Seminar introduction, community meet-and-greet, and pizza🍕

Abstract: In space or robotic vehicle trajectory planning, we often seek trajectories that satisfy mission-specific constraints while optimizing an objective, such as time or fuel consumption. Sequential Convex Programming (SCP) is a natural and fast meta-algorithm for this problem: it iteratively convexifies the constraints and exploits the speed of convex solvers. However, the trajectory of a rigid body evolves on a smooth manifold with a Lie group structure, yet state-of-the-art (SOTA) SCP algorithms completely ignore the intrinsic geometry and instead treat the state space extrinsically as a manifold embedded in a larger Euclidean space. We propose a novel intrinsic SCP algorithm, called Lie Error-State Group Optimization (LESGO), for rigid-body trajectory optimization. By exploiting Lie theory and the symmetries of rigid-body kinematics, we establish several theoretical advantages of LESGO over extrinsic formulations. In a lunar landing powered descent guidance experiment, we demonstrate that the theoretical advantages translate into a significant reduction in runtime compared with Dual Quaternion Guidance (DQG), the SOTA SCP method for this application. In particular, LESGO achieves runtimes comfortably below 1 second* on flight hardware while enforcing full constraint satisfaction, a first for this application. This capability enables real-time hazard avoidance and closed-loop Guidance Navigation and Control (GNC) design during landing, which in turn enable safer and more precise landings.

*extrapolated from laptop time and previous runs, pending verification.

Abstract: Many problems in optimal transport, collective dynamics, and mean-field control require finding a path between two prescribed probability distributions while satisfying a coupled Hamilton–Jacobi and transport system. Directly solving these boundary-value PDEs becomes prohibitively expensive in moderate and high dimensions.

This coupled PDE system can be interpreted as a Hamiltonian system in Wasserstein space, where the evolving states are probability distributions rather than individual particles. In this talk, we first introduce this perspective and explain how external forces, interactions, and congestion determine the evolution of the distribution. We then review the flow-matching training scheme and the iterative rectification procedure before extending both ideas to the Hamiltonian setting. At each rectification step, the current velocity field is used to construct Hamiltonian paths between the endpoint distributions. These paths provide the training data for the next velocity field. Repeating this procedure brings the learned flow closer to the prescribed Hamiltonian dynamics.

We illustrate the method through examples involving obstacle avoidance and interacting particle systems. The results show that Hamiltonian flows between distributions can be learned from samples without discretizing the governing PDEs in space.

Paper: Any-Order Flexible Length Masked Diffusion by Jaeyeon Kim, Lee Cheuk-Kit, Carles Domingo-Enrich, Yilun Du, Sham Kakade, Timothy Ngotiaoco, Sitan Chen, and Michael Albergo. https://arxiv.org/abs/2509.01025

Description: In this talk, Kevin will present and discuss the paper Any-Order Flexible Length Masked Diffusion. The talk will introduce the basics of discrete diffusion for language modeling, an important alternative to autoregressive LLMs, with a focus on masked diffusion and its extension to flexible-length generation.

Abstract: Dr. Yang will present a new scheme for solving compressible Euler equations on curvilinear meshes based on the discontinuous Galerkin method. The scheme is provably entropy stable and positivity preserving and is therefore highly robust. In addition, we design a special numerical flux so that the scheme can be coupled with adaptive mesh refinement (AMR). Numerical examples will be presented to illustrate the effectiveness of the scheme.

Abstract: We develop adaptive Chebyshev and Fourier-Chebyshev spectral collocation methods for the nonlinear prescribed mean curvature equations used to model the height of a fluid interface. The nonlinearity is treated with Newton’s method. Various geometries and symmetries are considered, and the resulting methods are used to solve the free boundary problems that arise from the equilibrium of a floating drop.

Abstract: We propose Sampled Local WeakIdent (SLW-Ident), a framework for identifying changing governing equations from a single set of given data. Unlike typical approaches that use finite-element-based approximations to represent varying coefficients, this work explores a local approach to identifying differential equations.

Local WeakIdent provides accurate local identification with small patch sizes and is computationally efficient but can be sensitive to local perturbations. SLW-Ident stabilizes this process while incorporating global information: patches are sampled throughout the domain, governing equations are identified locally, and residual errors are then used to detect transitions between different equations. Within each region governed by one equation, the most frequently identified equation is selected, allowing recovery of both constant- and varying-coefficient PDEs.

The method is supported by uncertainty quantification theory relating to the statistical error of dominant support selection to the number of sampled patches. Numerical experiments show that SLW-Ident can accurately recover changing PDE regions and their governing equations even from noisy data. 

Abstract: Large language models (LLMs) have demonstrated remarkable capabilities across diverse tasks, yet their increasing adoption in high-stakes domains raises fundamental concerns about reliability, uncertainty, and trustworthiness. Despite advances in model performance and reasoning capabilities, critical challenges remain: How can unsupported or misleading outputs be reliably identified? To what extent can LLMs recognize the boundaries of their own knowledge? And how can robust evaluation and safeguard mechanisms be developed when representative labeled data is scarce?

This seminar examines these challenges through three complementary research directions, with an emphasis on financial applications. First, a systematic benchmarking study of hallucination detection in retrieval-augmented generation (RAG) compares prompt optimization, fine-tuned models, and LLM-as-a-Judge approaches. Second, an empirical investigation of epistemic calibration across diverse LLM families and reasoning configurations examines persistent overconfidence and the relationship between reasoning performance and uncertainty calibration. Third, a structured synthetic data generation framework for multi-turn investment advice detection explores how diverse, context-dependent scenarios and uncertainty-aware evaluation strategies can address data scarcity and support more effective AI guardrails.

Collectively, these studies highlight the limitations of conventional accuracy-centric evaluation and the need for more comprehensive approaches to assessing and improving LLM reliability. The findings provide insights into factual grounding, epistemic uncertainty, and evaluation of data quality, with broader implications for trustworthy AI systems in finance and other high-stakes domains.

Paper: DFlash: Block Diffusion for Flash Speculative Decoding, by Jian Chen, Yesheng Liang, and Zhijian Liu. https://arxiv.org/abs/2602.06036

Abstract: In this talk, Kijung will present and discuss recent advances in speculative decoding via parallel drafting, with a focus on the DFlash paper. Speculative decoding is an important approach for accelerating large language model inference while preserving the model’s output distribution. Recent approaches such as DFlash and DSpark aim to improve LLM inference efficiency by generating multiple draft candidates in parallel and are increasingly relevant to production-scale language model systems.

Paper: Verifiable Hidden Dynamics Play: Generating Agentic RL Environments from Solved Mechanisms https://arxiv.org/pdf/2609.27321

Abstract: Scaling agentic reinforcement learning requires diverse interactive environments and reliable rewards. Hand-built simulators are costly to expand, while generated environments and learned judges need validation of dynamics and scoring. This talk approaches that problem through the modeling mindset of operations research, which captures decision structures shared across operational settings through variables, constraints, and objectives.

VHD-Play applies this idea by sampling and solving mathematical mechanisms, then turning them into executable environments with varied scenarios and tool interfaces. Rewards follow the same objectives, supported by independent solver references and execution of replay checks. The framework builds 3,300 environments across 11 mechanism families and 28 application domains at a cost of roughly one to three cents per environment. Training on only three mechanism families improves performance on unseen families and external benchmarks, including a year-long storefront simulation.

The talk will also discuss an asymmetric self-play perspective, where the environment builder has access to the full mechanism while the agent learns only through restricted interaction, allowing the system to construct environments that increasingly challenge the learned policy.

Abstract: TBD

Abstract: TBD