Upcoming Seminars and Events: (NBPS runs on Tuesday afternoons from 2.05 pm to 3 pm in the academic year 24/25)
Tuesday, August 12, 2025
Youngsik Hwang (Ulsan National Institute of Science and Technology – UNIST)
Time: 2.05 – 3.00 pm
Location: JCMB 5323
Title
Dual Cone Gradient Descent: A General Framework for Multi-Objective Optimization in Artificial Intelligence
Abstract
Many contemporary AI problems can be formulated as multi-objective optimization tasks, where objectives may be in conflict. Conventional scalarization-based methods are susceptible to gradient conflict, loss domination, and the absence of Pareto optimality guarantees. This talk introduces Dual Cone Gradient Descent (DCGD), a principled algorithm that constrains search directions to the dual cone of objective gradients, thereby ensuring non-conflicting descent and convergence to Pareto-stationary points, even in nonconvex regimes. Empirical evaluations on physics-informed neural networks and machine unlearning tasks demonstrate DCGD’s capacity to improve convergence stability, solution quality, and controllability along the Pareto frontier.
Tuesday, June 10, 2025
Theresa Lange (Scuola Normale Superiore Pisa)
Time: 2.05 – 3.00 pm
Location: JCMB 5323
Title: Non-uniqueness of Leray-Hopf solutions for the 3D fractional Navier-Stokes equations perturbed by transport noise
Abstract:
For the 3D fractional Navier-Stokes equations perturbed by transport noise, we prove the existence of infinitely many Hölder continuous analytically weak, probabilistically strong Leray-Hopf solutions. In the deterministic case, global existence is known ever since the seminal works by Leray (1934) and Hopf (1950), yet recent results show non-uniqueness via the method of convex integration. In contrast to the active field of regularisation by transport noise, we demonstrate that the convex integration method applies also in the presence of such random perturbations, and derive global-in-time solutions which satisfy the energy inequality pathwise on a non-empty random interval [0, tau].
This is joint work with Marco Rehmeier (TU Berlin) and Andre Schenke. The activity was carried out within the project: NoisyFluid “Noise in Fluids”, Grant Agreement 101053472, CUP E53C22001720006.
Kotaro Tsugawa(Chuo University)
Time: 3.05 – 4.00 pm
Location: JCMB 5323
Title: Cancellations and unconditional well-posedness of fifth-order KdV-type and fifth-order modified KdV-type equations
Abstract:
The fifth-order KdV and fifth-order modified KdV equations are known as the second equations in the integrable KdV and mKdV hierarchies, respectively. In this study, we consider these equations with general coefficients, including non-integrable cases, and establish local well-posedness with unconditional uniqueness. A major difficulty arises from the presence of third-order derivatives in the nonlinear terms. To address this, we apply normal form reduction to the resonant parts and exploit cancellations arising from an appropriate algebraic transformation in the non-resonant parts. This is joint work with Takamori Kato.
