, in particular stochastic reconfiguration (SR) and its variants. Among them, SPRING, inspired by the randomized Kaczmarz method, has shown strong empirical performance but is sensitive to the choice of a momentum-like parameter $\mu$. We analyze this sensitivity and reveal a qualitative difference between $\mu<1$ and $\mu=1$. For $0\leq\mu<1$, we establish first-order convergence under weak moment assumptions allowing heavy-tailed Monte Carlo noise; for $\mu=1$, we construct counterexamples showing divergence through accumulation along kernel-related directions. Motivated by these results, we propose PRIME-SR, an adaptive SR method that adjusts the momentum parameter based on spectral information and subspace overlap. Numerical experiments show that PRIME-SR achieves performance comparable to well-tuned SPRING while substantially improving robustness in neural wavefunction optimization.