My group's research connects generative AI and world modeling, physics-based simulation, physics-embedded machine learning, and computational design. A common theme is the construction of geometric and dynamical representations that make complex systems easier to generate, reconstruct, simulate, and control. Our recent work extends flow maps from physical transport to generative modeling, and combines learned visual priors with explicit representations of geometry, dynamics, sound, and executable scene structure. These directions bring together computer graphics, computational physics, scientific machine learning, and computational fabrication. We study both the mathematical foundations of transport and the computational systems needed to build and interact with physical and virtual worlds.

Generative AI & World Modeling

Since 2025, our group has connected generative transport with geometry and physical dynamics to build models that generate images and 3D shapes, reconstruct dynamic scenes, and support interaction with virtual worlds. We study both the mathematical foundations of efficient generation and world representations that expose geometry, motion, sound, and executable scene structure.

Representative Works:

• Fast Generative Transport: We develop one-step and few-step generators using finite-time flow maps. Our work includes Functional Mean Flow for functional data, Euler Mean Flows and Cumulative Flow Maps for efficient transport, and Orbit-Space Particle Flow Matching for geometric generation. Recent studies extend these foundations through variational optimal transport, long-short flow-map formulations, and reinforcement learning of few-step generators.
• Composable Worlds and Agents: We build world representations for construction, interaction, and reasoning. Recursive Code World Models represents complex 3D scenes as executable programs, while Audible World Models grounds generated sound in scene geometry. Our wildfire monitoring framework combines simulation context and vision-language agents to interpret and report evolving physical events.

Physics-based Simulation

My group investigates computational methods for simulating fluid systems featured by complex interfacial dynamics and vortical evolution. A particular focus is placed on small-scale fluid systems such as thin sheets, filaments, bubbles, foams, droplets, and aerosols, along with their interactions with vortical structures, which exhibit intricate multiscale and multiphysics behavior. These fluid structures play critical roles in biological and physiological systems and also represent visually complex phenomena of significant interest to the computer graphics community. To address these simulation challenges, we develop geometric representations that combine continuous mathematical formulations with discrete data structures to model dynamic processes involving complex geometry and topology. On the modeling side, we introduce new gauge formulations of the Navier-Stokes equations—including impulse-based and Clebsch-based models—to simulate incompressible flows with strong vortical and interfacial features. On the numerical side, we construct Lagrangian discretizations ranging from mesh-based representations to particle systems and spacetime flow maps. Our representation pipeline has progressed from simplicial and embedded meshes to moving particles, and most recently to unified flow-map-based schemes for tracking spacetime evolution.

These advances have enabled the simulation of a broad class of small-scale fluid phenomena that were previously inaccessible. Notable examples include cherries floating on water, soap bubble bursting and foam dynamics, horseshoe vortices generated by locomotion, and capillary interactions between droplets and solids. These simulations have helped visualize and analyze fluid processes underlying biological locomotion, respiratory droplet transmission, and fluid-surface interactions, and have supported interdisciplinary collaborations in graphics, physics, and bioengineering.

Representative Works:

• Thin-Film Fluid Dynamics: Our Moving Eulerian-Lagrangian Particle Method and Thin-Film SPH simulate soap films and foam dynamics, while Vortex Particle-on-Mesh captures vortex transport on deforming films.
• Interfacial Solid-Fluid Interaction: We model capillary-driven contact through surface-tension-dominant solid-fluid coupling and hydrophobic and hydrophilic interactions, enabling elastocapillary phenomena involving droplets and deformable solids.
• Gauge Fluid Methods: We proposed novel gauge-based formulations—including impulse and Clebsch variables—for incompressible flow, improving the long-range preservation of vorticity and interfacial structure in fluid systems.
• Flow Map Algorithms: Particle Flow Maps use particle trajectories as spacetime samples for long-range transport. Extensions include compressible flow, particle-laden fluids, solid-fluid coupling, and real-time simulation. These methods support coupled interfacial and vortical dynamics; see the PFM website for more details.

Physics-Embedded Machine Learning

We develop machine learning methods that embed physical and geometric principles into neural architectures and simulation frameworks, with a focus on data efficiency, generalization, and physical consistency. Our neural architectures and time integration schemes incorporate constraints to predict Hamiltonian and transport systems from limited observations while preserving geometric or symplectic structure. We also combine differentiable geometric discretizations, neural surrogates, and implicit representations to improve physical simulation. Our neural flow maps represent long-term velocity fields for accurate fluid transport. Recent work extends these ideas to neural operators and neural PDE solvers, using boundary-integral formulations, incompressibility constraints, and analytic spatial derivatives to learn reusable solution maps and physical fields.

Representative Works:

• Prior-Embedded Neural Networks: We designed structure-preserving neural models that incorporate symplectic and sparsity constraints to enable stable long-horizon predictions in Hamiltonian systems under sparse data conditions.
• Neural Operators and PDE Solvers: Neural Harmonic Measure Operator learns geometry-dependent boundary kernels for elliptic PDEs with varying boundary and source data. The Variational Optimal Transport Operator predicts divergence-free flows for new source-target density pairs. Hermite-NGP provides analytic spatial derivatives for neural PDE solvers.
• Simulation with Neural Representations: Neural Flow Maps encode long-term fluid velocity fields for accurate transport, while FluidNexus combines generative visual priors and physics-integrated representations for 3D fluid reconstruction and prediction from a single video.

Computational Design and Fabrication

Our group develops computational methods to automate the design and exploration of complex physical systems. We combine simulation-based models, data-driven representations, and interactive design tools, including CompAct for compliant mechanisms, to simplify the design of physical functionalities and embodied intelligence. The examples shown span a wide range of physical domains.

Our methodology is structured around two key components. First, we construct novel representations of the design space that enable efficient search over high-dimensional and nonconvex domains, overcoming traditional limitations such as the curse of dimensionality and the prevalence of poor local minima. For example, we introduced differentiable Voronoi diagram representations for topology optimization in thin-shell structures inspired by biological forms, such as dragonfly wings. Similarly, we have used continuous implicit representations for metamaterial design to explore microstructural properties such as stiffness, elastic modulus, and density. Second, we develop differentiable physics simulators that enable gradient-based optimization for complex physical systems where conventional methods are either unstable or inefficient. These simulators allow end-to-end coupling of physical simulation and design objectives, and have been applied to domains such as magnetic thin-shell robots, soft-bodied aerial drones, microfluidic circuits, and functional grippers. These tools provide a computational foundation for discovering novel designs across scales and applications.