7 papers
MintFlow: Minimal Trajectory Intervention for Constrained Flow Matching
Yesom Park, Kelvin Kan, Qifan Chen +2
Flow matching models excel at generative modeling, and many downstream applications require their samples to satisfy prescribed constraints, such as observed measurements and physi…
Implicit Neural Optimal Transport via Fixed-Point Optimization
Yesom Park, Eric Gelphman, Stanley Osher +1
We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approache…
Scalable Fixed-Point Framework for High-Dimensional Hamilton-Jacobi Equations
Yesom Park, Stanley Osher
We propose a novel, mesh-free, and gradient-free fixed-point approach for computing viscosity solutions of high-dimensional Hamilton-Jacobi (HJ) equations. By leveraging the Hopf-L…
SymPlex: A Structure-Aware Transformer for Symbolic PDE Solving
Yesom Park, Annie C. Lu, Shao-Ching Huang +3
We propose SymPlex, a reinforcement learning framework for discovering analytical symbolic solutions to partial differential equations (PDEs) without access to ground-truth express…
Dynamical Implicit Neural Representations
Yesom Park, Kelvin Kan, Thomas Flynn +4
Implicit Neural Representations (INRs) provide a powerful continuous framework for modeling complex visual and geometric signals, but spectral bias remains a fundamental challenge,…
Neural Hamilton--Jacobi Characteristic Flows for Optimal Transport
Yesom Park, Shu Liu, Mo Zhou +1
We present a novel framework for solving optimal transport (OT) problems based on the Hamilton--Jacobi (HJ) equation, whose viscosity solution uniquely characterizes the OT map. By…
Neural Implicit Solution Formula for Efficiently Solving Hamilton-Jacobi Equations
Yesom Park, Stanley Osher
This paper presents an implicit solution formula for the Hamilton-Jacobi partial differential equation (HJ PDE). The formula is derived using the method of characteristics and is s…