Date/Time : 30 Sep 2026 16:30
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Melvin Leok, University of California San Diego

Adjoint systems are widely used to inform control, optimization, and design in systems described by ODEs or DAEs. At the level of PDEs, advection equations and mean field games also have the structure of adjoint systems, and all adjoint systems have a Hamiltonian structure.

We utilize symplectic and presymplectic geometry to investigate the properties of adjoint systems associated with ODEs and DAEs, respectively. We show that the adjoint-variational quadratic conservation laws, which are critical to adjoint sensitivity analysis, arise from (pre)symplecticity of such adjoint systems.

We develop structure-preserving numerical methods for such systems using Galerkin Hamiltonian variational integrators which admit discrete analogues of these quadratic conservation laws. This can be used to train neural networks arising from time-discretizations of neural ODEs, even ones based on implicit-in-time discretization.

Finally, we investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete levels and the relations between these levels. We show that the adjoint system associated with an evolutionary PDE has an infinite-dimensional Hamiltonian structure, which is useful for connecting the fully continuous, semi-discrete, and fully discrete levels.

Add to calendar :

Date/Time : 24 Sep 2026 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : David Lee, Australian Bureau of Meteorology

Energy conserving variational discretisations that preserve the skew symmetric structure of the non-canonical Hamiltonian form of the moist compressible Euler equations are extended to conserve the quadratic variance of thermodynamic tracers. This is important for the simulation of thermal processes since tracer variance represents a convex invariant of the equations of motion, so its conservation is strongly related to the stable simulation of those processes.

Moist processes are incorporated into the energy and tracer variance stable formulation such that the intrinsic thermodynamic variables (pressure, temperature and chemical potentials of the different moisture species) are derived via the derivatives of a thermodynamic potential (the internal energy) with respect to the prognostic model variables (density, entropy and mass fractions of the moisture species). This ensures thermodynamic consistency for the representation of non-equilibrium moist phase exchanges.

A neural network is then trained to learn the phase exchanges within the thermodynamically consistent framework, via kilometer scale output of a regional weather model. The resulting energy and tracer variance conserving, thermodynamically consistent model of the moist compressible Euler equations is then used to simulate three phase convection at sub-kilometer scale.

Add to calendar :

Date/Time : 16 Sep 2026 16:30
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Jackie Lok, National University of Singapore

Recently, a class of algorithms based on combining classical fixed-point iterations with repeated random sparsification has been successfully applied to very large-scale linear algebra problems, where storing the full solution vector itself may be prohibitive. However, a general mathematical understanding of when this approach can achieve dimension-independent computational and storage requirements remains limited.

In this talk, we study a randomly sparsified power method for computing the leading eigenvector of a column-stochastic matrix. We prove a dimension-independent error bound that depends on the approximate sparsity of the solution vector and the mixing time of the Markov chain associated with the matrix, establishing the possibility for high-quality approximation in very high dimensions. On the other hand, we show that a deterministically sparsified counterpart can fail, demonstrating a provable separation between deterministic and random sparsification.

Add to calendar :

Date/Time : 19 Aug 2026 16:30
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Liu Lei, Chongqing University

Nonlinear waves on nonzero asymptotic backgrounds, such as breathers and rogue waves, have been hot research topics in recent years. Starting with the three-wave resonant interactions system, we identify a specific rogue waves-building mechanism based on modulational instability (MI) which includes zero wavenumber in the gain band. An essential finding is that this mechanism works solely under a linear relation between the MI gain and a vanishingly small wavenumber of the modulational perturbation. We also report the emergence of a previously unexplored species of solitary waves-time-localized solitons, which coincides with the condition for the occurrence of the zero-wavenumber-gain MI. These results can be extended to the Massive Thirring model

Add to calendar :

Date/Time : 04 Aug 2026 11:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Timo Sprekeler, Texas A&M University

In this talk, we discuss a computational multiscale method for the mixed formulation of Darcy’s problem, based on a stable localized orthogonal decomposition in Raviart-Thomas finite element spaces. In the spirit of numerical homogenization, the construction provides low-dimensional coarse approximation spaces that incorporate fine-scale information from the heterogeneous coefficients by solving local patch problems on a fine mesh. The resulting numerical scheme is applicable beyond periodicity and scale-separation. This is joint work with Patrick Henning (Bochum) and Hao Li (Hong Kong).

Add to calendar :

Date/Time : 29 Jul 2026 16:30
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Yang Siyao, University of Chicago

High-dimensional probability distributions arise throughout scientific computing, yet their estimation, representation, and evaluation are often hindered by the curse of dimensionality. In this talk, I will present a tensor-train-based framework for learning high-dimensional densities from samples. The method first smooths the empirical distribution to reduce its large variance, compresses the resulting coefficient tensor using efficient tensor-train algorithms, and then applies a deconvolution step to recover a functional density estimator. The proposed method can achieve computational complexity linear in both the dimension and the number of samples. Its performance is demonstrated on several tasks, including high-dimensional Boltzmann distribution estimation and image generation.

I will then discuss an application of this framework to molecular dynamics called TT-Metadynamics. In this method, the growing sum of Gaussian bias potentials generated during metadynamics is periodically compressed into a functional tensor train. This avoids exponential grid storage and prevents the cost of evaluating the bias potential from increasing with simulation time. The method enables free-energy exploration with up to 14 collective variables and performs favorably compared with standard metadynamics in high-dimensional examples.

Add to calendar :

Date/Time : 15 Jul 2026 14:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Wang Hao, Sichuan University

Solid-state phase transitions typically follow a Minimum Energy Path (MEP). Classical methods such as G-SSNEB compute the MEP in the full high-dimensional configuration space, which becomes prohibitive when paths must be scanned over pressures, defect types, and system sizes. We propose the Preset Structure Strain Path (PSSP) method, which uses feature extraction and transfer learning to compute MEPs efficiently across these conditions. PSSP is based on the fact that in defective systems, lattice strain sets the direction of the MEP, while the local atomistic environment changes little but governs the energy. PSSP fully exploits this separation by presetting the displacement field as a transferable feature and optimizing only the lattice evolution in a low-dimensional space. By doing this, the strain paths learned in one setting can be reused under different pressures, defects and system sizes. The advantage of PSSP is verified that it reduces the energy and force evaluations to less than 2% of G-SSNEB but preserving the accuracy of the energy barrier in a satisfactory level.

Add to calendar :

Date/Time : 15 Apr 2026 16:30
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Zhang Junyi, Nanyang Technological University

Quantum Approximate Optimization Algorithm (QAOA) was proposed as a variational quantum algorithm for solving combinatorial optimization problems. In this talk, I will discuss some recent observations in quantum circuit dynamics of QAOA. We identify three dynamical phases in the quantum circuits: 1) quasi-adiabatic phase, 2) quantum chaotic phase, and 3) shallow circuit phase. Particularly, we find that the quasi-adiabatic phase and the shallow circuit phase are separated by a dynamical quantum critical point indicated by the entanglement entropy. Moreover, the quantum chaotic phase emerges in digitized quantum circuit while absent for continuous unitary evolution. Our study calls for better understanding of quantum algorithms realized in quantum circuits.

Add to calendar :

Date/Time : 08 Apr 2026 16:30
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Feng Yue, Xi'an Jiaotong University

In this talk, I will introduce the long-time problem for the nonlinear Schrodinger equation (NLSE) with weak nonlinearity, which is characterized by with a dimensionless parameter. We solve the NLSE using various temporal discretization, including finite difference methods, exponential integrators and time-splitting methods combined with different spatial discretization. By introducing a new technique–Regularity Compensation Oscillation (RCO) which controls the high frequency modes by the regularity of the exact solution and analyzes the low frequency modes by phase cancellation and energy method, we carry out the improved uniform error bounds for the time-splitting Fourier pseudospectral method in the long-time regime. In addition, we design new exponential integrators for the low-regularity initial data and extend this result to other dispersive PDEs.

Add to calendar :